diff options
Diffstat (limited to 'docs')
154 files changed, 5178 insertions, 3737 deletions
diff --git a/docs/cache_nbrun b/docs/cache_nbrun new file mode 100644 index 0000000..1510b2b --- /dev/null +++ b/docs/cache_nbrun @@ -0,0 +1 @@ +{"plot_otda_mapping_colors_images.ipynb": "4f0587a00a3c082799a75a0ed36e9ce1", "plot_optim_OTreg.ipynb": "71d3c106b3f395a6b1001078a6ca6f8d", "plot_barycenter_1D.ipynb": "6fd8167f98816dc832fe0c58b1d5527b", "plot_WDA.ipynb": "27f8de4c6d7db46497076523673eedfb", "plot_OT_L1_vs_L2.ipynb": "e15219bf651a7e39e7c5c3934069894c", "plot_otda_color_images.ipynb": "d047d635f4987c81072383241590e21f", "plot_otda_classes.ipynb": "44bb8cd93317b5d342cd62e26d9bbe60", "plot_otda_d2.ipynb": "8ac4fd2ff899df0858ce1e5fead37f33", "plot_otda_mapping.ipynb": "d335a15af828aaa3439a1c67570d79d6", "plot_compute_emd.ipynb": "bd95981189df6adcb113d9b360ead734", "plot_OT_1D.ipynb": "e44c83f6112388ae18657cb0ad76d0e9", "plot_OT_2D_samples.ipynb": "3f125714daa35ff3cfe5dae1f71265c4"}
\ No newline at end of file diff --git a/docs/nb_build b/docs/nb_build new file mode 100755 index 0000000..6abc6cf --- /dev/null +++ b/docs/nb_build @@ -0,0 +1,15 @@ +#!/bin/bash + + +# remove comment +sed -i "s/#'sphinx\_gallery/'sphinx\_gallery/" source/conf.py +sed -i "s/sys.modules.update/#sys.modules.update/" source/conf.py + +make html + +# put comment again +sed -i "s/'sphinx\_gallery/#'sphinx\_gallery/" source/conf.py +sed -i "s/#sys.modules.update/sys.modules.update/" source/conf.py + +#rsync --out-format="%n" --update source/auto_examples/*.ipynb ../notebooks2 +./nb_run_conv diff --git a/docs/nb_run_conv b/docs/nb_run_conv new file mode 100755 index 0000000..ad5e432 --- /dev/null +++ b/docs/nb_run_conv @@ -0,0 +1,82 @@ +#!/usr/bin/env python +# -*- coding: utf-8 -*- +""" + +Convert sphinx gallery notebook from empty to image filled + +Created on Fri Sep 1 16:43:45 2017 + +@author: rflamary +""" + +import sys +import json +import glob +import hashlib +import subprocess + +import os + +cache_file='cache_nbrun' + +path_doc='source/auto_examples/' +path_nb='../notebooks/' + +def load_json(fname): + try: + f=open(fname) + nb=json.load(f) + f.close() + except (OSError, IOError) : + nb={} + return nb + +def save_json(fname,nb): + f=open(fname,'w') + f.write(json.dumps(nb)) + f.close() + + +def md5(fname): + hash_md5 = hashlib.md5() + with open(fname, "rb") as f: + for chunk in iter(lambda: f.read(4096), b""): + hash_md5.update(chunk) + return hash_md5.hexdigest() + +def to_update(fname,cache): + if fname in cache: + if md5(path_doc+fname)==cache[fname]: + res=False + else: + res=True + else: + res=True + + return res + +def update(fname,cache): + + # jupyter nbconvert --to notebook --execute mynotebook.ipynb --output targte + subprocess.check_call(['cp',path_doc+fname,path_nb]) + print(' '.join(['jupyter','nbconvert','--to','notebook','--ExecutePreprocessor.timeout=600','--execute',path_nb+fname,'--inplace'])) + subprocess.check_call(['jupyter','nbconvert','--to','notebook','--ExecutePreprocessor.timeout=600','--execute',path_nb+fname,'--inplace']) + cache[fname]=md5(path_doc+fname) + + + +cache=load_json(cache_file) + +lst_file=glob.glob(path_doc+'*.ipynb') + +lst_file=[os.path.basename(name) for name in lst_file] + +for fname in lst_file: + if to_update(fname,cache): + print('Updating file: {}'.format(fname)) + update(fname,cache) + save_json(cache_file,cache) + + + + diff --git a/docs/source/auto_examples/auto_examples_jupyter.zip b/docs/source/auto_examples/auto_examples_jupyter.zip Binary files differindex 7c3de28..fc1d4de 100644 --- a/docs/source/auto_examples/auto_examples_jupyter.zip +++ b/docs/source/auto_examples/auto_examples_jupyter.zip diff --git a/docs/source/auto_examples/auto_examples_python.zip b/docs/source/auto_examples/auto_examples_python.zip Binary files differindex 97377e1..282bc58 100644 --- a/docs/source/auto_examples/auto_examples_python.zip +++ b/docs/source/auto_examples/auto_examples_python.zip diff --git a/docs/source/auto_examples/demo_OT_1D_test.ipynb b/docs/source/auto_examples/demo_OT_1D_test.ipynb deleted file mode 100644 index 87317ea..0000000 --- a/docs/source/auto_examples/demo_OT_1D_test.ipynb +++ /dev/null @@ -1,54 +0,0 @@ -{ - "nbformat_minor": 0, - "nbformat": 4, - "cells": [ - { - "execution_count": null, - "cell_type": "code", - "source": [ - "%matplotlib inline" - ], - "outputs": [], - "metadata": { - "collapsed": false - } - }, - { - "source": [ - "\nDemo for 1D optimal transport\n\n@author: rflamary\n\n" - ], - "cell_type": "markdown", - "metadata": {} - }, - { - "execution_count": null, - "cell_type": "code", - "source": [ - "import numpy as np\nimport matplotlib.pylab as pl\nimport ot\nfrom ot.datasets import get_1D_gauss as gauss\n\n\n#%% parameters\n\nn=100 # nb bins\n\n# bin positions\nx=np.arange(n,dtype=np.float64)\n\n# Gaussian distributions\na=gauss(n,m=n*.2,s=5) # m= mean, s= std\nb=gauss(n,m=n*.6,s=10)\n\n# loss matrix\nM=ot.dist(x.reshape((n,1)),x.reshape((n,1)))\nM/=M.max()\n\n#%% plot the distributions\n\npl.figure(1)\npl.plot(x,a,'b',label='Source distribution')\npl.plot(x,b,'r',label='Target distribution')\npl.legend()\n\n#%% plot distributions and loss matrix\n\npl.figure(2)\not.plot.plot1D_mat(a,b,M,'Cost matrix M')\n\n#%% EMD\n\nG0=ot.emd(a,b,M)\n\npl.figure(3)\not.plot.plot1D_mat(a,b,G0,'OT matrix G0')\n\n#%% Sinkhorn\n\nlambd=1e-3\nGs=ot.sinkhorn(a,b,M,lambd,verbose=True)\n\npl.figure(4)\not.plot.plot1D_mat(a,b,Gs,'OT matrix Sinkhorn')\n\n#%% Sinkhorn\n\nlambd=1e-4\nGss,log=ot.bregman.sinkhorn_stabilized(a,b,M,lambd,verbose=True,log=True)\nGss2,log2=ot.bregman.sinkhorn_stabilized(a,b,M,lambd,verbose=True,log=True,warmstart=log['warmstart'])\n\npl.figure(5)\not.plot.plot1D_mat(a,b,Gss,'OT matrix Sinkhorn stabilized')\n\n#%% Sinkhorn\n\nlambd=1e-11\nGss=ot.bregman.sinkhorn_epsilon_scaling(a,b,M,lambd,verbose=True)\n\npl.figure(5)\not.plot.plot1D_mat(a,b,Gss,'OT matrix Sinkhorn stabilized')" - ], - "outputs": [], - "metadata": { - "collapsed": false - } - } - ], - "metadata": { - "kernelspec": { - "display_name": "Python 2", - "name": "python2", - "language": "python" - }, - "language_info": { - "mimetype": "text/x-python", - "nbconvert_exporter": "python", - "name": "python", - "file_extension": ".py", - "version": "2.7.12", - "pygments_lexer": "ipython2", - "codemirror_mode": { - "version": 2, - "name": "ipython" - } - } - } -}
\ No newline at end of file diff --git a/docs/source/auto_examples/demo_OT_1D_test.py b/docs/source/auto_examples/demo_OT_1D_test.py deleted file mode 100644 index 9edc377..0000000 --- a/docs/source/auto_examples/demo_OT_1D_test.py +++ /dev/null @@ -1,71 +0,0 @@ -# -*- coding: utf-8 -*- -""" -Demo for 1D optimal transport - -@author: rflamary -""" - -import numpy as np -import matplotlib.pylab as pl -import ot -from ot.datasets import get_1D_gauss as gauss - - -#%% parameters - -n=100 # nb bins - -# bin positions -x=np.arange(n,dtype=np.float64) - -# Gaussian distributions -a=gauss(n,m=n*.2,s=5) # m= mean, s= std -b=gauss(n,m=n*.6,s=10) - -# loss matrix -M=ot.dist(x.reshape((n,1)),x.reshape((n,1))) -M/=M.max() - -#%% plot the distributions - -pl.figure(1) -pl.plot(x,a,'b',label='Source distribution') -pl.plot(x,b,'r',label='Target distribution') -pl.legend() - -#%% plot distributions and loss matrix - -pl.figure(2) -ot.plot.plot1D_mat(a,b,M,'Cost matrix M') - -#%% EMD - -G0=ot.emd(a,b,M) - -pl.figure(3) -ot.plot.plot1D_mat(a,b,G0,'OT matrix G0') - -#%% Sinkhorn - -lambd=1e-3 -Gs=ot.sinkhorn(a,b,M,lambd,verbose=True) - -pl.figure(4) -ot.plot.plot1D_mat(a,b,Gs,'OT matrix Sinkhorn') - -#%% Sinkhorn - -lambd=1e-4 -Gss,log=ot.bregman.sinkhorn_stabilized(a,b,M,lambd,verbose=True,log=True) -Gss2,log2=ot.bregman.sinkhorn_stabilized(a,b,M,lambd,verbose=True,log=True,warmstart=log['warmstart']) - -pl.figure(5) -ot.plot.plot1D_mat(a,b,Gss,'OT matrix Sinkhorn stabilized') - -#%% Sinkhorn - -lambd=1e-11 -Gss=ot.bregman.sinkhorn_epsilon_scaling(a,b,M,lambd,verbose=True) - -pl.figure(5) -ot.plot.plot1D_mat(a,b,Gss,'OT matrix Sinkhorn stabilized') diff --git a/docs/source/auto_examples/demo_OT_1D_test.rst b/docs/source/auto_examples/demo_OT_1D_test.rst deleted file mode 100644 index aebeb1d..0000000 --- a/docs/source/auto_examples/demo_OT_1D_test.rst +++ /dev/null @@ -1,99 +0,0 @@ - - -.. _sphx_glr_auto_examples_demo_OT_1D_test.py: - - -Demo for 1D optimal transport - -@author: rflamary - - - -.. code-block:: python - - - import numpy as np - import matplotlib.pylab as pl - import ot - from ot.datasets import get_1D_gauss as gauss - - - #%% parameters - - n=100 # nb bins - - # bin positions - x=np.arange(n,dtype=np.float64) - - # Gaussian distributions - a=gauss(n,m=n*.2,s=5) # m= mean, s= std - b=gauss(n,m=n*.6,s=10) - - # loss matrix - M=ot.dist(x.reshape((n,1)),x.reshape((n,1))) - M/=M.max() - - #%% plot the distributions - - pl.figure(1) - pl.plot(x,a,'b',label='Source distribution') - pl.plot(x,b,'r',label='Target distribution') - pl.legend() - - #%% plot distributions and loss matrix - - pl.figure(2) - ot.plot.plot1D_mat(a,b,M,'Cost matrix M') - - #%% EMD - - G0=ot.emd(a,b,M) - - pl.figure(3) - ot.plot.plot1D_mat(a,b,G0,'OT matrix G0') - - #%% Sinkhorn - - lambd=1e-3 - Gs=ot.sinkhorn(a,b,M,lambd,verbose=True) - - pl.figure(4) - ot.plot.plot1D_mat(a,b,Gs,'OT matrix Sinkhorn') - - #%% Sinkhorn - - lambd=1e-4 - Gss,log=ot.bregman.sinkhorn_stabilized(a,b,M,lambd,verbose=True,log=True) - Gss2,log2=ot.bregman.sinkhorn_stabilized(a,b,M,lambd,verbose=True,log=True,warmstart=log['warmstart']) - - pl.figure(5) - ot.plot.plot1D_mat(a,b,Gss,'OT matrix Sinkhorn stabilized') - - #%% Sinkhorn - - lambd=1e-11 - Gss=ot.bregman.sinkhorn_epsilon_scaling(a,b,M,lambd,verbose=True) - - pl.figure(5) - ot.plot.plot1D_mat(a,b,Gss,'OT matrix Sinkhorn stabilized') - -**Total running time of the script:** ( 0 minutes 0.000 seconds) - - - -.. container:: sphx-glr-footer - - - .. container:: sphx-glr-download - - :download:`Download Python source code: demo_OT_1D_test.py <demo_OT_1D_test.py>` - - - - .. container:: sphx-glr-download - - :download:`Download Jupyter notebook: demo_OT_1D_test.ipynb <demo_OT_1D_test.ipynb>` - -.. rst-class:: sphx-glr-signature - - `Generated by Sphinx-Gallery <http://sphinx-gallery.readthedocs.io>`_ diff --git a/docs/source/auto_examples/demo_OT_2D_sampleslarge.ipynb b/docs/source/auto_examples/demo_OT_2D_sampleslarge.ipynb deleted file mode 100644 index 584a936..0000000 --- a/docs/source/auto_examples/demo_OT_2D_sampleslarge.ipynb +++ /dev/null @@ -1,54 +0,0 @@ -{ - "nbformat_minor": 0, - "nbformat": 4, - "cells": [ - { - "execution_count": null, - "cell_type": "code", - "source": [ - "%matplotlib inline" - ], - "outputs": [], - "metadata": { - "collapsed": false - } - }, - { - "source": [ - "\nDemo for 2D Optimal transport between empirical distributions\n\n@author: rflamary\n\n" - ], - "cell_type": "markdown", - "metadata": {} - }, - { - "execution_count": null, - "cell_type": "code", - "source": [ - "import numpy as np\nimport matplotlib.pylab as pl\nimport ot\n\n#%% parameters and data generation\n\nn=5000 # nb samples\n\nmu_s=np.array([0,0])\ncov_s=np.array([[1,0],[0,1]])\n\nmu_t=np.array([4,4])\ncov_t=np.array([[1,-.8],[-.8,1]])\n\nxs=ot.datasets.get_2D_samples_gauss(n,mu_s,cov_s)\nxt=ot.datasets.get_2D_samples_gauss(n,mu_t,cov_t)\n\na,b = ot.unif(n),ot.unif(n) # uniform distribution on samples\n\n# loss matrix\nM=ot.dist(xs,xt)\nM/=M.max()\n\n#%% plot samples\n\n#pl.figure(1)\n#pl.plot(xs[:,0],xs[:,1],'+b',label='Source samples')\n#pl.plot(xt[:,0],xt[:,1],'xr',label='Target samples')\n#pl.legend(loc=0)\n#pl.title('Source and traget distributions')\n#\n#pl.figure(2)\n#pl.imshow(M,interpolation='nearest')\n#pl.title('Cost matrix M')\n#\n\n#%% EMD\n\nG0=ot.emd(a,b,M)\n\n#pl.figure(3)\n#pl.imshow(G0,interpolation='nearest')\n#pl.title('OT matrix G0')\n#\n#pl.figure(4)\n#ot.plot.plot2D_samples_mat(xs,xt,G0,c=[.5,.5,1])\n#pl.plot(xs[:,0],xs[:,1],'+b',label='Source samples')\n#pl.plot(xt[:,0],xt[:,1],'xr',label='Target samples')\n#pl.legend(loc=0)\n#pl.title('OT matrix with samples')\n\n\n#%% sinkhorn\n\n# reg term\nlambd=5e-3\n\nGs=ot.sinkhorn(a,b,M,lambd)\n\n#pl.figure(5)\n#pl.imshow(Gs,interpolation='nearest')\n#pl.title('OT matrix sinkhorn')\n#\n#pl.figure(6)\n#ot.plot.plot2D_samples_mat(xs,xt,Gs,color=[.5,.5,1])\n#pl.plot(xs[:,0],xs[:,1],'+b',label='Source samples')\n#pl.plot(xt[:,0],xt[:,1],'xr',label='Target samples')\n#pl.legend(loc=0)\n#pl.title('OT matrix Sinkhorn with samples')\n#" - ], - "outputs": [], - "metadata": { - "collapsed": false - } - } - ], - "metadata": { - "kernelspec": { - "display_name": "Python 2", - "name": "python2", - "language": "python" - }, - "language_info": { - "mimetype": "text/x-python", - "nbconvert_exporter": "python", - "name": "python", - "file_extension": ".py", - "version": "2.7.12", - "pygments_lexer": "ipython2", - "codemirror_mode": { - "version": 2, - "name": "ipython" - } - } - } -}
\ No newline at end of file diff --git a/docs/source/auto_examples/demo_OT_2D_sampleslarge.py b/docs/source/auto_examples/demo_OT_2D_sampleslarge.py deleted file mode 100644 index ee3e8f7..0000000 --- a/docs/source/auto_examples/demo_OT_2D_sampleslarge.py +++ /dev/null @@ -1,78 +0,0 @@ -# -*- coding: utf-8 -*- -""" -Demo for 2D Optimal transport between empirical distributions - -@author: rflamary -""" - -import numpy as np -import matplotlib.pylab as pl -import ot - -#%% parameters and data generation - -n=5000 # nb samples - -mu_s=np.array([0,0]) -cov_s=np.array([[1,0],[0,1]]) - -mu_t=np.array([4,4]) -cov_t=np.array([[1,-.8],[-.8,1]]) - -xs=ot.datasets.get_2D_samples_gauss(n,mu_s,cov_s) -xt=ot.datasets.get_2D_samples_gauss(n,mu_t,cov_t) - -a,b = ot.unif(n),ot.unif(n) # uniform distribution on samples - -# loss matrix -M=ot.dist(xs,xt) -M/=M.max() - -#%% plot samples - -#pl.figure(1) -#pl.plot(xs[:,0],xs[:,1],'+b',label='Source samples') -#pl.plot(xt[:,0],xt[:,1],'xr',label='Target samples') -#pl.legend(loc=0) -#pl.title('Source and traget distributions') -# -#pl.figure(2) -#pl.imshow(M,interpolation='nearest') -#pl.title('Cost matrix M') -# - -#%% EMD - -G0=ot.emd(a,b,M) - -#pl.figure(3) -#pl.imshow(G0,interpolation='nearest') -#pl.title('OT matrix G0') -# -#pl.figure(4) -#ot.plot.plot2D_samples_mat(xs,xt,G0,c=[.5,.5,1]) -#pl.plot(xs[:,0],xs[:,1],'+b',label='Source samples') -#pl.plot(xt[:,0],xt[:,1],'xr',label='Target samples') -#pl.legend(loc=0) -#pl.title('OT matrix with samples') - - -#%% sinkhorn - -# reg term -lambd=5e-3 - -Gs=ot.sinkhorn(a,b,M,lambd) - -#pl.figure(5) -#pl.imshow(Gs,interpolation='nearest') -#pl.title('OT matrix sinkhorn') -# -#pl.figure(6) -#ot.plot.plot2D_samples_mat(xs,xt,Gs,color=[.5,.5,1]) -#pl.plot(xs[:,0],xs[:,1],'+b',label='Source samples') -#pl.plot(xt[:,0],xt[:,1],'xr',label='Target samples') -#pl.legend(loc=0) -#pl.title('OT matrix Sinkhorn with samples') -# - diff --git a/docs/source/auto_examples/demo_OT_2D_sampleslarge.rst b/docs/source/auto_examples/demo_OT_2D_sampleslarge.rst deleted file mode 100644 index f5dbb0d..0000000 --- a/docs/source/auto_examples/demo_OT_2D_sampleslarge.rst +++ /dev/null @@ -1,106 +0,0 @@ - - -.. _sphx_glr_auto_examples_demo_OT_2D_sampleslarge.py: - - -Demo for 2D Optimal transport between empirical distributions - -@author: rflamary - - - -.. code-block:: python - - - import numpy as np - import matplotlib.pylab as pl - import ot - - #%% parameters and data generation - - n=5000 # nb samples - - mu_s=np.array([0,0]) - cov_s=np.array([[1,0],[0,1]]) - - mu_t=np.array([4,4]) - cov_t=np.array([[1,-.8],[-.8,1]]) - - xs=ot.datasets.get_2D_samples_gauss(n,mu_s,cov_s) - xt=ot.datasets.get_2D_samples_gauss(n,mu_t,cov_t) - - a,b = ot.unif(n),ot.unif(n) # uniform distribution on samples - - # loss matrix - M=ot.dist(xs,xt) - M/=M.max() - - #%% plot samples - - #pl.figure(1) - #pl.plot(xs[:,0],xs[:,1],'+b',label='Source samples') - #pl.plot(xt[:,0],xt[:,1],'xr',label='Target samples') - #pl.legend(loc=0) - #pl.title('Source and traget distributions') - # - #pl.figure(2) - #pl.imshow(M,interpolation='nearest') - #pl.title('Cost matrix M') - # - - #%% EMD - - G0=ot.emd(a,b,M) - - #pl.figure(3) - #pl.imshow(G0,interpolation='nearest') - #pl.title('OT matrix G0') - # - #pl.figure(4) - #ot.plot.plot2D_samples_mat(xs,xt,G0,c=[.5,.5,1]) - #pl.plot(xs[:,0],xs[:,1],'+b',label='Source samples') - #pl.plot(xt[:,0],xt[:,1],'xr',label='Target samples') - #pl.legend(loc=0) - #pl.title('OT matrix with samples') - - - #%% sinkhorn - - # reg term - lambd=5e-3 - - Gs=ot.sinkhorn(a,b,M,lambd) - - #pl.figure(5) - #pl.imshow(Gs,interpolation='nearest') - #pl.title('OT matrix sinkhorn') - # - #pl.figure(6) - #ot.plot.plot2D_samples_mat(xs,xt,Gs,color=[.5,.5,1]) - #pl.plot(xs[:,0],xs[:,1],'+b',label='Source samples') - #pl.plot(xt[:,0],xt[:,1],'xr',label='Target samples') - #pl.legend(loc=0) - #pl.title('OT matrix Sinkhorn with samples') - # - - -**Total running time of the script:** ( 0 minutes 0.000 seconds) - - - -.. container:: sphx-glr-footer - - - .. container:: sphx-glr-download - - :download:`Download Python source code: demo_OT_2D_sampleslarge.py <demo_OT_2D_sampleslarge.py>` - - - - .. container:: sphx-glr-download - - :download:`Download Jupyter notebook: demo_OT_2D_sampleslarge.ipynb <demo_OT_2D_sampleslarge.ipynb>` - -.. rst-class:: sphx-glr-signature - - `Generated by Sphinx-Gallery <http://sphinx-gallery.readthedocs.io>`_ diff --git a/docs/source/auto_examples/images/sphx_glr_plot_OTDA_2D_001.png b/docs/source/auto_examples/images/sphx_glr_plot_OTDA_2D_001.png Binary files differdeleted file mode 100644 index 7de2b45..0000000 --- a/docs/source/auto_examples/images/sphx_glr_plot_OTDA_2D_001.png +++ /dev/null diff --git a/docs/source/auto_examples/images/sphx_glr_plot_OTDA_2D_002.png b/docs/source/auto_examples/images/sphx_glr_plot_OTDA_2D_002.png Binary files differdeleted file mode 100644 index dc34efd..0000000 --- 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a/docs/source/auto_examples/images/thumb/sphx_glr_test_OT_2D_samples_stabilized_thumb.png b/docs/source/auto_examples/images/thumb/sphx_glr_test_OT_2D_samples_stabilized_thumb.png Binary files differdeleted file mode 100644 index cbc8e0f..0000000 --- a/docs/source/auto_examples/images/thumb/sphx_glr_test_OT_2D_samples_stabilized_thumb.png +++ /dev/null diff --git a/docs/source/auto_examples/index.rst b/docs/source/auto_examples/index.rst index 1695300..5d7a53d 100644 --- a/docs/source/auto_examples/index.rst +++ b/docs/source/auto_examples/index.rst @@ -1,9 +1,15 @@ +:orphan: + POT Examples ============ +This is a gallery of all the POT example files. + + + .. raw:: html - <div class="sphx-glr-thumbcontainer" tooltip="@author: rflamary "> + <div class="sphx-glr-thumbcontainer" tooltip="This example illustrates the computation of EMD and Sinkhorn transport plans and their visualiz..."> .. only:: html @@ -23,13 +29,13 @@ POT Examples .. raw:: html - <div class="sphx-glr-thumbcontainer" tooltip="@author: rflamary "> + <div class="sphx-glr-thumbcontainer" tooltip="Illustrates the use of the generic solver for regularized OT with user-designed regularization ..."> .. only:: html - .. figure:: /auto_examples/images/thumb/sphx_glr_plot_WDA_thumb.png + .. figure:: /auto_examples/images/thumb/sphx_glr_plot_optim_OTreg_thumb.png - :ref:`sphx_glr_auto_examples_plot_WDA.py` + :ref:`sphx_glr_auto_examples_plot_optim_OTreg.py` .. raw:: html @@ -39,17 +45,17 @@ POT Examples .. toctree:: :hidden: - /auto_examples/plot_WDA + /auto_examples/plot_optim_OTreg .. raw:: html - <div class="sphx-glr-thumbcontainer" tooltip=" "> + <div class="sphx-glr-thumbcontainer" tooltip="Illustration of 2D optimal transport between discributions that are weighted sum of diracs. The..."> .. only:: html - .. figure:: /auto_examples/images/thumb/sphx_glr_plot_optim_OTreg_thumb.png + .. figure:: /auto_examples/images/thumb/sphx_glr_plot_OT_2D_samples_thumb.png - :ref:`sphx_glr_auto_examples_plot_optim_OTreg.py` + :ref:`sphx_glr_auto_examples_plot_OT_2D_samples.py` .. raw:: html @@ -59,17 +65,17 @@ POT Examples .. toctree:: :hidden: - /auto_examples/plot_optim_OTreg + /auto_examples/plot_OT_2D_samples .. raw:: html - <div class="sphx-glr-thumbcontainer" tooltip="@author: rflamary "> + <div class="sphx-glr-thumbcontainer" tooltip="Shows how to compute multiple EMD and Sinkhorn with two differnt ground metrics and plot their ..."> .. only:: html - .. figure:: /auto_examples/images/thumb/sphx_glr_plot_OT_2D_samples_thumb.png + .. figure:: /auto_examples/images/thumb/sphx_glr_plot_compute_emd_thumb.png - :ref:`sphx_glr_auto_examples_plot_OT_2D_samples.py` + :ref:`sphx_glr_auto_examples_plot_compute_emd.py` .. raw:: html @@ -79,17 +85,17 @@ POT Examples .. toctree:: :hidden: - /auto_examples/plot_OT_2D_samples + /auto_examples/plot_compute_emd .. raw:: html - <div class="sphx-glr-thumbcontainer" tooltip="@author: rflamary "> + <div class="sphx-glr-thumbcontainer" tooltip="This example illustrate the use of WDA as proposed in [11]."> .. only:: html - .. figure:: /auto_examples/images/thumb/sphx_glr_plot_compute_emd_thumb.png + .. figure:: /auto_examples/images/thumb/sphx_glr_plot_WDA_thumb.png - :ref:`sphx_glr_auto_examples_plot_compute_emd.py` + :ref:`sphx_glr_auto_examples_plot_WDA.py` .. raw:: html @@ -99,17 +105,17 @@ POT Examples .. toctree:: :hidden: - /auto_examples/plot_compute_emd + /auto_examples/plot_WDA .. raw:: html - <div class="sphx-glr-thumbcontainer" tooltip="[6] Ferradans, S., Papadakis, N., Peyre, G., & Aujol, J. F. (2014). Regularized discrete optima..."> + <div class="sphx-glr-thumbcontainer" tooltip="This example presents a way of transferring colors between two image with Optimal Transport as ..."> .. only:: html - .. figure:: /auto_examples/images/thumb/sphx_glr_plot_OTDA_color_images_thumb.png + .. figure:: /auto_examples/images/thumb/sphx_glr_plot_otda_color_images_thumb.png - :ref:`sphx_glr_auto_examples_plot_OTDA_color_images.py` + :ref:`sphx_glr_auto_examples_plot_otda_color_images.py` .. raw:: html @@ -119,17 +125,17 @@ POT Examples .. toctree:: :hidden: - /auto_examples/plot_OTDA_color_images + /auto_examples/plot_otda_color_images .. raw:: html - <div class="sphx-glr-thumbcontainer" tooltip=""> + <div class="sphx-glr-thumbcontainer" tooltip="This example illustrates the computation of regularized Wassersyein Barycenter as proposed in [..."> .. only:: html - .. figure:: /auto_examples/images/thumb/sphx_glr_plot_OTDA_classes_thumb.png + .. figure:: /auto_examples/images/thumb/sphx_glr_plot_barycenter_1D_thumb.png - :ref:`sphx_glr_auto_examples_plot_OTDA_classes.py` + :ref:`sphx_glr_auto_examples_plot_barycenter_1D.py` .. raw:: html @@ -139,17 +145,17 @@ POT Examples .. toctree:: :hidden: - /auto_examples/plot_OTDA_classes + /auto_examples/plot_barycenter_1D .. raw:: html - <div class="sphx-glr-thumbcontainer" tooltip=""> + <div class="sphx-glr-thumbcontainer" tooltip="OT for domain adaptation with image color adaptation [6] with mapping estimation [8]."> .. only:: html - .. figure:: /auto_examples/images/thumb/sphx_glr_plot_OTDA_2D_thumb.png + .. figure:: /auto_examples/images/thumb/sphx_glr_plot_otda_mapping_colors_images_thumb.png - :ref:`sphx_glr_auto_examples_plot_OTDA_2D.py` + :ref:`sphx_glr_auto_examples_plot_otda_mapping_colors_images.py` .. raw:: html @@ -159,17 +165,17 @@ POT Examples .. toctree:: :hidden: - /auto_examples/plot_OTDA_2D + /auto_examples/plot_otda_mapping_colors_images .. raw:: html - <div class="sphx-glr-thumbcontainer" tooltip="Stole the figure idea from Fig. 1 and 2 in https://arxiv.org/pdf/1706.07650.pdf"> + <div class="sphx-glr-thumbcontainer" tooltip="This example presents how to use MappingTransport to estimate at the same time both the couplin..."> .. only:: html - .. figure:: /auto_examples/images/thumb/sphx_glr_plot_OT_L1_vs_L2_thumb.png + .. figure:: /auto_examples/images/thumb/sphx_glr_plot_otda_mapping_thumb.png - :ref:`sphx_glr_auto_examples_plot_OT_L1_vs_L2.py` + :ref:`sphx_glr_auto_examples_plot_otda_mapping.py` .. raw:: html @@ -179,17 +185,17 @@ POT Examples .. toctree:: :hidden: - /auto_examples/plot_OT_L1_vs_L2 + /auto_examples/plot_otda_mapping .. raw:: html - <div class="sphx-glr-thumbcontainer" tooltip=" @author: rflamary "> + <div class="sphx-glr-thumbcontainer" tooltip="This example introduces a domain adaptation in a 2D setting and the 4 OTDA approaches currently..."> .. only:: html - .. figure:: /auto_examples/images/thumb/sphx_glr_plot_barycenter_1D_thumb.png + .. figure:: /auto_examples/images/thumb/sphx_glr_plot_otda_classes_thumb.png - :ref:`sphx_glr_auto_examples_plot_barycenter_1D.py` + :ref:`sphx_glr_auto_examples_plot_otda_classes.py` .. raw:: html @@ -199,17 +205,17 @@ POT Examples .. toctree:: :hidden: - /auto_examples/plot_barycenter_1D + /auto_examples/plot_otda_classes .. raw:: html - <div class="sphx-glr-thumbcontainer" tooltip="[6] Ferradans, S., Papadakis, N., Peyre, G., & Aujol, J. F. (2014). Regularized discrete op..."> + <div class="sphx-glr-thumbcontainer" tooltip="This example introduces a domain adaptation in a 2D setting. It explicits the problem of domain..."> .. only:: html - .. figure:: /auto_examples/images/thumb/sphx_glr_plot_OTDA_mapping_color_images_thumb.png + .. figure:: /auto_examples/images/thumb/sphx_glr_plot_otda_d2_thumb.png - :ref:`sphx_glr_auto_examples_plot_OTDA_mapping_color_images.py` + :ref:`sphx_glr_auto_examples_plot_otda_d2.py` .. raw:: html @@ -219,17 +225,17 @@ POT Examples .. toctree:: :hidden: - /auto_examples/plot_OTDA_mapping_color_images + /auto_examples/plot_otda_d2 .. raw:: html - <div class="sphx-glr-thumbcontainer" tooltip="[8] M. Perrot, N. Courty, R. Flamary, A. Habrard, "Mapping estimation for discrete optimal ..."> + <div class="sphx-glr-thumbcontainer" tooltip="2D OT on empirical distributio with different gound metric."> .. only:: html - .. figure:: /auto_examples/images/thumb/sphx_glr_plot_OTDA_mapping_thumb.png + .. figure:: /auto_examples/images/thumb/sphx_glr_plot_OT_L1_vs_L2_thumb.png - :ref:`sphx_glr_auto_examples_plot_OTDA_mapping.py` + :ref:`sphx_glr_auto_examples_plot_OT_L1_vs_L2.py` .. raw:: html @@ -239,7 +245,7 @@ POT Examples .. toctree:: :hidden: - /auto_examples/plot_OTDA_mapping + /auto_examples/plot_OT_L1_vs_L2 .. raw:: html <div style='clear:both'></div> @@ -251,14 +257,14 @@ POT Examples .. container:: sphx-glr-download - :download:`Download all examples in Python source code: auto_examples_python.zip </auto_examples/auto_examples_python.zip>` + :download:`Download all examples in Python source code: auto_examples_python.zip <//home/rflamary/PYTHON/POT/docs/source/auto_examples/auto_examples_python.zip>` .. container:: sphx-glr-download - :download:`Download all examples in Jupyter notebooks: auto_examples_jupyter.zip </auto_examples/auto_examples_jupyter.zip>` + :download:`Download all examples in Jupyter notebooks: auto_examples_jupyter.zip <//home/rflamary/PYTHON/POT/docs/source/auto_examples/auto_examples_jupyter.zip>` .. rst-class:: sphx-glr-signature - `Generated by Sphinx-Gallery <http://sphinx-gallery.readthedocs.io>`_ + `Generated by Sphinx-Gallery <https://sphinx-gallery.readthedocs.io>`_ diff --git a/docs/source/auto_examples/plot_OTDA_2D.ipynb b/docs/source/auto_examples/plot_OTDA_2D.ipynb deleted file mode 100644 index 2ffb256..0000000 --- a/docs/source/auto_examples/plot_OTDA_2D.ipynb +++ /dev/null @@ -1,54 +0,0 @@ -{ - "nbformat_minor": 0, - "nbformat": 4, - "cells": [ - { - "execution_count": null, - "cell_type": "code", - "source": [ - "%matplotlib inline" - ], - "outputs": [], - "metadata": { - "collapsed": false - } - }, - { - "source": [ - "\n# OT for empirical distributions\n\n\n\n" - ], - "cell_type": "markdown", - "metadata": {} - }, - { - "execution_count": null, - "cell_type": "code", - "source": [ - "import numpy as np\nimport matplotlib.pylab as pl\nimport ot\n\n\n\n#%% parameters\n\nn=150 # nb bins\n\nxs,ys=ot.datasets.get_data_classif('3gauss',n)\nxt,yt=ot.datasets.get_data_classif('3gauss2',n)\n\na,b = ot.unif(n),ot.unif(n)\n# loss matrix\nM=ot.dist(xs,xt)\n#M/=M.max()\n\n#%% plot samples\n\npl.figure(1)\n\npl.subplot(2,2,1)\npl.scatter(xs[:,0],xs[:,1],c=ys,marker='+',label='Source samples')\npl.legend(loc=0)\npl.title('Source distributions')\n\npl.subplot(2,2,2)\npl.scatter(xt[:,0],xt[:,1],c=yt,marker='o',label='Target samples')\npl.legend(loc=0)\npl.title('target distributions')\n\npl.figure(2)\npl.imshow(M,interpolation='nearest')\npl.title('Cost matrix M')\n\n\n#%% OT estimation\n\n# EMD\nG0=ot.emd(a,b,M)\n\n# sinkhorn\nlambd=1e-1\nGs=ot.sinkhorn(a,b,M,lambd)\n\n\n# Group lasso regularization\nreg=1e-1\neta=1e0\nGg=ot.da.sinkhorn_lpl1_mm(a,ys.astype(np.int),b,M,reg,eta)\n\n\n#%% visu matrices\n\npl.figure(3)\n\npl.subplot(2,3,1)\npl.imshow(G0,interpolation='nearest')\npl.title('OT matrix ')\n\npl.subplot(2,3,2)\npl.imshow(Gs,interpolation='nearest')\npl.title('OT matrix Sinkhorn')\n\npl.subplot(2,3,3)\npl.imshow(Gg,interpolation='nearest')\npl.title('OT matrix Group lasso')\n\npl.subplot(2,3,4)\not.plot.plot2D_samples_mat(xs,xt,G0,c=[.5,.5,1])\npl.scatter(xs[:,0],xs[:,1],c=ys,marker='+',label='Source samples')\npl.scatter(xt[:,0],xt[:,1],c=yt,marker='o',label='Target samples')\n\n\npl.subplot(2,3,5)\not.plot.plot2D_samples_mat(xs,xt,Gs,c=[.5,.5,1])\npl.scatter(xs[:,0],xs[:,1],c=ys,marker='+',label='Source samples')\npl.scatter(xt[:,0],xt[:,1],c=yt,marker='o',label='Target samples')\n\npl.subplot(2,3,6)\not.plot.plot2D_samples_mat(xs,xt,Gg,c=[.5,.5,1])\npl.scatter(xs[:,0],xs[:,1],c=ys,marker='+',label='Source samples')\npl.scatter(xt[:,0],xt[:,1],c=yt,marker='o',label='Target samples')\n\n#%% sample interpolation\n\nxst0=n*G0.dot(xt)\nxsts=n*Gs.dot(xt)\nxstg=n*Gg.dot(xt)\n\npl.figure(4)\npl.subplot(2,3,1)\n\n\npl.scatter(xt[:,0],xt[:,1],c=yt,marker='o',label='Target samples',alpha=0.5)\npl.scatter(xst0[:,0],xst0[:,1],c=ys,marker='+',label='Transp samples',s=30)\npl.title('Interp samples')\npl.legend(loc=0)\n\npl.subplot(2,3,2)\n\n\npl.scatter(xt[:,0],xt[:,1],c=yt,marker='o',label='Target samples',alpha=0.5)\npl.scatter(xsts[:,0],xsts[:,1],c=ys,marker='+',label='Transp samples',s=30)\npl.title('Interp samples Sinkhorn')\n\npl.subplot(2,3,3)\n\npl.scatter(xt[:,0],xt[:,1],c=yt,marker='o',label='Target samples',alpha=0.5)\npl.scatter(xstg[:,0],xstg[:,1],c=ys,marker='+',label='Transp samples',s=30)\npl.title('Interp samples Grouplasso')" - ], - "outputs": [], - "metadata": { - "collapsed": false - } - } - ], - "metadata": { - "kernelspec": { - "display_name": "Python 2", - "name": "python2", - "language": "python" - }, - "language_info": { - "mimetype": "text/x-python", - "nbconvert_exporter": "python", - "name": "python", - "file_extension": ".py", - "version": "2.7.12", - "pygments_lexer": "ipython2", - "codemirror_mode": { - "version": 2, - "name": "ipython" - } - } - } -}
\ No newline at end of file diff --git a/docs/source/auto_examples/plot_OTDA_2D.py b/docs/source/auto_examples/plot_OTDA_2D.py deleted file mode 100644 index a1fb804..0000000 --- a/docs/source/auto_examples/plot_OTDA_2D.py +++ /dev/null @@ -1,120 +0,0 @@ -# -*- coding: utf-8 -*- -""" -============================== -OT for empirical distributions -============================== - -""" - -import numpy as np -import matplotlib.pylab as pl -import ot - - - -#%% parameters - -n=150 # nb bins - -xs,ys=ot.datasets.get_data_classif('3gauss',n) -xt,yt=ot.datasets.get_data_classif('3gauss2',n) - -a,b = ot.unif(n),ot.unif(n) -# loss matrix -M=ot.dist(xs,xt) -#M/=M.max() - -#%% plot samples - -pl.figure(1) - -pl.subplot(2,2,1) -pl.scatter(xs[:,0],xs[:,1],c=ys,marker='+',label='Source samples') -pl.legend(loc=0) -pl.title('Source distributions') - -pl.subplot(2,2,2) -pl.scatter(xt[:,0],xt[:,1],c=yt,marker='o',label='Target samples') -pl.legend(loc=0) -pl.title('target distributions') - -pl.figure(2) -pl.imshow(M,interpolation='nearest') -pl.title('Cost matrix M') - - -#%% OT estimation - -# EMD -G0=ot.emd(a,b,M) - -# sinkhorn -lambd=1e-1 -Gs=ot.sinkhorn(a,b,M,lambd) - - -# Group lasso regularization -reg=1e-1 -eta=1e0 -Gg=ot.da.sinkhorn_lpl1_mm(a,ys.astype(np.int),b,M,reg,eta) - - -#%% visu matrices - -pl.figure(3) - -pl.subplot(2,3,1) -pl.imshow(G0,interpolation='nearest') -pl.title('OT matrix ') - -pl.subplot(2,3,2) -pl.imshow(Gs,interpolation='nearest') -pl.title('OT matrix Sinkhorn') - -pl.subplot(2,3,3) -pl.imshow(Gg,interpolation='nearest') -pl.title('OT matrix Group lasso') - -pl.subplot(2,3,4) -ot.plot.plot2D_samples_mat(xs,xt,G0,c=[.5,.5,1]) -pl.scatter(xs[:,0],xs[:,1],c=ys,marker='+',label='Source samples') -pl.scatter(xt[:,0],xt[:,1],c=yt,marker='o',label='Target samples') - - -pl.subplot(2,3,5) -ot.plot.plot2D_samples_mat(xs,xt,Gs,c=[.5,.5,1]) -pl.scatter(xs[:,0],xs[:,1],c=ys,marker='+',label='Source samples') -pl.scatter(xt[:,0],xt[:,1],c=yt,marker='o',label='Target samples') - -pl.subplot(2,3,6) -ot.plot.plot2D_samples_mat(xs,xt,Gg,c=[.5,.5,1]) -pl.scatter(xs[:,0],xs[:,1],c=ys,marker='+',label='Source samples') -pl.scatter(xt[:,0],xt[:,1],c=yt,marker='o',label='Target samples') - -#%% sample interpolation - -xst0=n*G0.dot(xt) -xsts=n*Gs.dot(xt) -xstg=n*Gg.dot(xt) - -pl.figure(4) -pl.subplot(2,3,1) - - -pl.scatter(xt[:,0],xt[:,1],c=yt,marker='o',label='Target samples',alpha=0.5) -pl.scatter(xst0[:,0],xst0[:,1],c=ys,marker='+',label='Transp samples',s=30) -pl.title('Interp samples') -pl.legend(loc=0) - -pl.subplot(2,3,2) - - -pl.scatter(xt[:,0],xt[:,1],c=yt,marker='o',label='Target samples',alpha=0.5) -pl.scatter(xsts[:,0],xsts[:,1],c=ys,marker='+',label='Transp samples',s=30) -pl.title('Interp samples Sinkhorn') - -pl.subplot(2,3,3) - -pl.scatter(xt[:,0],xt[:,1],c=yt,marker='o',label='Target samples',alpha=0.5) -pl.scatter(xstg[:,0],xstg[:,1],c=ys,marker='+',label='Transp samples',s=30) -pl.title('Interp samples Grouplasso')
\ No newline at end of file diff --git a/docs/source/auto_examples/plot_OTDA_2D.rst b/docs/source/auto_examples/plot_OTDA_2D.rst deleted file mode 100644 index b535bb0..0000000 --- a/docs/source/auto_examples/plot_OTDA_2D.rst +++ /dev/null @@ -1,175 +0,0 @@ - - -.. _sphx_glr_auto_examples_plot_OTDA_2D.py: - - -============================== -OT for empirical distributions -============================== - - - - - -.. rst-class:: sphx-glr-horizontal - - - * - - .. image:: /auto_examples/images/sphx_glr_plot_OTDA_2D_001.png - :scale: 47 - - * - - .. image:: /auto_examples/images/sphx_glr_plot_OTDA_2D_002.png - :scale: 47 - - * - - .. image:: /auto_examples/images/sphx_glr_plot_OTDA_2D_003.png - :scale: 47 - - * - - .. image:: /auto_examples/images/sphx_glr_plot_OTDA_2D_004.png - :scale: 47 - - - - - -.. code-block:: python - - - import numpy as np - import matplotlib.pylab as pl - import ot - - - - #%% parameters - - n=150 # nb bins - - xs,ys=ot.datasets.get_data_classif('3gauss',n) - xt,yt=ot.datasets.get_data_classif('3gauss2',n) - - a,b = ot.unif(n),ot.unif(n) - # loss matrix - M=ot.dist(xs,xt) - #M/=M.max() - - #%% plot samples - - pl.figure(1) - - pl.subplot(2,2,1) - pl.scatter(xs[:,0],xs[:,1],c=ys,marker='+',label='Source samples') - pl.legend(loc=0) - pl.title('Source distributions') - - pl.subplot(2,2,2) - pl.scatter(xt[:,0],xt[:,1],c=yt,marker='o',label='Target samples') - pl.legend(loc=0) - pl.title('target distributions') - - pl.figure(2) - pl.imshow(M,interpolation='nearest') - pl.title('Cost matrix M') - - - #%% OT estimation - - # EMD - G0=ot.emd(a,b,M) - - # sinkhorn - lambd=1e-1 - Gs=ot.sinkhorn(a,b,M,lambd) - - - # Group lasso regularization - reg=1e-1 - eta=1e0 - Gg=ot.da.sinkhorn_lpl1_mm(a,ys.astype(np.int),b,M,reg,eta) - - - #%% visu matrices - - pl.figure(3) - - pl.subplot(2,3,1) - pl.imshow(G0,interpolation='nearest') - pl.title('OT matrix ') - - pl.subplot(2,3,2) - pl.imshow(Gs,interpolation='nearest') - pl.title('OT matrix Sinkhorn') - - pl.subplot(2,3,3) - pl.imshow(Gg,interpolation='nearest') - pl.title('OT matrix Group lasso') - - pl.subplot(2,3,4) - ot.plot.plot2D_samples_mat(xs,xt,G0,c=[.5,.5,1]) - pl.scatter(xs[:,0],xs[:,1],c=ys,marker='+',label='Source samples') - pl.scatter(xt[:,0],xt[:,1],c=yt,marker='o',label='Target samples') - - - pl.subplot(2,3,5) - ot.plot.plot2D_samples_mat(xs,xt,Gs,c=[.5,.5,1]) - pl.scatter(xs[:,0],xs[:,1],c=ys,marker='+',label='Source samples') - pl.scatter(xt[:,0],xt[:,1],c=yt,marker='o',label='Target samples') - - pl.subplot(2,3,6) - ot.plot.plot2D_samples_mat(xs,xt,Gg,c=[.5,.5,1]) - pl.scatter(xs[:,0],xs[:,1],c=ys,marker='+',label='Source samples') - pl.scatter(xt[:,0],xt[:,1],c=yt,marker='o',label='Target samples') - - #%% sample interpolation - - xst0=n*G0.dot(xt) - xsts=n*Gs.dot(xt) - xstg=n*Gg.dot(xt) - - pl.figure(4) - pl.subplot(2,3,1) - - - pl.scatter(xt[:,0],xt[:,1],c=yt,marker='o',label='Target samples',alpha=0.5) - pl.scatter(xst0[:,0],xst0[:,1],c=ys,marker='+',label='Transp samples',s=30) - pl.title('Interp samples') - pl.legend(loc=0) - - pl.subplot(2,3,2) - - - pl.scatter(xt[:,0],xt[:,1],c=yt,marker='o',label='Target samples',alpha=0.5) - pl.scatter(xsts[:,0],xsts[:,1],c=ys,marker='+',label='Transp samples',s=30) - pl.title('Interp samples Sinkhorn') - - pl.subplot(2,3,3) - - pl.scatter(xt[:,0],xt[:,1],c=yt,marker='o',label='Target samples',alpha=0.5) - pl.scatter(xstg[:,0],xstg[:,1],c=ys,marker='+',label='Transp samples',s=30) - pl.title('Interp samples Grouplasso') -**Total running time of the script:** ( 0 minutes 17.372 seconds) - - - -.. container:: sphx-glr-footer - - - .. container:: sphx-glr-download - - :download:`Download Python source code: plot_OTDA_2D.py <plot_OTDA_2D.py>` - - - - .. container:: sphx-glr-download - - :download:`Download Jupyter notebook: plot_OTDA_2D.ipynb <plot_OTDA_2D.ipynb>` - -.. rst-class:: sphx-glr-signature - - `Generated by Sphinx-Gallery <http://sphinx-gallery.readthedocs.io>`_ diff --git a/docs/source/auto_examples/plot_OTDA_classes.ipynb b/docs/source/auto_examples/plot_OTDA_classes.ipynb deleted file mode 100644 index d9fcb87..0000000 --- a/docs/source/auto_examples/plot_OTDA_classes.ipynb +++ /dev/null @@ -1,54 +0,0 @@ -{ - "nbformat_minor": 0, - "nbformat": 4, - "cells": [ - { - "execution_count": null, - "cell_type": "code", - "source": [ - "%matplotlib inline" - ], - "outputs": [], - "metadata": { - "collapsed": false - } - }, - { - "source": [ - "\n# OT for domain adaptation\n\n\n\n" - ], - "cell_type": "markdown", - "metadata": {} - }, - { - "execution_count": null, - "cell_type": "code", - "source": [ - "import matplotlib.pylab as pl\nimport ot\n\n\n\n\n#%% parameters\n\nn=150 # nb samples in source and target datasets\n\nxs,ys=ot.datasets.get_data_classif('3gauss',n)\nxt,yt=ot.datasets.get_data_classif('3gauss2',n)\n\n\n\n\n#%% plot samples\n\npl.figure(1)\n\npl.subplot(2,2,1)\npl.scatter(xs[:,0],xs[:,1],c=ys,marker='+',label='Source samples')\npl.legend(loc=0)\npl.title('Source distributions')\n\npl.subplot(2,2,2)\npl.scatter(xt[:,0],xt[:,1],c=yt,marker='o',label='Target samples')\npl.legend(loc=0)\npl.title('target distributions')\n\n\n#%% OT estimation\n\n# LP problem\nda_emd=ot.da.OTDA() # init class\nda_emd.fit(xs,xt) # fit distributions\nxst0=da_emd.interp() # interpolation of source samples\n\n\n# sinkhorn regularization\nlambd=1e-1\nda_entrop=ot.da.OTDA_sinkhorn()\nda_entrop.fit(xs,xt,reg=lambd)\nxsts=da_entrop.interp()\n\n# non-convex Group lasso regularization\nreg=1e-1\neta=1e0\nda_lpl1=ot.da.OTDA_lpl1()\nda_lpl1.fit(xs,ys,xt,reg=reg,eta=eta)\nxstg=da_lpl1.interp()\n\n\n# True Group lasso regularization\nreg=1e-1\neta=2e0\nda_l1l2=ot.da.OTDA_l1l2()\nda_l1l2.fit(xs,ys,xt,reg=reg,eta=eta,numItermax=20,verbose=True)\nxstgl=da_l1l2.interp()\n\n\n#%% plot interpolated source samples\npl.figure(4,(15,8))\n\nparam_img={'interpolation':'nearest','cmap':'jet'}\n\npl.subplot(2,4,1)\npl.imshow(da_emd.G,**param_img)\npl.title('OT matrix')\n\n\npl.subplot(2,4,2)\npl.imshow(da_entrop.G,**param_img)\npl.title('OT matrix sinkhorn')\n\npl.subplot(2,4,3)\npl.imshow(da_lpl1.G,**param_img)\npl.title('OT matrix non-convex Group Lasso')\n\npl.subplot(2,4,4)\npl.imshow(da_l1l2.G,**param_img)\npl.title('OT matrix Group Lasso')\n\n\npl.subplot(2,4,5)\npl.scatter(xt[:,0],xt[:,1],c=yt,marker='o',label='Target samples',alpha=0.3)\npl.scatter(xst0[:,0],xst0[:,1],c=ys,marker='+',label='Transp samples',s=30)\npl.title('Interp samples')\npl.legend(loc=0)\n\npl.subplot(2,4,6)\npl.scatter(xt[:,0],xt[:,1],c=yt,marker='o',label='Target samples',alpha=0.3)\npl.scatter(xsts[:,0],xsts[:,1],c=ys,marker='+',label='Transp samples',s=30)\npl.title('Interp samples Sinkhorn')\n\npl.subplot(2,4,7)\npl.scatter(xt[:,0],xt[:,1],c=yt,marker='o',label='Target samples',alpha=0.3)\npl.scatter(xstg[:,0],xstg[:,1],c=ys,marker='+',label='Transp samples',s=30)\npl.title('Interp samples non-convex Group Lasso')\n\npl.subplot(2,4,8)\npl.scatter(xt[:,0],xt[:,1],c=yt,marker='o',label='Target samples',alpha=0.3)\npl.scatter(xstgl[:,0],xstgl[:,1],c=ys,marker='+',label='Transp samples',s=30)\npl.title('Interp samples Group Lasso')" - ], - "outputs": [], - "metadata": { - "collapsed": false - } - } - ], - "metadata": { - "kernelspec": { - "display_name": "Python 2", - "name": "python2", - "language": "python" - }, - "language_info": { - "mimetype": "text/x-python", - "nbconvert_exporter": "python", - "name": "python", - "file_extension": ".py", - "version": "2.7.12", - "pygments_lexer": "ipython2", - "codemirror_mode": { - "version": 2, - "name": "ipython" - } - } - } -}
\ No newline at end of file diff --git a/docs/source/auto_examples/plot_OTDA_classes.py b/docs/source/auto_examples/plot_OTDA_classes.py deleted file mode 100644 index 089b45b..0000000 --- a/docs/source/auto_examples/plot_OTDA_classes.py +++ /dev/null @@ -1,112 +0,0 @@ -# -*- coding: utf-8 -*- -""" -======================== -OT for domain adaptation -======================== - -""" - -import matplotlib.pylab as pl -import ot - - - - -#%% parameters - -n=150 # nb samples in source and target datasets - -xs,ys=ot.datasets.get_data_classif('3gauss',n) -xt,yt=ot.datasets.get_data_classif('3gauss2',n) - - - - -#%% plot samples - -pl.figure(1) - -pl.subplot(2,2,1) -pl.scatter(xs[:,0],xs[:,1],c=ys,marker='+',label='Source samples') -pl.legend(loc=0) -pl.title('Source distributions') - -pl.subplot(2,2,2) -pl.scatter(xt[:,0],xt[:,1],c=yt,marker='o',label='Target samples') -pl.legend(loc=0) -pl.title('target distributions') - - -#%% OT estimation - -# LP problem -da_emd=ot.da.OTDA() # init class -da_emd.fit(xs,xt) # fit distributions -xst0=da_emd.interp() # interpolation of source samples - - -# sinkhorn regularization -lambd=1e-1 -da_entrop=ot.da.OTDA_sinkhorn() -da_entrop.fit(xs,xt,reg=lambd) -xsts=da_entrop.interp() - -# non-convex Group lasso regularization -reg=1e-1 -eta=1e0 -da_lpl1=ot.da.OTDA_lpl1() -da_lpl1.fit(xs,ys,xt,reg=reg,eta=eta) -xstg=da_lpl1.interp() - - -# True Group lasso regularization -reg=1e-1 -eta=2e0 -da_l1l2=ot.da.OTDA_l1l2() -da_l1l2.fit(xs,ys,xt,reg=reg,eta=eta,numItermax=20,verbose=True) -xstgl=da_l1l2.interp() - - -#%% plot interpolated source samples -pl.figure(4,(15,8)) - -param_img={'interpolation':'nearest','cmap':'jet'} - -pl.subplot(2,4,1) -pl.imshow(da_emd.G,**param_img) -pl.title('OT matrix') - - -pl.subplot(2,4,2) -pl.imshow(da_entrop.G,**param_img) -pl.title('OT matrix sinkhorn') - -pl.subplot(2,4,3) -pl.imshow(da_lpl1.G,**param_img) -pl.title('OT matrix non-convex Group Lasso') - -pl.subplot(2,4,4) -pl.imshow(da_l1l2.G,**param_img) -pl.title('OT matrix Group Lasso') - - -pl.subplot(2,4,5) -pl.scatter(xt[:,0],xt[:,1],c=yt,marker='o',label='Target samples',alpha=0.3) -pl.scatter(xst0[:,0],xst0[:,1],c=ys,marker='+',label='Transp samples',s=30) -pl.title('Interp samples') -pl.legend(loc=0) - -pl.subplot(2,4,6) -pl.scatter(xt[:,0],xt[:,1],c=yt,marker='o',label='Target samples',alpha=0.3) -pl.scatter(xsts[:,0],xsts[:,1],c=ys,marker='+',label='Transp samples',s=30) -pl.title('Interp samples Sinkhorn') - -pl.subplot(2,4,7) -pl.scatter(xt[:,0],xt[:,1],c=yt,marker='o',label='Target samples',alpha=0.3) -pl.scatter(xstg[:,0],xstg[:,1],c=ys,marker='+',label='Transp samples',s=30) -pl.title('Interp samples non-convex Group Lasso') - -pl.subplot(2,4,8) -pl.scatter(xt[:,0],xt[:,1],c=yt,marker='o',label='Target samples',alpha=0.3) -pl.scatter(xstgl[:,0],xstgl[:,1],c=ys,marker='+',label='Transp samples',s=30) -pl.title('Interp samples Group Lasso')
\ No newline at end of file diff --git a/docs/source/auto_examples/plot_OTDA_classes.rst b/docs/source/auto_examples/plot_OTDA_classes.rst deleted file mode 100644 index 097e9fc..0000000 --- a/docs/source/auto_examples/plot_OTDA_classes.rst +++ /dev/null @@ -1,190 +0,0 @@ - - -.. _sphx_glr_auto_examples_plot_OTDA_classes.py: - - -======================== -OT for domain adaptation -======================== - - - - - -.. rst-class:: sphx-glr-horizontal - - - * - - .. image:: /auto_examples/images/sphx_glr_plot_OTDA_classes_001.png - :scale: 47 - - * - - .. image:: /auto_examples/images/sphx_glr_plot_OTDA_classes_004.png - :scale: 47 - - -.. rst-class:: sphx-glr-script-out - - Out:: - - It. |Loss |Delta loss - -------------------------------- - 0|9.171271e+00|0.000000e+00 - 1|2.133783e+00|-3.298127e+00 - 2|1.895941e+00|-1.254484e-01 - 3|1.844628e+00|-2.781709e-02 - 4|1.824983e+00|-1.076467e-02 - 5|1.815453e+00|-5.249337e-03 - 6|1.808104e+00|-4.064733e-03 - 7|1.803558e+00|-2.520475e-03 - 8|1.801061e+00|-1.386155e-03 - 9|1.799391e+00|-9.279565e-04 - 10|1.797176e+00|-1.232778e-03 - 11|1.795465e+00|-9.529479e-04 - 12|1.795316e+00|-8.322362e-05 - 13|1.794523e+00|-4.418932e-04 - 14|1.794444e+00|-4.390599e-05 - 15|1.794395e+00|-2.710318e-05 - 16|1.793713e+00|-3.804028e-04 - 17|1.793110e+00|-3.359479e-04 - 18|1.792829e+00|-1.569563e-04 - 19|1.792621e+00|-1.159469e-04 - It. |Loss |Delta loss - -------------------------------- - 20|1.791334e+00|-7.187689e-04 - - - - -| - - -.. code-block:: python - - - import matplotlib.pylab as pl - import ot - - - - - #%% parameters - - n=150 # nb samples in source and target datasets - - xs,ys=ot.datasets.get_data_classif('3gauss',n) - xt,yt=ot.datasets.get_data_classif('3gauss2',n) - - - - - #%% plot samples - - pl.figure(1) - - pl.subplot(2,2,1) - pl.scatter(xs[:,0],xs[:,1],c=ys,marker='+',label='Source samples') - pl.legend(loc=0) - pl.title('Source distributions') - - pl.subplot(2,2,2) - pl.scatter(xt[:,0],xt[:,1],c=yt,marker='o',label='Target samples') - pl.legend(loc=0) - pl.title('target distributions') - - - #%% OT estimation - - # LP problem - da_emd=ot.da.OTDA() # init class - da_emd.fit(xs,xt) # fit distributions - xst0=da_emd.interp() # interpolation of source samples - - - # sinkhorn regularization - lambd=1e-1 - da_entrop=ot.da.OTDA_sinkhorn() - da_entrop.fit(xs,xt,reg=lambd) - xsts=da_entrop.interp() - - # non-convex Group lasso regularization - reg=1e-1 - eta=1e0 - da_lpl1=ot.da.OTDA_lpl1() - da_lpl1.fit(xs,ys,xt,reg=reg,eta=eta) - xstg=da_lpl1.interp() - - - # True Group lasso regularization - reg=1e-1 - eta=2e0 - da_l1l2=ot.da.OTDA_l1l2() - da_l1l2.fit(xs,ys,xt,reg=reg,eta=eta,numItermax=20,verbose=True) - xstgl=da_l1l2.interp() - - - #%% plot interpolated source samples - pl.figure(4,(15,8)) - - param_img={'interpolation':'nearest','cmap':'jet'} - - pl.subplot(2,4,1) - pl.imshow(da_emd.G,**param_img) - pl.title('OT matrix') - - - pl.subplot(2,4,2) - pl.imshow(da_entrop.G,**param_img) - pl.title('OT matrix sinkhorn') - - pl.subplot(2,4,3) - pl.imshow(da_lpl1.G,**param_img) - pl.title('OT matrix non-convex Group Lasso') - - pl.subplot(2,4,4) - pl.imshow(da_l1l2.G,**param_img) - pl.title('OT matrix Group Lasso') - - - pl.subplot(2,4,5) - pl.scatter(xt[:,0],xt[:,1],c=yt,marker='o',label='Target samples',alpha=0.3) - pl.scatter(xst0[:,0],xst0[:,1],c=ys,marker='+',label='Transp samples',s=30) - pl.title('Interp samples') - pl.legend(loc=0) - - pl.subplot(2,4,6) - pl.scatter(xt[:,0],xt[:,1],c=yt,marker='o',label='Target samples',alpha=0.3) - pl.scatter(xsts[:,0],xsts[:,1],c=ys,marker='+',label='Transp samples',s=30) - pl.title('Interp samples Sinkhorn') - - pl.subplot(2,4,7) - pl.scatter(xt[:,0],xt[:,1],c=yt,marker='o',label='Target samples',alpha=0.3) - pl.scatter(xstg[:,0],xstg[:,1],c=ys,marker='+',label='Transp samples',s=30) - pl.title('Interp samples non-convex Group Lasso') - - pl.subplot(2,4,8) - pl.scatter(xt[:,0],xt[:,1],c=yt,marker='o',label='Target samples',alpha=0.3) - pl.scatter(xstgl[:,0],xstgl[:,1],c=ys,marker='+',label='Transp samples',s=30) - pl.title('Interp samples Group Lasso') -**Total running time of the script:** ( 0 minutes 2.225 seconds) - - - -.. container:: sphx-glr-footer - - - .. container:: sphx-glr-download - - :download:`Download Python source code: plot_OTDA_classes.py <plot_OTDA_classes.py>` - - - - .. container:: sphx-glr-download - - :download:`Download Jupyter notebook: plot_OTDA_classes.ipynb <plot_OTDA_classes.ipynb>` - -.. rst-class:: sphx-glr-signature - - `Generated by Sphinx-Gallery <http://sphinx-gallery.readthedocs.io>`_ diff --git a/docs/source/auto_examples/plot_OTDA_color_images.ipynb b/docs/source/auto_examples/plot_OTDA_color_images.ipynb deleted file mode 100644 index d174828..0000000 --- a/docs/source/auto_examples/plot_OTDA_color_images.ipynb +++ /dev/null @@ -1,54 +0,0 @@ -{ - "nbformat_minor": 0, - "nbformat": 4, - "cells": [ - { - "execution_count": null, - "cell_type": "code", - "source": [ - "%matplotlib inline" - ], - "outputs": [], - "metadata": { - "collapsed": false - } - }, - { - "source": [ - "\n========================================================\nOT for domain adaptation with image color adaptation [6]\n========================================================\n\n[6] Ferradans, S., Papadakis, N., Peyre, G., & Aujol, J. F. (2014). Regularized discrete optimal transport. SIAM Journal on Imaging Sciences, 7(3), 1853-1882.\n\n" - ], - "cell_type": "markdown", - "metadata": {} - }, - { - "execution_count": null, - "cell_type": "code", - "source": [ - "import numpy as np\nimport scipy.ndimage as spi\nimport matplotlib.pylab as pl\nimport ot\n\n\n#%% Loading images\n\nI1=spi.imread('../data/ocean_day.jpg').astype(np.float64)/256\nI2=spi.imread('../data/ocean_sunset.jpg').astype(np.float64)/256\n\n#%% Plot images\n\npl.figure(1)\n\npl.subplot(1,2,1)\npl.imshow(I1)\npl.title('Image 1')\n\npl.subplot(1,2,2)\npl.imshow(I2)\npl.title('Image 2')\n\npl.show()\n\n#%% Image conversion and dataset generation\n\ndef im2mat(I):\n \"\"\"Converts and image to matrix (one pixel per line)\"\"\"\n return I.reshape((I.shape[0]*I.shape[1],I.shape[2]))\n\ndef mat2im(X,shape):\n \"\"\"Converts back a matrix to an image\"\"\"\n return X.reshape(shape)\n\nX1=im2mat(I1)\nX2=im2mat(I2)\n\n# training samples\nnb=1000\nidx1=np.random.randint(X1.shape[0],size=(nb,))\nidx2=np.random.randint(X2.shape[0],size=(nb,))\n\nxs=X1[idx1,:]\nxt=X2[idx2,:]\n\n#%% Plot image distributions\n\n\npl.figure(2,(10,5))\n\npl.subplot(1,2,1)\npl.scatter(xs[:,0],xs[:,2],c=xs)\npl.axis([0,1,0,1])\npl.xlabel('Red')\npl.ylabel('Blue')\npl.title('Image 1')\n\npl.subplot(1,2,2)\n#pl.imshow(I2)\npl.scatter(xt[:,0],xt[:,2],c=xt)\npl.axis([0,1,0,1])\npl.xlabel('Red')\npl.ylabel('Blue')\npl.title('Image 2')\n\npl.show()\n\n\n\n#%% domain adaptation between images\n\n# LP problem\nda_emd=ot.da.OTDA() # init class\nda_emd.fit(xs,xt) # fit distributions\n\n\n# sinkhorn regularization\nlambd=1e-1\nda_entrop=ot.da.OTDA_sinkhorn()\nda_entrop.fit(xs,xt,reg=lambd)\n\n\n\n#%% prediction between images (using out of sample prediction as in [6])\n\nX1t=da_emd.predict(X1)\nX2t=da_emd.predict(X2,-1)\n\n\nX1te=da_entrop.predict(X1)\nX2te=da_entrop.predict(X2,-1)\n\n\ndef minmax(I):\n return np.minimum(np.maximum(I,0),1)\n\nI1t=minmax(mat2im(X1t,I1.shape))\nI2t=minmax(mat2im(X2t,I2.shape))\n\nI1te=minmax(mat2im(X1te,I1.shape))\nI2te=minmax(mat2im(X2te,I2.shape))\n\n#%% plot all images\n\npl.figure(2,(10,8))\n\npl.subplot(2,3,1)\n\npl.imshow(I1)\npl.title('Image 1')\n\npl.subplot(2,3,2)\npl.imshow(I1t)\npl.title('Image 1 Adapt')\n\n\npl.subplot(2,3,3)\npl.imshow(I1te)\npl.title('Image 1 Adapt (reg)')\n\npl.subplot(2,3,4)\n\npl.imshow(I2)\npl.title('Image 2')\n\npl.subplot(2,3,5)\npl.imshow(I2t)\npl.title('Image 2 Adapt')\n\n\npl.subplot(2,3,6)\npl.imshow(I2te)\npl.title('Image 2 Adapt (reg)')\n\npl.show()" - ], - "outputs": [], - "metadata": { - "collapsed": false - } - } - ], - "metadata": { - "kernelspec": { - "display_name": "Python 2", - "name": "python2", - "language": "python" - }, - "language_info": { - "mimetype": "text/x-python", - "nbconvert_exporter": "python", - "name": "python", - "file_extension": ".py", - "version": "2.7.12", - "pygments_lexer": "ipython2", - "codemirror_mode": { - "version": 2, - "name": "ipython" - } - } - } -}
\ No newline at end of file diff --git a/docs/source/auto_examples/plot_OTDA_color_images.py b/docs/source/auto_examples/plot_OTDA_color_images.py deleted file mode 100644 index 68eee44..0000000 --- a/docs/source/auto_examples/plot_OTDA_color_images.py +++ /dev/null @@ -1,145 +0,0 @@ -# -*- coding: utf-8 -*- -""" -======================================================== -OT for domain adaptation with image color adaptation [6] -======================================================== - -[6] Ferradans, S., Papadakis, N., Peyre, G., & Aujol, J. F. (2014). Regularized discrete optimal transport. SIAM Journal on Imaging Sciences, 7(3), 1853-1882. -""" - -import numpy as np -import scipy.ndimage as spi -import matplotlib.pylab as pl -import ot - - -#%% Loading images - -I1=spi.imread('../data/ocean_day.jpg').astype(np.float64)/256 -I2=spi.imread('../data/ocean_sunset.jpg').astype(np.float64)/256 - -#%% Plot images - -pl.figure(1) - -pl.subplot(1,2,1) -pl.imshow(I1) -pl.title('Image 1') - -pl.subplot(1,2,2) -pl.imshow(I2) -pl.title('Image 2') - -pl.show() - -#%% Image conversion and dataset generation - -def im2mat(I): - """Converts and image to matrix (one pixel per line)""" - return I.reshape((I.shape[0]*I.shape[1],I.shape[2])) - -def mat2im(X,shape): - """Converts back a matrix to an image""" - return X.reshape(shape) - -X1=im2mat(I1) -X2=im2mat(I2) - -# training samples -nb=1000 -idx1=np.random.randint(X1.shape[0],size=(nb,)) -idx2=np.random.randint(X2.shape[0],size=(nb,)) - -xs=X1[idx1,:] -xt=X2[idx2,:] - -#%% Plot image distributions - - -pl.figure(2,(10,5)) - -pl.subplot(1,2,1) -pl.scatter(xs[:,0],xs[:,2],c=xs) -pl.axis([0,1,0,1]) -pl.xlabel('Red') -pl.ylabel('Blue') -pl.title('Image 1') - -pl.subplot(1,2,2) -#pl.imshow(I2) -pl.scatter(xt[:,0],xt[:,2],c=xt) -pl.axis([0,1,0,1]) -pl.xlabel('Red') -pl.ylabel('Blue') -pl.title('Image 2') - -pl.show() - - - -#%% domain adaptation between images - -# LP problem -da_emd=ot.da.OTDA() # init class -da_emd.fit(xs,xt) # fit distributions - - -# sinkhorn regularization -lambd=1e-1 -da_entrop=ot.da.OTDA_sinkhorn() -da_entrop.fit(xs,xt,reg=lambd) - - - -#%% prediction between images (using out of sample prediction as in [6]) - -X1t=da_emd.predict(X1) -X2t=da_emd.predict(X2,-1) - - -X1te=da_entrop.predict(X1) -X2te=da_entrop.predict(X2,-1) - - -def minmax(I): - return np.minimum(np.maximum(I,0),1) - -I1t=minmax(mat2im(X1t,I1.shape)) -I2t=minmax(mat2im(X2t,I2.shape)) - -I1te=minmax(mat2im(X1te,I1.shape)) -I2te=minmax(mat2im(X2te,I2.shape)) - -#%% plot all images - -pl.figure(2,(10,8)) - -pl.subplot(2,3,1) - -pl.imshow(I1) -pl.title('Image 1') - -pl.subplot(2,3,2) -pl.imshow(I1t) -pl.title('Image 1 Adapt') - - -pl.subplot(2,3,3) -pl.imshow(I1te) -pl.title('Image 1 Adapt (reg)') - -pl.subplot(2,3,4) - -pl.imshow(I2) -pl.title('Image 2') - -pl.subplot(2,3,5) -pl.imshow(I2t) -pl.title('Image 2 Adapt') - - -pl.subplot(2,3,6) -pl.imshow(I2te) -pl.title('Image 2 Adapt (reg)') - -pl.show() diff --git a/docs/source/auto_examples/plot_OTDA_color_images.rst b/docs/source/auto_examples/plot_OTDA_color_images.rst deleted file mode 100644 index a982a90..0000000 --- a/docs/source/auto_examples/plot_OTDA_color_images.rst +++ /dev/null @@ -1,191 +0,0 @@ - - -.. _sphx_glr_auto_examples_plot_OTDA_color_images.py: - - -======================================================== -OT for domain adaptation with image color adaptation [6] -======================================================== - -[6] Ferradans, S., Papadakis, N., Peyre, G., & Aujol, J. F. (2014). Regularized discrete optimal transport. SIAM Journal on Imaging Sciences, 7(3), 1853-1882. - - - - -.. rst-class:: sphx-glr-horizontal - - - * - - .. image:: /auto_examples/images/sphx_glr_plot_OTDA_color_images_001.png - :scale: 47 - - * - - .. image:: /auto_examples/images/sphx_glr_plot_OTDA_color_images_002.png - :scale: 47 - - - - - -.. code-block:: python - - - import numpy as np - import scipy.ndimage as spi - import matplotlib.pylab as pl - import ot - - - #%% Loading images - - I1=spi.imread('../data/ocean_day.jpg').astype(np.float64)/256 - I2=spi.imread('../data/ocean_sunset.jpg').astype(np.float64)/256 - - #%% Plot images - - pl.figure(1) - - pl.subplot(1,2,1) - pl.imshow(I1) - pl.title('Image 1') - - pl.subplot(1,2,2) - pl.imshow(I2) - pl.title('Image 2') - - pl.show() - - #%% Image conversion and dataset generation - - def im2mat(I): - """Converts and image to matrix (one pixel per line)""" - return I.reshape((I.shape[0]*I.shape[1],I.shape[2])) - - def mat2im(X,shape): - """Converts back a matrix to an image""" - return X.reshape(shape) - - X1=im2mat(I1) - X2=im2mat(I2) - - # training samples - nb=1000 - idx1=np.random.randint(X1.shape[0],size=(nb,)) - idx2=np.random.randint(X2.shape[0],size=(nb,)) - - xs=X1[idx1,:] - xt=X2[idx2,:] - - #%% Plot image distributions - - - pl.figure(2,(10,5)) - - pl.subplot(1,2,1) - pl.scatter(xs[:,0],xs[:,2],c=xs) - pl.axis([0,1,0,1]) - pl.xlabel('Red') - pl.ylabel('Blue') - pl.title('Image 1') - - pl.subplot(1,2,2) - #pl.imshow(I2) - pl.scatter(xt[:,0],xt[:,2],c=xt) - pl.axis([0,1,0,1]) - pl.xlabel('Red') - pl.ylabel('Blue') - pl.title('Image 2') - - pl.show() - - - - #%% domain adaptation between images - - # LP problem - da_emd=ot.da.OTDA() # init class - da_emd.fit(xs,xt) # fit distributions - - - # sinkhorn regularization - lambd=1e-1 - da_entrop=ot.da.OTDA_sinkhorn() - da_entrop.fit(xs,xt,reg=lambd) - - - - #%% prediction between images (using out of sample prediction as in [6]) - - X1t=da_emd.predict(X1) - X2t=da_emd.predict(X2,-1) - - - X1te=da_entrop.predict(X1) - X2te=da_entrop.predict(X2,-1) - - - def minmax(I): - return np.minimum(np.maximum(I,0),1) - - I1t=minmax(mat2im(X1t,I1.shape)) - I2t=minmax(mat2im(X2t,I2.shape)) - - I1te=minmax(mat2im(X1te,I1.shape)) - I2te=minmax(mat2im(X2te,I2.shape)) - - #%% plot all images - - pl.figure(2,(10,8)) - - pl.subplot(2,3,1) - - pl.imshow(I1) - pl.title('Image 1') - - pl.subplot(2,3,2) - pl.imshow(I1t) - pl.title('Image 1 Adapt') - - - pl.subplot(2,3,3) - pl.imshow(I1te) - pl.title('Image 1 Adapt (reg)') - - pl.subplot(2,3,4) - - pl.imshow(I2) - pl.title('Image 2') - - pl.subplot(2,3,5) - pl.imshow(I2t) - pl.title('Image 2 Adapt') - - - pl.subplot(2,3,6) - pl.imshow(I2te) - pl.title('Image 2 Adapt (reg)') - - pl.show() - -**Total running time of the script:** ( 0 minutes 24.815 seconds) - - - -.. container:: sphx-glr-footer - - - .. container:: sphx-glr-download - - :download:`Download Python source code: plot_OTDA_color_images.py <plot_OTDA_color_images.py>` - - - - .. container:: sphx-glr-download - - :download:`Download Jupyter notebook: plot_OTDA_color_images.ipynb <plot_OTDA_color_images.ipynb>` - -.. rst-class:: sphx-glr-signature - - `Generated by Sphinx-Gallery <http://sphinx-gallery.readthedocs.io>`_ diff --git a/docs/source/auto_examples/plot_OTDA_mapping.ipynb b/docs/source/auto_examples/plot_OTDA_mapping.ipynb deleted file mode 100644 index ec405af..0000000 --- a/docs/source/auto_examples/plot_OTDA_mapping.ipynb +++ /dev/null @@ -1,54 +0,0 @@ -{ - "nbformat_minor": 0, - "nbformat": 4, - "cells": [ - { - "execution_count": null, - "cell_type": "code", - "source": [ - "%matplotlib inline" - ], - "outputs": [], - "metadata": { - "collapsed": false - } - }, - { - "source": [ - "\n===============================================\nOT mapping estimation for domain adaptation [8]\n===============================================\n\n[8] M. Perrot, N. Courty, R. Flamary, A. Habrard, \"Mapping estimation for\n discrete optimal transport\", Neural Information Processing Systems (NIPS), 2016.\n\n" - ], - "cell_type": "markdown", - "metadata": {} - }, - { - "execution_count": null, - "cell_type": "code", - "source": [ - "import numpy as np\nimport matplotlib.pylab as pl\nimport ot\n\n\n\n#%% dataset generation\n\nnp.random.seed(0) # makes example reproducible\n\nn=100 # nb samples in source and target datasets\ntheta=2*np.pi/20\nnz=0.1\nxs,ys=ot.datasets.get_data_classif('gaussrot',n,nz=nz)\nxt,yt=ot.datasets.get_data_classif('gaussrot',n,theta=theta,nz=nz)\n\n# one of the target mode changes its variance (no linear mapping)\nxt[yt==2]*=3\nxt=xt+4\n\n\n#%% plot samples\n\npl.figure(1,(8,5))\npl.clf()\n\npl.scatter(xs[:,0],xs[:,1],c=ys,marker='+',label='Source samples')\npl.scatter(xt[:,0],xt[:,1],c=yt,marker='o',label='Target samples')\n\npl.legend(loc=0)\npl.title('Source and target distributions')\n\n\n\n#%% OT linear mapping estimation\n\neta=1e-8 # quadratic regularization for regression\nmu=1e0 # weight of the OT linear term\nbias=True # estimate a bias\n\not_mapping=ot.da.OTDA_mapping_linear()\not_mapping.fit(xs,xt,mu=mu,eta=eta,bias=bias,numItermax = 20,verbose=True)\n\nxst=ot_mapping.predict(xs) # use the estimated mapping\nxst0=ot_mapping.interp() # use barycentric mapping\n\n\npl.figure(2,(10,7))\npl.clf()\npl.subplot(2,2,1)\npl.scatter(xt[:,0],xt[:,1],c=yt,marker='o',label='Target samples',alpha=.3)\npl.scatter(xst0[:,0],xst0[:,1],c=ys,marker='+',label='barycentric mapping')\npl.title(\"barycentric mapping\")\n\npl.subplot(2,2,2)\npl.scatter(xt[:,0],xt[:,1],c=yt,marker='o',label='Target samples',alpha=.3)\npl.scatter(xst[:,0],xst[:,1],c=ys,marker='+',label='Learned mapping')\npl.title(\"Learned mapping\")\n\n\n\n#%% Kernel mapping estimation\n\neta=1e-5 # quadratic regularization for regression\nmu=1e-1 # weight of the OT linear term\nbias=True # estimate a bias\nsigma=1 # sigma bandwidth fot gaussian kernel\n\n\not_mapping_kernel=ot.da.OTDA_mapping_kernel()\not_mapping_kernel.fit(xs,xt,mu=mu,eta=eta,sigma=sigma,bias=bias,numItermax = 10,verbose=True)\n\nxst_kernel=ot_mapping_kernel.predict(xs) # use the estimated mapping\nxst0_kernel=ot_mapping_kernel.interp() # use barycentric mapping\n\n\n#%% Plotting the mapped samples\n\npl.figure(2,(10,7))\npl.clf()\npl.subplot(2,2,1)\npl.scatter(xt[:,0],xt[:,1],c=yt,marker='o',label='Target samples',alpha=.2)\npl.scatter(xst0[:,0],xst0[:,1],c=ys,marker='+',label='Mapped source samples')\npl.title(\"Bary. mapping (linear)\")\npl.legend(loc=0)\n\npl.subplot(2,2,2)\npl.scatter(xt[:,0],xt[:,1],c=yt,marker='o',label='Target samples',alpha=.2)\npl.scatter(xst[:,0],xst[:,1],c=ys,marker='+',label='Learned mapping')\npl.title(\"Estim. mapping (linear)\")\n\npl.subplot(2,2,3)\npl.scatter(xt[:,0],xt[:,1],c=yt,marker='o',label='Target samples',alpha=.2)\npl.scatter(xst0_kernel[:,0],xst0_kernel[:,1],c=ys,marker='+',label='barycentric mapping')\npl.title(\"Bary. mapping (kernel)\")\n\npl.subplot(2,2,4)\npl.scatter(xt[:,0],xt[:,1],c=yt,marker='o',label='Target samples',alpha=.2)\npl.scatter(xst_kernel[:,0],xst_kernel[:,1],c=ys,marker='+',label='Learned mapping')\npl.title(\"Estim. mapping (kernel)\")" - ], - "outputs": [], - "metadata": { - "collapsed": false - } - } - ], - "metadata": { - "kernelspec": { - "display_name": "Python 2", - "name": "python2", - "language": "python" - }, - "language_info": { - "mimetype": "text/x-python", - "nbconvert_exporter": "python", - "name": "python", - "file_extension": ".py", - "version": "2.7.12", - "pygments_lexer": "ipython2", - "codemirror_mode": { - "version": 2, - "name": "ipython" - } - } - } -}
\ No newline at end of file diff --git a/docs/source/auto_examples/plot_OTDA_mapping.py b/docs/source/auto_examples/plot_OTDA_mapping.py deleted file mode 100644 index 78b57e7..0000000 --- a/docs/source/auto_examples/plot_OTDA_mapping.py +++ /dev/null @@ -1,110 +0,0 @@ -# -*- coding: utf-8 -*- -""" -=============================================== -OT mapping estimation for domain adaptation [8] -=============================================== - -[8] M. Perrot, N. Courty, R. Flamary, A. Habrard, "Mapping estimation for - discrete optimal transport", Neural Information Processing Systems (NIPS), 2016. -""" - -import numpy as np -import matplotlib.pylab as pl -import ot - - - -#%% dataset generation - -np.random.seed(0) # makes example reproducible - -n=100 # nb samples in source and target datasets -theta=2*np.pi/20 -nz=0.1 -xs,ys=ot.datasets.get_data_classif('gaussrot',n,nz=nz) -xt,yt=ot.datasets.get_data_classif('gaussrot',n,theta=theta,nz=nz) - -# one of the target mode changes its variance (no linear mapping) -xt[yt==2]*=3 -xt=xt+4 - - -#%% plot samples - -pl.figure(1,(8,5)) -pl.clf() - -pl.scatter(xs[:,0],xs[:,1],c=ys,marker='+',label='Source samples') -pl.scatter(xt[:,0],xt[:,1],c=yt,marker='o',label='Target samples') - -pl.legend(loc=0) -pl.title('Source and target distributions') - - - -#%% OT linear mapping estimation - -eta=1e-8 # quadratic regularization for regression -mu=1e0 # weight of the OT linear term -bias=True # estimate a bias - -ot_mapping=ot.da.OTDA_mapping_linear() -ot_mapping.fit(xs,xt,mu=mu,eta=eta,bias=bias,numItermax = 20,verbose=True) - -xst=ot_mapping.predict(xs) # use the estimated mapping -xst0=ot_mapping.interp() # use barycentric mapping - - -pl.figure(2,(10,7)) -pl.clf() -pl.subplot(2,2,1) -pl.scatter(xt[:,0],xt[:,1],c=yt,marker='o',label='Target samples',alpha=.3) -pl.scatter(xst0[:,0],xst0[:,1],c=ys,marker='+',label='barycentric mapping') -pl.title("barycentric mapping") - -pl.subplot(2,2,2) -pl.scatter(xt[:,0],xt[:,1],c=yt,marker='o',label='Target samples',alpha=.3) -pl.scatter(xst[:,0],xst[:,1],c=ys,marker='+',label='Learned mapping') -pl.title("Learned mapping") - - - -#%% Kernel mapping estimation - -eta=1e-5 # quadratic regularization for regression -mu=1e-1 # weight of the OT linear term -bias=True # estimate a bias -sigma=1 # sigma bandwidth fot gaussian kernel - - -ot_mapping_kernel=ot.da.OTDA_mapping_kernel() -ot_mapping_kernel.fit(xs,xt,mu=mu,eta=eta,sigma=sigma,bias=bias,numItermax = 10,verbose=True) - -xst_kernel=ot_mapping_kernel.predict(xs) # use the estimated mapping -xst0_kernel=ot_mapping_kernel.interp() # use barycentric mapping - - -#%% Plotting the mapped samples - -pl.figure(2,(10,7)) -pl.clf() -pl.subplot(2,2,1) -pl.scatter(xt[:,0],xt[:,1],c=yt,marker='o',label='Target samples',alpha=.2) -pl.scatter(xst0[:,0],xst0[:,1],c=ys,marker='+',label='Mapped source samples') -pl.title("Bary. mapping (linear)") -pl.legend(loc=0) - -pl.subplot(2,2,2) -pl.scatter(xt[:,0],xt[:,1],c=yt,marker='o',label='Target samples',alpha=.2) -pl.scatter(xst[:,0],xst[:,1],c=ys,marker='+',label='Learned mapping') -pl.title("Estim. mapping (linear)") - -pl.subplot(2,2,3) -pl.scatter(xt[:,0],xt[:,1],c=yt,marker='o',label='Target samples',alpha=.2) -pl.scatter(xst0_kernel[:,0],xst0_kernel[:,1],c=ys,marker='+',label='barycentric mapping') -pl.title("Bary. mapping (kernel)") - -pl.subplot(2,2,4) -pl.scatter(xt[:,0],xt[:,1],c=yt,marker='o',label='Target samples',alpha=.2) -pl.scatter(xst_kernel[:,0],xst_kernel[:,1],c=ys,marker='+',label='Learned mapping') -pl.title("Estim. mapping (kernel)") diff --git a/docs/source/auto_examples/plot_OTDA_mapping.rst b/docs/source/auto_examples/plot_OTDA_mapping.rst deleted file mode 100644 index 18da90d..0000000 --- a/docs/source/auto_examples/plot_OTDA_mapping.rst +++ /dev/null @@ -1,186 +0,0 @@ - - -.. _sphx_glr_auto_examples_plot_OTDA_mapping.py: - - -=============================================== -OT mapping estimation for domain adaptation [8] -=============================================== - -[8] M. Perrot, N. Courty, R. Flamary, A. Habrard, "Mapping estimation for - discrete optimal transport", Neural Information Processing Systems (NIPS), 2016. - - - - -.. rst-class:: sphx-glr-horizontal - - - * - - .. image:: /auto_examples/images/sphx_glr_plot_OTDA_mapping_001.png - :scale: 47 - - * - - .. image:: /auto_examples/images/sphx_glr_plot_OTDA_mapping_002.png - :scale: 47 - - -.. rst-class:: sphx-glr-script-out - - Out:: - - It. |Loss |Delta loss - -------------------------------- - 0|4.009366e+03|0.000000e+00 - 1|3.999933e+03|-2.352753e-03 - 2|3.999520e+03|-1.031984e-04 - 3|3.999362e+03|-3.936391e-05 - 4|3.999281e+03|-2.032868e-05 - 5|3.999238e+03|-1.083083e-05 - 6|3.999229e+03|-2.125291e-06 - It. |Loss |Delta loss - -------------------------------- - 0|4.026841e+02|0.000000e+00 - 1|3.990791e+02|-8.952439e-03 - 2|3.987954e+02|-7.107124e-04 - 3|3.986554e+02|-3.512453e-04 - 4|3.985721e+02|-2.087997e-04 - 5|3.985141e+02|-1.456184e-04 - 6|3.984729e+02|-1.034624e-04 - 7|3.984435e+02|-7.366943e-05 - 8|3.984199e+02|-5.922497e-05 - 9|3.984016e+02|-4.593063e-05 - 10|3.983867e+02|-3.733061e-05 - - - - -| - - -.. code-block:: python - - - import numpy as np - import matplotlib.pylab as pl - import ot - - - - #%% dataset generation - - np.random.seed(0) # makes example reproducible - - n=100 # nb samples in source and target datasets - theta=2*np.pi/20 - nz=0.1 - xs,ys=ot.datasets.get_data_classif('gaussrot',n,nz=nz) - xt,yt=ot.datasets.get_data_classif('gaussrot',n,theta=theta,nz=nz) - - # one of the target mode changes its variance (no linear mapping) - xt[yt==2]*=3 - xt=xt+4 - - - #%% plot samples - - pl.figure(1,(8,5)) - pl.clf() - - pl.scatter(xs[:,0],xs[:,1],c=ys,marker='+',label='Source samples') - pl.scatter(xt[:,0],xt[:,1],c=yt,marker='o',label='Target samples') - - pl.legend(loc=0) - pl.title('Source and target distributions') - - - - #%% OT linear mapping estimation - - eta=1e-8 # quadratic regularization for regression - mu=1e0 # weight of the OT linear term - bias=True # estimate a bias - - ot_mapping=ot.da.OTDA_mapping_linear() - ot_mapping.fit(xs,xt,mu=mu,eta=eta,bias=bias,numItermax = 20,verbose=True) - - xst=ot_mapping.predict(xs) # use the estimated mapping - xst0=ot_mapping.interp() # use barycentric mapping - - - pl.figure(2,(10,7)) - pl.clf() - pl.subplot(2,2,1) - pl.scatter(xt[:,0],xt[:,1],c=yt,marker='o',label='Target samples',alpha=.3) - pl.scatter(xst0[:,0],xst0[:,1],c=ys,marker='+',label='barycentric mapping') - pl.title("barycentric mapping") - - pl.subplot(2,2,2) - pl.scatter(xt[:,0],xt[:,1],c=yt,marker='o',label='Target samples',alpha=.3) - pl.scatter(xst[:,0],xst[:,1],c=ys,marker='+',label='Learned mapping') - pl.title("Learned mapping") - - - - #%% Kernel mapping estimation - - eta=1e-5 # quadratic regularization for regression - mu=1e-1 # weight of the OT linear term - bias=True # estimate a bias - sigma=1 # sigma bandwidth fot gaussian kernel - - - ot_mapping_kernel=ot.da.OTDA_mapping_kernel() - ot_mapping_kernel.fit(xs,xt,mu=mu,eta=eta,sigma=sigma,bias=bias,numItermax = 10,verbose=True) - - xst_kernel=ot_mapping_kernel.predict(xs) # use the estimated mapping - xst0_kernel=ot_mapping_kernel.interp() # use barycentric mapping - - - #%% Plotting the mapped samples - - pl.figure(2,(10,7)) - pl.clf() - pl.subplot(2,2,1) - pl.scatter(xt[:,0],xt[:,1],c=yt,marker='o',label='Target samples',alpha=.2) - pl.scatter(xst0[:,0],xst0[:,1],c=ys,marker='+',label='Mapped source samples') - pl.title("Bary. mapping (linear)") - pl.legend(loc=0) - - pl.subplot(2,2,2) - pl.scatter(xt[:,0],xt[:,1],c=yt,marker='o',label='Target samples',alpha=.2) - pl.scatter(xst[:,0],xst[:,1],c=ys,marker='+',label='Learned mapping') - pl.title("Estim. mapping (linear)") - - pl.subplot(2,2,3) - pl.scatter(xt[:,0],xt[:,1],c=yt,marker='o',label='Target samples',alpha=.2) - pl.scatter(xst0_kernel[:,0],xst0_kernel[:,1],c=ys,marker='+',label='barycentric mapping') - pl.title("Bary. mapping (kernel)") - - pl.subplot(2,2,4) - pl.scatter(xt[:,0],xt[:,1],c=yt,marker='o',label='Target samples',alpha=.2) - pl.scatter(xst_kernel[:,0],xst_kernel[:,1],c=ys,marker='+',label='Learned mapping') - pl.title("Estim. mapping (kernel)") - -**Total running time of the script:** ( 0 minutes 0.882 seconds) - - - -.. container:: sphx-glr-footer - - - .. container:: sphx-glr-download - - :download:`Download Python source code: plot_OTDA_mapping.py <plot_OTDA_mapping.py>` - - - - .. container:: sphx-glr-download - - :download:`Download Jupyter notebook: plot_OTDA_mapping.ipynb <plot_OTDA_mapping.ipynb>` - -.. rst-class:: sphx-glr-signature - - `Generated by Sphinx-Gallery <http://sphinx-gallery.readthedocs.io>`_ diff --git a/docs/source/auto_examples/plot_OTDA_mapping_color_images.ipynb b/docs/source/auto_examples/plot_OTDA_mapping_color_images.ipynb deleted file mode 100644 index 1136cc3..0000000 --- a/docs/source/auto_examples/plot_OTDA_mapping_color_images.ipynb +++ /dev/null @@ -1,54 +0,0 @@ -{ - "nbformat_minor": 0, - "nbformat": 4, - "cells": [ - { - "execution_count": null, - "cell_type": "code", - "source": [ - "%matplotlib inline" - ], - "outputs": [], - "metadata": { - "collapsed": false - } - }, - { - "source": [ - "\n====================================================================================\nOT for domain adaptation with image color adaptation [6] with mapping estimation [8]\n====================================================================================\n\n[6] Ferradans, S., Papadakis, N., Peyre, G., & Aujol, J. F. (2014). Regularized\n discrete optimal transport. SIAM Journal on Imaging Sciences, 7(3), 1853-1882.\n[8] M. Perrot, N. Courty, R. Flamary, A. Habrard, \"Mapping estimation for\n discrete optimal transport\", Neural Information Processing Systems (NIPS), 2016.\n\n\n" - ], - "cell_type": "markdown", - "metadata": {} - }, - { - "execution_count": null, - "cell_type": "code", - "source": [ - "import numpy as np\nimport scipy.ndimage as spi\nimport matplotlib.pylab as pl\nimport ot\n\n\n#%% Loading images\n\nI1=spi.imread('../data/ocean_day.jpg').astype(np.float64)/256\nI2=spi.imread('../data/ocean_sunset.jpg').astype(np.float64)/256\n\n#%% Plot images\n\npl.figure(1)\n\npl.subplot(1,2,1)\npl.imshow(I1)\npl.title('Image 1')\n\npl.subplot(1,2,2)\npl.imshow(I2)\npl.title('Image 2')\n\npl.show()\n\n#%% Image conversion and dataset generation\n\ndef im2mat(I):\n \"\"\"Converts and image to matrix (one pixel per line)\"\"\"\n return I.reshape((I.shape[0]*I.shape[1],I.shape[2]))\n\ndef mat2im(X,shape):\n \"\"\"Converts back a matrix to an image\"\"\"\n return X.reshape(shape)\n\nX1=im2mat(I1)\nX2=im2mat(I2)\n\n# training samples\nnb=1000\nidx1=np.random.randint(X1.shape[0],size=(nb,))\nidx2=np.random.randint(X2.shape[0],size=(nb,))\n\nxs=X1[idx1,:]\nxt=X2[idx2,:]\n\n#%% Plot image distributions\n\n\npl.figure(2,(10,5))\n\npl.subplot(1,2,1)\npl.scatter(xs[:,0],xs[:,2],c=xs)\npl.axis([0,1,0,1])\npl.xlabel('Red')\npl.ylabel('Blue')\npl.title('Image 1')\n\npl.subplot(1,2,2)\n#pl.imshow(I2)\npl.scatter(xt[:,0],xt[:,2],c=xt)\npl.axis([0,1,0,1])\npl.xlabel('Red')\npl.ylabel('Blue')\npl.title('Image 2')\n\npl.show()\n\n\n\n#%% domain adaptation between images\ndef minmax(I):\n return np.minimum(np.maximum(I,0),1)\n# LP problem\nda_emd=ot.da.OTDA() # init class\nda_emd.fit(xs,xt) # fit distributions\n\nX1t=da_emd.predict(X1) # out of sample\nI1t=minmax(mat2im(X1t,I1.shape))\n\n# sinkhorn regularization\nlambd=1e-1\nda_entrop=ot.da.OTDA_sinkhorn()\nda_entrop.fit(xs,xt,reg=lambd)\n\nX1te=da_entrop.predict(X1)\nI1te=minmax(mat2im(X1te,I1.shape))\n\n# linear mapping estimation\neta=1e-8 # quadratic regularization for regression\nmu=1e0 # weight of the OT linear term\nbias=True # estimate a bias\n\not_mapping=ot.da.OTDA_mapping_linear()\not_mapping.fit(xs,xt,mu=mu,eta=eta,bias=bias,numItermax = 20,verbose=True)\n\nX1tl=ot_mapping.predict(X1) # use the estimated mapping\nI1tl=minmax(mat2im(X1tl,I1.shape))\n\n# nonlinear mapping estimation\neta=1e-2 # quadratic regularization for regression\nmu=1e0 # weight of the OT linear term\nbias=False # estimate a bias\nsigma=1 # sigma bandwidth fot gaussian kernel\n\n\not_mapping_kernel=ot.da.OTDA_mapping_kernel()\not_mapping_kernel.fit(xs,xt,mu=mu,eta=eta,sigma=sigma,bias=bias,numItermax = 10,verbose=True)\n\nX1tn=ot_mapping_kernel.predict(X1) # use the estimated mapping\nI1tn=minmax(mat2im(X1tn,I1.shape))\n#%% plot images\n\n\npl.figure(2,(10,8))\n\npl.subplot(2,3,1)\n\npl.imshow(I1)\npl.title('Im. 1')\n\npl.subplot(2,3,2)\n\npl.imshow(I2)\npl.title('Im. 2')\n\n\npl.subplot(2,3,3)\npl.imshow(I1t)\npl.title('Im. 1 Interp LP')\n\npl.subplot(2,3,4)\npl.imshow(I1te)\npl.title('Im. 1 Interp Entrop')\n\n\npl.subplot(2,3,5)\npl.imshow(I1tl)\npl.title('Im. 1 Linear mapping')\n\npl.subplot(2,3,6)\npl.imshow(I1tn)\npl.title('Im. 1 nonlinear mapping')\n\npl.show()" - ], - "outputs": [], - "metadata": { - "collapsed": false - } - } - ], - "metadata": { - "kernelspec": { - "display_name": "Python 2", - "name": "python2", - "language": "python" - }, - "language_info": { - "mimetype": "text/x-python", - "nbconvert_exporter": "python", - "name": "python", - "file_extension": ".py", - "version": "2.7.12", - "pygments_lexer": "ipython2", - "codemirror_mode": { - "version": 2, - "name": "ipython" - } - } - } -}
\ No newline at end of file diff --git a/docs/source/auto_examples/plot_OTDA_mapping_color_images.py b/docs/source/auto_examples/plot_OTDA_mapping_color_images.py deleted file mode 100644 index f07dc6c..0000000 --- a/docs/source/auto_examples/plot_OTDA_mapping_color_images.py +++ /dev/null @@ -1,158 +0,0 @@ -# -*- coding: utf-8 -*- -""" -==================================================================================== -OT for domain adaptation with image color adaptation [6] with mapping estimation [8] -==================================================================================== - -[6] Ferradans, S., Papadakis, N., Peyre, G., & Aujol, J. F. (2014). Regularized - discrete optimal transport. SIAM Journal on Imaging Sciences, 7(3), 1853-1882. -[8] M. Perrot, N. Courty, R. Flamary, A. Habrard, "Mapping estimation for - discrete optimal transport", Neural Information Processing Systems (NIPS), 2016. - -""" - -import numpy as np -import scipy.ndimage as spi -import matplotlib.pylab as pl -import ot - - -#%% Loading images - -I1=spi.imread('../data/ocean_day.jpg').astype(np.float64)/256 -I2=spi.imread('../data/ocean_sunset.jpg').astype(np.float64)/256 - -#%% Plot images - -pl.figure(1) - -pl.subplot(1,2,1) -pl.imshow(I1) -pl.title('Image 1') - -pl.subplot(1,2,2) -pl.imshow(I2) -pl.title('Image 2') - -pl.show() - -#%% Image conversion and dataset generation - -def im2mat(I): - """Converts and image to matrix (one pixel per line)""" - return I.reshape((I.shape[0]*I.shape[1],I.shape[2])) - -def mat2im(X,shape): - """Converts back a matrix to an image""" - return X.reshape(shape) - -X1=im2mat(I1) -X2=im2mat(I2) - -# training samples -nb=1000 -idx1=np.random.randint(X1.shape[0],size=(nb,)) -idx2=np.random.randint(X2.shape[0],size=(nb,)) - -xs=X1[idx1,:] -xt=X2[idx2,:] - -#%% Plot image distributions - - -pl.figure(2,(10,5)) - -pl.subplot(1,2,1) -pl.scatter(xs[:,0],xs[:,2],c=xs) -pl.axis([0,1,0,1]) -pl.xlabel('Red') -pl.ylabel('Blue') -pl.title('Image 1') - -pl.subplot(1,2,2) -#pl.imshow(I2) -pl.scatter(xt[:,0],xt[:,2],c=xt) -pl.axis([0,1,0,1]) -pl.xlabel('Red') -pl.ylabel('Blue') -pl.title('Image 2') - -pl.show() - - - -#%% domain adaptation between images -def minmax(I): - return np.minimum(np.maximum(I,0),1) -# LP problem -da_emd=ot.da.OTDA() # init class -da_emd.fit(xs,xt) # fit distributions - -X1t=da_emd.predict(X1) # out of sample -I1t=minmax(mat2im(X1t,I1.shape)) - -# sinkhorn regularization -lambd=1e-1 -da_entrop=ot.da.OTDA_sinkhorn() -da_entrop.fit(xs,xt,reg=lambd) - -X1te=da_entrop.predict(X1) -I1te=minmax(mat2im(X1te,I1.shape)) - -# linear mapping estimation -eta=1e-8 # quadratic regularization for regression -mu=1e0 # weight of the OT linear term -bias=True # estimate a bias - -ot_mapping=ot.da.OTDA_mapping_linear() -ot_mapping.fit(xs,xt,mu=mu,eta=eta,bias=bias,numItermax = 20,verbose=True) - -X1tl=ot_mapping.predict(X1) # use the estimated mapping -I1tl=minmax(mat2im(X1tl,I1.shape)) - -# nonlinear mapping estimation -eta=1e-2 # quadratic regularization for regression -mu=1e0 # weight of the OT linear term -bias=False # estimate a bias -sigma=1 # sigma bandwidth fot gaussian kernel - - -ot_mapping_kernel=ot.da.OTDA_mapping_kernel() -ot_mapping_kernel.fit(xs,xt,mu=mu,eta=eta,sigma=sigma,bias=bias,numItermax = 10,verbose=True) - -X1tn=ot_mapping_kernel.predict(X1) # use the estimated mapping -I1tn=minmax(mat2im(X1tn,I1.shape)) -#%% plot images - - -pl.figure(2,(10,8)) - -pl.subplot(2,3,1) - -pl.imshow(I1) -pl.title('Im. 1') - -pl.subplot(2,3,2) - -pl.imshow(I2) -pl.title('Im. 2') - - -pl.subplot(2,3,3) -pl.imshow(I1t) -pl.title('Im. 1 Interp LP') - -pl.subplot(2,3,4) -pl.imshow(I1te) -pl.title('Im. 1 Interp Entrop') - - -pl.subplot(2,3,5) -pl.imshow(I1tl) -pl.title('Im. 1 Linear mapping') - -pl.subplot(2,3,6) -pl.imshow(I1tn) -pl.title('Im. 1 nonlinear mapping') - -pl.show() diff --git a/docs/source/auto_examples/plot_OTDA_mapping_color_images.rst b/docs/source/auto_examples/plot_OTDA_mapping_color_images.rst deleted file mode 100644 index 60be3a4..0000000 --- a/docs/source/auto_examples/plot_OTDA_mapping_color_images.rst +++ /dev/null @@ -1,246 +0,0 @@ - - -.. _sphx_glr_auto_examples_plot_OTDA_mapping_color_images.py: - - -==================================================================================== -OT for domain adaptation with image color adaptation [6] with mapping estimation [8] -==================================================================================== - -[6] Ferradans, S., Papadakis, N., Peyre, G., & Aujol, J. F. (2014). Regularized - discrete optimal transport. SIAM Journal on Imaging Sciences, 7(3), 1853-1882. -[8] M. Perrot, N. Courty, R. Flamary, A. Habrard, "Mapping estimation for - discrete optimal transport", Neural Information Processing Systems (NIPS), 2016. - - - - - -.. rst-class:: sphx-glr-horizontal - - - * - - .. image:: /auto_examples/images/sphx_glr_plot_OTDA_mapping_color_images_001.png - :scale: 47 - - * - - .. image:: /auto_examples/images/sphx_glr_plot_OTDA_mapping_color_images_002.png - :scale: 47 - - -.. rst-class:: sphx-glr-script-out - - Out:: - - It. |Loss |Delta loss - -------------------------------- - 0|3.624802e+02|0.000000e+00 - 1|3.547180e+02|-2.141395e-02 - 2|3.545494e+02|-4.753955e-04 - 3|3.544646e+02|-2.391784e-04 - 4|3.544126e+02|-1.466280e-04 - 5|3.543775e+02|-9.921805e-05 - 6|3.543518e+02|-7.245828e-05 - 7|3.543323e+02|-5.491924e-05 - 8|3.543170e+02|-4.342401e-05 - 9|3.543046e+02|-3.472174e-05 - 10|3.542945e+02|-2.878681e-05 - 11|3.542859e+02|-2.417065e-05 - 12|3.542786e+02|-2.058131e-05 - 13|3.542723e+02|-1.768262e-05 - 14|3.542668e+02|-1.551616e-05 - 15|3.542620e+02|-1.371909e-05 - 16|3.542577e+02|-1.213326e-05 - 17|3.542538e+02|-1.085481e-05 - 18|3.542531e+02|-1.996006e-06 - It. |Loss |Delta loss - -------------------------------- - 0|3.555768e+02|0.000000e+00 - 1|3.510071e+02|-1.285164e-02 - 2|3.509110e+02|-2.736701e-04 - 3|3.508748e+02|-1.031476e-04 - 4|3.508506e+02|-6.910585e-05 - 5|3.508330e+02|-5.014608e-05 - 6|3.508195e+02|-3.839166e-05 - 7|3.508090e+02|-3.004218e-05 - 8|3.508005e+02|-2.417627e-05 - 9|3.507935e+02|-2.004621e-05 - 10|3.507876e+02|-1.681731e-05 - - - - -| - - -.. code-block:: python - - - import numpy as np - import scipy.ndimage as spi - import matplotlib.pylab as pl - import ot - - - #%% Loading images - - I1=spi.imread('../data/ocean_day.jpg').astype(np.float64)/256 - I2=spi.imread('../data/ocean_sunset.jpg').astype(np.float64)/256 - - #%% Plot images - - pl.figure(1) - - pl.subplot(1,2,1) - pl.imshow(I1) - pl.title('Image 1') - - pl.subplot(1,2,2) - pl.imshow(I2) - pl.title('Image 2') - - pl.show() - - #%% Image conversion and dataset generation - - def im2mat(I): - """Converts and image to matrix (one pixel per line)""" - return I.reshape((I.shape[0]*I.shape[1],I.shape[2])) - - def mat2im(X,shape): - """Converts back a matrix to an image""" - return X.reshape(shape) - - X1=im2mat(I1) - X2=im2mat(I2) - - # training samples - nb=1000 - idx1=np.random.randint(X1.shape[0],size=(nb,)) - idx2=np.random.randint(X2.shape[0],size=(nb,)) - - xs=X1[idx1,:] - xt=X2[idx2,:] - - #%% Plot image distributions - - - pl.figure(2,(10,5)) - - pl.subplot(1,2,1) - pl.scatter(xs[:,0],xs[:,2],c=xs) - pl.axis([0,1,0,1]) - pl.xlabel('Red') - pl.ylabel('Blue') - pl.title('Image 1') - - pl.subplot(1,2,2) - #pl.imshow(I2) - pl.scatter(xt[:,0],xt[:,2],c=xt) - pl.axis([0,1,0,1]) - pl.xlabel('Red') - pl.ylabel('Blue') - pl.title('Image 2') - - pl.show() - - - - #%% domain adaptation between images - def minmax(I): - return np.minimum(np.maximum(I,0),1) - # LP problem - da_emd=ot.da.OTDA() # init class - da_emd.fit(xs,xt) # fit distributions - - X1t=da_emd.predict(X1) # out of sample - I1t=minmax(mat2im(X1t,I1.shape)) - - # sinkhorn regularization - lambd=1e-1 - da_entrop=ot.da.OTDA_sinkhorn() - da_entrop.fit(xs,xt,reg=lambd) - - X1te=da_entrop.predict(X1) - I1te=minmax(mat2im(X1te,I1.shape)) - - # linear mapping estimation - eta=1e-8 # quadratic regularization for regression - mu=1e0 # weight of the OT linear term - bias=True # estimate a bias - - ot_mapping=ot.da.OTDA_mapping_linear() - ot_mapping.fit(xs,xt,mu=mu,eta=eta,bias=bias,numItermax = 20,verbose=True) - - X1tl=ot_mapping.predict(X1) # use the estimated mapping - I1tl=minmax(mat2im(X1tl,I1.shape)) - - # nonlinear mapping estimation - eta=1e-2 # quadratic regularization for regression - mu=1e0 # weight of the OT linear term - bias=False # estimate a bias - sigma=1 # sigma bandwidth fot gaussian kernel - - - ot_mapping_kernel=ot.da.OTDA_mapping_kernel() - ot_mapping_kernel.fit(xs,xt,mu=mu,eta=eta,sigma=sigma,bias=bias,numItermax = 10,verbose=True) - - X1tn=ot_mapping_kernel.predict(X1) # use the estimated mapping - I1tn=minmax(mat2im(X1tn,I1.shape)) - #%% plot images - - - pl.figure(2,(10,8)) - - pl.subplot(2,3,1) - - pl.imshow(I1) - pl.title('Im. 1') - - pl.subplot(2,3,2) - - pl.imshow(I2) - pl.title('Im. 2') - - - pl.subplot(2,3,3) - pl.imshow(I1t) - pl.title('Im. 1 Interp LP') - - pl.subplot(2,3,4) - pl.imshow(I1te) - pl.title('Im. 1 Interp Entrop') - - - pl.subplot(2,3,5) - pl.imshow(I1tl) - pl.title('Im. 1 Linear mapping') - - pl.subplot(2,3,6) - pl.imshow(I1tn) - pl.title('Im. 1 nonlinear mapping') - - pl.show() - -**Total running time of the script:** ( 1 minutes 59.537 seconds) - - - -.. container:: sphx-glr-footer - - - .. container:: sphx-glr-download - - :download:`Download Python source code: plot_OTDA_mapping_color_images.py <plot_OTDA_mapping_color_images.py>` - - - - .. container:: sphx-glr-download - - :download:`Download Jupyter notebook: plot_OTDA_mapping_color_images.ipynb <plot_OTDA_mapping_color_images.ipynb>` - -.. rst-class:: sphx-glr-signature - - `Generated by Sphinx-Gallery <http://sphinx-gallery.readthedocs.io>`_ diff --git a/docs/source/auto_examples/plot_OT_1D.ipynb b/docs/source/auto_examples/plot_OT_1D.ipynb index 8715b97..26748c2 100644 --- a/docs/source/auto_examples/plot_OT_1D.ipynb +++ b/docs/source/auto_examples/plot_OT_1D.ipynb @@ -15,7 +15,7 @@ }, { "source": [ - "\n# 1D optimal transport\n\n\n@author: rflamary\n\n" + "\n# 1D optimal transport\n\n\nThis example illustrates the computation of EMD and Sinkhorn transport plans\nand their visualization.\n\n\n" ], "cell_type": "markdown", "metadata": {} @@ -24,7 +24,79 @@ "execution_count": null, "cell_type": "code", "source": [ - "import numpy as np\nimport matplotlib.pylab as pl\nimport ot\nfrom ot.datasets import get_1D_gauss as gauss\n\n\n#%% parameters\n\nn=100 # nb bins\n\n# bin positions\nx=np.arange(n,dtype=np.float64)\n\n# Gaussian distributions\na=gauss(n,m=20,s=5) # m= mean, s= std\nb=gauss(n,m=60,s=10)\n\n# loss matrix\nM=ot.dist(x.reshape((n,1)),x.reshape((n,1)))\nM/=M.max()\n\n#%% plot the distributions\n\npl.figure(1)\npl.plot(x,a,'b',label='Source distribution')\npl.plot(x,b,'r',label='Target distribution')\npl.legend()\n\n#%% plot distributions and loss matrix\n\npl.figure(2)\not.plot.plot1D_mat(a,b,M,'Cost matrix M')\n\n#%% EMD\n\nG0=ot.emd(a,b,M)\n\npl.figure(3)\not.plot.plot1D_mat(a,b,G0,'OT matrix G0')\n\n#%% Sinkhorn\n\nlambd=1e-3\nGs=ot.sinkhorn(a,b,M,lambd,verbose=True)\n\npl.figure(4)\not.plot.plot1D_mat(a,b,Gs,'OT matrix Sinkhorn')" + "# Author: Remi Flamary <remi.flamary@unice.fr>\n#\n# License: MIT License\n\nimport numpy as np\nimport matplotlib.pylab as pl\nimport ot\nfrom ot.datasets import get_1D_gauss as gauss" + ], + "outputs": [], + "metadata": { + "collapsed": false + } + }, + { + "source": [ + "Generate data\n-------------\n\n" + ], + "cell_type": "markdown", + "metadata": {} + }, + { + "execution_count": null, + "cell_type": "code", + "source": [ + "#%% parameters\n\nn = 100 # nb bins\n\n# bin positions\nx = np.arange(n, dtype=np.float64)\n\n# Gaussian distributions\na = gauss(n, m=20, s=5) # m= mean, s= std\nb = gauss(n, m=60, s=10)\n\n# loss matrix\nM = ot.dist(x.reshape((n, 1)), x.reshape((n, 1)))\nM /= M.max()" + ], + "outputs": [], + "metadata": { + "collapsed": false + } + }, + { + "source": [ + "Plot distributions and loss matrix\n----------------------------------\n\n" + ], + "cell_type": "markdown", + "metadata": {} + }, + { + "execution_count": null, + "cell_type": "code", + "source": [ + "#%% plot the distributions\n\npl.figure(1, figsize=(6.4, 3))\npl.plot(x, a, 'b', label='Source distribution')\npl.plot(x, b, 'r', label='Target distribution')\npl.legend()\n\n#%% plot distributions and loss matrix\n\npl.figure(2, figsize=(5, 5))\not.plot.plot1D_mat(a, b, M, 'Cost matrix M')" + ], + "outputs": [], + "metadata": { + "collapsed": false + } + }, + { + "source": [ + "Solve EMD\n---------\n\n" + ], + "cell_type": "markdown", + "metadata": {} + }, + { + "execution_count": null, + "cell_type": "code", + "source": [ + "#%% EMD\n\nG0 = ot.emd(a, b, M)\n\npl.figure(3, figsize=(5, 5))\not.plot.plot1D_mat(a, b, G0, 'OT matrix G0')" + ], + "outputs": [], + "metadata": { + "collapsed": false + } + }, + { + "source": [ + "Solve Sinkhorn\n--------------\n\n" + ], + "cell_type": "markdown", + "metadata": {} + }, + { + "execution_count": null, + "cell_type": "code", + "source": [ + "#%% Sinkhorn\n\nlambd = 1e-3\nGs = ot.sinkhorn(a, b, M, lambd, verbose=True)\n\npl.figure(4, figsize=(5, 5))\not.plot.plot1D_mat(a, b, Gs, 'OT matrix Sinkhorn')\n\npl.show()" ], "outputs": [], "metadata": { diff --git a/docs/source/auto_examples/plot_OT_1D.py b/docs/source/auto_examples/plot_OT_1D.py index 6661aa3..719058f 100644 --- a/docs/source/auto_examples/plot_OT_1D.py +++ b/docs/source/auto_examples/plot_OT_1D.py @@ -4,53 +4,80 @@ 1D optimal transport ==================== -@author: rflamary +This example illustrates the computation of EMD and Sinkhorn transport plans +and their visualization. + """ +# Author: Remi Flamary <remi.flamary@unice.fr> +# +# License: MIT License + import numpy as np import matplotlib.pylab as pl import ot from ot.datasets import get_1D_gauss as gauss +############################################################################## +# Generate data +# ------------- + #%% parameters -n=100 # nb bins +n = 100 # nb bins # bin positions -x=np.arange(n,dtype=np.float64) +x = np.arange(n, dtype=np.float64) # Gaussian distributions -a=gauss(n,m=20,s=5) # m= mean, s= std -b=gauss(n,m=60,s=10) +a = gauss(n, m=20, s=5) # m= mean, s= std +b = gauss(n, m=60, s=10) # loss matrix -M=ot.dist(x.reshape((n,1)),x.reshape((n,1))) -M/=M.max() +M = ot.dist(x.reshape((n, 1)), x.reshape((n, 1))) +M /= M.max() + + +############################################################################## +# Plot distributions and loss matrix +# ---------------------------------- #%% plot the distributions -pl.figure(1) -pl.plot(x,a,'b',label='Source distribution') -pl.plot(x,b,'r',label='Target distribution') +pl.figure(1, figsize=(6.4, 3)) +pl.plot(x, a, 'b', label='Source distribution') +pl.plot(x, b, 'r', label='Target distribution') pl.legend() #%% plot distributions and loss matrix -pl.figure(2) -ot.plot.plot1D_mat(a,b,M,'Cost matrix M') +pl.figure(2, figsize=(5, 5)) +ot.plot.plot1D_mat(a, b, M, 'Cost matrix M') + +############################################################################## +# Solve EMD +# --------- + #%% EMD -G0=ot.emd(a,b,M) +G0 = ot.emd(a, b, M) + +pl.figure(3, figsize=(5, 5)) +ot.plot.plot1D_mat(a, b, G0, 'OT matrix G0') + +############################################################################## +# Solve Sinkhorn +# -------------- -pl.figure(3) -ot.plot.plot1D_mat(a,b,G0,'OT matrix G0') #%% Sinkhorn -lambd=1e-3 -Gs=ot.sinkhorn(a,b,M,lambd,verbose=True) +lambd = 1e-3 +Gs = ot.sinkhorn(a, b, M, lambd, verbose=True) + +pl.figure(4, figsize=(5, 5)) +ot.plot.plot1D_mat(a, b, Gs, 'OT matrix Sinkhorn') -pl.figure(4) -ot.plot.plot1D_mat(a,b,Gs,'OT matrix Sinkhorn') +pl.show() diff --git a/docs/source/auto_examples/plot_OT_1D.rst b/docs/source/auto_examples/plot_OT_1D.rst index 44b715b..b91916e 100644 --- a/docs/source/auto_examples/plot_OT_1D.rst +++ b/docs/source/auto_examples/plot_OT_1D.rst @@ -7,7 +7,80 @@ 1D optimal transport ==================== -@author: rflamary +This example illustrates the computation of EMD and Sinkhorn transport plans +and their visualization. + + + + +.. code-block:: python + + + # Author: Remi Flamary <remi.flamary@unice.fr> + # + # License: MIT License + + import numpy as np + import matplotlib.pylab as pl + import ot + from ot.datasets import get_1D_gauss as gauss + + + + + + + +Generate data +------------- + + + +.. code-block:: python + + + + #%% parameters + + n = 100 # nb bins + + # bin positions + x = np.arange(n, dtype=np.float64) + + # Gaussian distributions + a = gauss(n, m=20, s=5) # m= mean, s= std + b = gauss(n, m=60, s=10) + + # loss matrix + M = ot.dist(x.reshape((n, 1)), x.reshape((n, 1))) + M /= M.max() + + + + + + + + +Plot distributions and loss matrix +---------------------------------- + + + +.. code-block:: python + + + #%% plot the distributions + + pl.figure(1, figsize=(6.4, 3)) + pl.plot(x, a, 'b', label='Source distribution') + pl.plot(x, b, 'r', label='Target distribution') + pl.legend() + + #%% plot distributions and loss matrix + + pl.figure(2, figsize=(5, 5)) + ot.plot.plot1D_mat(a, b, M, 'Cost matrix M') @@ -25,94 +98,80 @@ .. image:: /auto_examples/images/sphx_glr_plot_OT_1D_002.png :scale: 47 - * - .. image:: /auto_examples/images/sphx_glr_plot_OT_1D_003.png - :scale: 47 - * - .. image:: /auto_examples/images/sphx_glr_plot_OT_1D_004.png - :scale: 47 +Solve EMD +--------- -.. rst-class:: sphx-glr-script-out - Out:: +.. code-block:: python - It. |Err - ------------------- - 0|8.187970e-02| - 10|3.460174e-02| - 20|6.633335e-03| - 30|9.797798e-04| - 40|1.389606e-04| - 50|1.959016e-05| - 60|2.759079e-06| - 70|3.885166e-07| - 80|5.470605e-08| - 90|7.702918e-09| - 100|1.084609e-09| - 110|1.527180e-10| + #%% EMD + G0 = ot.emd(a, b, M) -| + pl.figure(3, figsize=(5, 5)) + ot.plot.plot1D_mat(a, b, G0, 'OT matrix G0') -.. code-block:: python - import numpy as np - import matplotlib.pylab as pl - import ot - from ot.datasets import get_1D_gauss as gauss +.. image:: /auto_examples/images/sphx_glr_plot_OT_1D_005.png + :align: center - #%% parameters - n=100 # nb bins - # bin positions - x=np.arange(n,dtype=np.float64) +Solve Sinkhorn +-------------- - # Gaussian distributions - a=gauss(n,m=20,s=5) # m= mean, s= std - b=gauss(n,m=60,s=10) - # loss matrix - M=ot.dist(x.reshape((n,1)),x.reshape((n,1))) - M/=M.max() - #%% plot the distributions +.. code-block:: python - pl.figure(1) - pl.plot(x,a,'b',label='Source distribution') - pl.plot(x,b,'r',label='Target distribution') - pl.legend() - #%% plot distributions and loss matrix - pl.figure(2) - ot.plot.plot1D_mat(a,b,M,'Cost matrix M') + #%% Sinkhorn - #%% EMD + lambd = 1e-3 + Gs = ot.sinkhorn(a, b, M, lambd, verbose=True) - G0=ot.emd(a,b,M) + pl.figure(4, figsize=(5, 5)) + ot.plot.plot1D_mat(a, b, Gs, 'OT matrix Sinkhorn') - pl.figure(3) - ot.plot.plot1D_mat(a,b,G0,'OT matrix G0') + pl.show() - #%% Sinkhorn - lambd=1e-3 - Gs=ot.sinkhorn(a,b,M,lambd,verbose=True) - pl.figure(4) - ot.plot.plot1D_mat(a,b,Gs,'OT matrix Sinkhorn') +.. image:: /auto_examples/images/sphx_glr_plot_OT_1D_007.png + :align: center + + +.. rst-class:: sphx-glr-script-out + + Out:: + + It. |Err + ------------------- + 0|8.187970e-02| + 10|3.460174e-02| + 20|6.633335e-03| + 30|9.797798e-04| + 40|1.389606e-04| + 50|1.959016e-05| + 60|2.759079e-06| + 70|3.885166e-07| + 80|5.470605e-08| + 90|7.702918e-09| + 100|1.084609e-09| + 110|1.527180e-10| + -**Total running time of the script:** ( 0 minutes 0.674 seconds) +**Total running time of the script:** ( 0 minutes 0.748 seconds) @@ -131,4 +190,4 @@ .. rst-class:: sphx-glr-signature - `Generated by Sphinx-Gallery <http://sphinx-gallery.readthedocs.io>`_ + `Generated by Sphinx-Gallery <https://sphinx-gallery.readthedocs.io>`_ diff --git a/docs/source/auto_examples/plot_OT_2D_samples.ipynb b/docs/source/auto_examples/plot_OT_2D_samples.ipynb index fad0467..41a37f3 100644 --- a/docs/source/auto_examples/plot_OT_2D_samples.ipynb +++ b/docs/source/auto_examples/plot_OT_2D_samples.ipynb @@ -15,7 +15,7 @@ }, { "source": [ - "\n# 2D Optimal transport between empirical distributions\n\n\n@author: rflamary\n\n" + "\n# 2D Optimal transport between empirical distributions\n\n\nIllustration of 2D optimal transport between discributions that are weighted\nsum of diracs. The OT matrix is plotted with the samples.\n\n\n" ], "cell_type": "markdown", "metadata": {} @@ -24,7 +24,79 @@ "execution_count": null, "cell_type": "code", "source": [ - "import numpy as np\nimport matplotlib.pylab as pl\nimport ot\n\n#%% parameters and data generation\n\nn=50 # nb samples\n\nmu_s=np.array([0,0])\ncov_s=np.array([[1,0],[0,1]])\n\nmu_t=np.array([4,4])\ncov_t=np.array([[1,-.8],[-.8,1]])\n\nxs=ot.datasets.get_2D_samples_gauss(n,mu_s,cov_s)\nxt=ot.datasets.get_2D_samples_gauss(n,mu_t,cov_t)\n\na,b = ot.unif(n),ot.unif(n) # uniform distribution on samples\n\n# loss matrix\nM=ot.dist(xs,xt)\nM/=M.max()\n\n#%% plot samples\n\npl.figure(1)\npl.plot(xs[:,0],xs[:,1],'+b',label='Source samples')\npl.plot(xt[:,0],xt[:,1],'xr',label='Target samples')\npl.legend(loc=0)\npl.title('Source and traget distributions')\n\npl.figure(2)\npl.imshow(M,interpolation='nearest')\npl.title('Cost matrix M')\n\n\n#%% EMD\n\nG0=ot.emd(a,b,M)\n\npl.figure(3)\npl.imshow(G0,interpolation='nearest')\npl.title('OT matrix G0')\n\npl.figure(4)\not.plot.plot2D_samples_mat(xs,xt,G0,c=[.5,.5,1])\npl.plot(xs[:,0],xs[:,1],'+b',label='Source samples')\npl.plot(xt[:,0],xt[:,1],'xr',label='Target samples')\npl.legend(loc=0)\npl.title('OT matrix with samples')\n\n\n#%% sinkhorn\n\n# reg term\nlambd=5e-4\n\nGs=ot.sinkhorn(a,b,M,lambd)\n\npl.figure(5)\npl.imshow(Gs,interpolation='nearest')\npl.title('OT matrix sinkhorn')\n\npl.figure(6)\not.plot.plot2D_samples_mat(xs,xt,Gs,color=[.5,.5,1])\npl.plot(xs[:,0],xs[:,1],'+b',label='Source samples')\npl.plot(xt[:,0],xt[:,1],'xr',label='Target samples')\npl.legend(loc=0)\npl.title('OT matrix Sinkhorn with samples')" + "# Author: Remi Flamary <remi.flamary@unice.fr>\n#\n# License: MIT License\n\nimport numpy as np\nimport matplotlib.pylab as pl\nimport ot" + ], + "outputs": [], + "metadata": { + "collapsed": false + } + }, + { + "source": [ + "Generate data\n-------------\n\n" + ], + "cell_type": "markdown", + "metadata": {} + }, + { + "execution_count": null, + "cell_type": "code", + "source": [ + "#%% parameters and data generation\n\nn = 50 # nb samples\n\nmu_s = np.array([0, 0])\ncov_s = np.array([[1, 0], [0, 1]])\n\nmu_t = np.array([4, 4])\ncov_t = np.array([[1, -.8], [-.8, 1]])\n\nxs = ot.datasets.get_2D_samples_gauss(n, mu_s, cov_s)\nxt = ot.datasets.get_2D_samples_gauss(n, mu_t, cov_t)\n\na, b = np.ones((n,)) / n, np.ones((n,)) / n # uniform distribution on samples\n\n# loss matrix\nM = ot.dist(xs, xt)\nM /= M.max()" + ], + "outputs": [], + "metadata": { + "collapsed": false + } + }, + { + "source": [ + "Plot data\n---------\n\n" + ], + "cell_type": "markdown", + "metadata": {} + }, + { + "execution_count": null, + "cell_type": "code", + "source": [ + "#%% plot samples\n\npl.figure(1)\npl.plot(xs[:, 0], xs[:, 1], '+b', label='Source samples')\npl.plot(xt[:, 0], xt[:, 1], 'xr', label='Target samples')\npl.legend(loc=0)\npl.title('Source and target distributions')\n\npl.figure(2)\npl.imshow(M, interpolation='nearest')\npl.title('Cost matrix M')" + ], + "outputs": [], + "metadata": { + "collapsed": false + } + }, + { + "source": [ + "Compute EMD\n-----------\n\n" + ], + "cell_type": "markdown", + "metadata": {} + }, + { + "execution_count": null, + "cell_type": "code", + "source": [ + "#%% EMD\n\nG0 = ot.emd(a, b, M)\n\npl.figure(3)\npl.imshow(G0, interpolation='nearest')\npl.title('OT matrix G0')\n\npl.figure(4)\not.plot.plot2D_samples_mat(xs, xt, G0, c=[.5, .5, 1])\npl.plot(xs[:, 0], xs[:, 1], '+b', label='Source samples')\npl.plot(xt[:, 0], xt[:, 1], 'xr', label='Target samples')\npl.legend(loc=0)\npl.title('OT matrix with samples')" + ], + "outputs": [], + "metadata": { + "collapsed": false + } + }, + { + "source": [ + "Compute Sinkhorn\n----------------\n\n" + ], + "cell_type": "markdown", + "metadata": {} + }, + { + "execution_count": null, + "cell_type": "code", + "source": [ + "#%% sinkhorn\n\n# reg term\nlambd = 1e-3\n\nGs = ot.sinkhorn(a, b, M, lambd)\n\npl.figure(5)\npl.imshow(Gs, interpolation='nearest')\npl.title('OT matrix sinkhorn')\n\npl.figure(6)\not.plot.plot2D_samples_mat(xs, xt, Gs, color=[.5, .5, 1])\npl.plot(xs[:, 0], xs[:, 1], '+b', label='Source samples')\npl.plot(xt[:, 0], xt[:, 1], 'xr', label='Target samples')\npl.legend(loc=0)\npl.title('OT matrix Sinkhorn with samples')\n\npl.show()" ], "outputs": [], "metadata": { diff --git a/docs/source/auto_examples/plot_OT_2D_samples.py b/docs/source/auto_examples/plot_OT_2D_samples.py index edfb781..9818ec5 100644 --- a/docs/source/auto_examples/plot_OT_2D_samples.py +++ b/docs/source/auto_examples/plot_OT_2D_samples.py @@ -4,75 +4,98 @@ 2D Optimal transport between empirical distributions ==================================================== -@author: rflamary +Illustration of 2D optimal transport between discributions that are weighted +sum of diracs. The OT matrix is plotted with the samples. + """ +# Author: Remi Flamary <remi.flamary@unice.fr> +# +# License: MIT License + import numpy as np import matplotlib.pylab as pl import ot +############################################################################## +# Generate data +# ------------- + #%% parameters and data generation -n=50 # nb samples +n = 50 # nb samples -mu_s=np.array([0,0]) -cov_s=np.array([[1,0],[0,1]]) +mu_s = np.array([0, 0]) +cov_s = np.array([[1, 0], [0, 1]]) -mu_t=np.array([4,4]) -cov_t=np.array([[1,-.8],[-.8,1]]) +mu_t = np.array([4, 4]) +cov_t = np.array([[1, -.8], [-.8, 1]]) -xs=ot.datasets.get_2D_samples_gauss(n,mu_s,cov_s) -xt=ot.datasets.get_2D_samples_gauss(n,mu_t,cov_t) +xs = ot.datasets.get_2D_samples_gauss(n, mu_s, cov_s) +xt = ot.datasets.get_2D_samples_gauss(n, mu_t, cov_t) -a,b = ot.unif(n),ot.unif(n) # uniform distribution on samples +a, b = np.ones((n,)) / n, np.ones((n,)) / n # uniform distribution on samples # loss matrix -M=ot.dist(xs,xt) -M/=M.max() +M = ot.dist(xs, xt) +M /= M.max() + +############################################################################## +# Plot data +# --------- #%% plot samples pl.figure(1) -pl.plot(xs[:,0],xs[:,1],'+b',label='Source samples') -pl.plot(xt[:,0],xt[:,1],'xr',label='Target samples') +pl.plot(xs[:, 0], xs[:, 1], '+b', label='Source samples') +pl.plot(xt[:, 0], xt[:, 1], 'xr', label='Target samples') pl.legend(loc=0) -pl.title('Source and traget distributions') +pl.title('Source and target distributions') pl.figure(2) -pl.imshow(M,interpolation='nearest') +pl.imshow(M, interpolation='nearest') pl.title('Cost matrix M') +############################################################################## +# Compute EMD +# ----------- #%% EMD -G0=ot.emd(a,b,M) +G0 = ot.emd(a, b, M) pl.figure(3) -pl.imshow(G0,interpolation='nearest') +pl.imshow(G0, interpolation='nearest') pl.title('OT matrix G0') pl.figure(4) -ot.plot.plot2D_samples_mat(xs,xt,G0,c=[.5,.5,1]) -pl.plot(xs[:,0],xs[:,1],'+b',label='Source samples') -pl.plot(xt[:,0],xt[:,1],'xr',label='Target samples') +ot.plot.plot2D_samples_mat(xs, xt, G0, c=[.5, .5, 1]) +pl.plot(xs[:, 0], xs[:, 1], '+b', label='Source samples') +pl.plot(xt[:, 0], xt[:, 1], 'xr', label='Target samples') pl.legend(loc=0) pl.title('OT matrix with samples') +############################################################################## +# Compute Sinkhorn +# ---------------- + #%% sinkhorn # reg term -lambd=5e-4 +lambd = 1e-3 -Gs=ot.sinkhorn(a,b,M,lambd) +Gs = ot.sinkhorn(a, b, M, lambd) pl.figure(5) -pl.imshow(Gs,interpolation='nearest') +pl.imshow(Gs, interpolation='nearest') pl.title('OT matrix sinkhorn') pl.figure(6) -ot.plot.plot2D_samples_mat(xs,xt,Gs,color=[.5,.5,1]) -pl.plot(xs[:,0],xs[:,1],'+b',label='Source samples') -pl.plot(xt[:,0],xt[:,1],'xr',label='Target samples') +ot.plot.plot2D_samples_mat(xs, xt, Gs, color=[.5, .5, 1]) +pl.plot(xs[:, 0], xs[:, 1], '+b', label='Source samples') +pl.plot(xt[:, 0], xt[:, 1], 'xr', label='Target samples') pl.legend(loc=0) pl.title('OT matrix Sinkhorn with samples') + +pl.show() diff --git a/docs/source/auto_examples/plot_OT_2D_samples.rst b/docs/source/auto_examples/plot_OT_2D_samples.rst index e05e591..0ad9cf0 100644 --- a/docs/source/auto_examples/plot_OT_2D_samples.rst +++ b/docs/source/auto_examples/plot_OT_2D_samples.rst @@ -7,131 +7,191 @@ 2D Optimal transport between empirical distributions ==================================================== -@author: rflamary +Illustration of 2D optimal transport between discributions that are weighted +sum of diracs. The OT matrix is plotted with the samples. -.. rst-class:: sphx-glr-horizontal +.. code-block:: python - * + # Author: Remi Flamary <remi.flamary@unice.fr> + # + # License: MIT License - .. image:: /auto_examples/images/sphx_glr_plot_OT_2D_samples_001.png - :scale: 47 + import numpy as np + import matplotlib.pylab as pl + import ot - * - .. image:: /auto_examples/images/sphx_glr_plot_OT_2D_samples_002.png - :scale: 47 - * - .. image:: /auto_examples/images/sphx_glr_plot_OT_2D_samples_003.png - :scale: 47 - * - .. image:: /auto_examples/images/sphx_glr_plot_OT_2D_samples_004.png - :scale: 47 - * +Generate data +------------- - .. image:: /auto_examples/images/sphx_glr_plot_OT_2D_samples_005.png - :scale: 47 - * - .. image:: /auto_examples/images/sphx_glr_plot_OT_2D_samples_006.png - :scale: 47 +.. code-block:: python -.. rst-class:: sphx-glr-script-out + #%% parameters and data generation - Out:: + n = 50 # nb samples - ('Warning: numerical errors at iteration', 0) + mu_s = np.array([0, 0]) + cov_s = np.array([[1, 0], [0, 1]]) + mu_t = np.array([4, 4]) + cov_t = np.array([[1, -.8], [-.8, 1]]) + xs = ot.datasets.get_2D_samples_gauss(n, mu_s, cov_s) + xt = ot.datasets.get_2D_samples_gauss(n, mu_t, cov_t) + a, b = np.ones((n,)) / n, np.ones((n,)) / n # uniform distribution on samples -| + # loss matrix + M = ot.dist(xs, xt) + M /= M.max() -.. code-block:: python - import numpy as np - import matplotlib.pylab as pl - import ot - #%% parameters and data generation - n=50 # nb samples - mu_s=np.array([0,0]) - cov_s=np.array([[1,0],[0,1]]) +Plot data +--------- - mu_t=np.array([4,4]) - cov_t=np.array([[1,-.8],[-.8,1]]) - xs=ot.datasets.get_2D_samples_gauss(n,mu_s,cov_s) - xt=ot.datasets.get_2D_samples_gauss(n,mu_t,cov_t) - a,b = ot.unif(n),ot.unif(n) # uniform distribution on samples +.. code-block:: python - # loss matrix - M=ot.dist(xs,xt) - M/=M.max() #%% plot samples pl.figure(1) - pl.plot(xs[:,0],xs[:,1],'+b',label='Source samples') - pl.plot(xt[:,0],xt[:,1],'xr',label='Target samples') + pl.plot(xs[:, 0], xs[:, 1], '+b', label='Source samples') + pl.plot(xt[:, 0], xt[:, 1], 'xr', label='Target samples') pl.legend(loc=0) - pl.title('Source and traget distributions') + pl.title('Source and target distributions') pl.figure(2) - pl.imshow(M,interpolation='nearest') + pl.imshow(M, interpolation='nearest') pl.title('Cost matrix M') + + +.. rst-class:: sphx-glr-horizontal + + + * + + .. image:: /auto_examples/images/sphx_glr_plot_OT_2D_samples_001.png + :scale: 47 + + * + + .. image:: /auto_examples/images/sphx_glr_plot_OT_2D_samples_002.png + :scale: 47 + + + + +Compute EMD +----------- + + + +.. code-block:: python + + #%% EMD - G0=ot.emd(a,b,M) + G0 = ot.emd(a, b, M) pl.figure(3) - pl.imshow(G0,interpolation='nearest') + pl.imshow(G0, interpolation='nearest') pl.title('OT matrix G0') pl.figure(4) - ot.plot.plot2D_samples_mat(xs,xt,G0,c=[.5,.5,1]) - pl.plot(xs[:,0],xs[:,1],'+b',label='Source samples') - pl.plot(xt[:,0],xt[:,1],'xr',label='Target samples') + ot.plot.plot2D_samples_mat(xs, xt, G0, c=[.5, .5, 1]) + pl.plot(xs[:, 0], xs[:, 1], '+b', label='Source samples') + pl.plot(xt[:, 0], xt[:, 1], 'xr', label='Target samples') pl.legend(loc=0) pl.title('OT matrix with samples') + + + +.. rst-class:: sphx-glr-horizontal + + + * + + .. image:: /auto_examples/images/sphx_glr_plot_OT_2D_samples_005.png + :scale: 47 + + * + + .. image:: /auto_examples/images/sphx_glr_plot_OT_2D_samples_006.png + :scale: 47 + + + + +Compute Sinkhorn +---------------- + + + +.. code-block:: python + + #%% sinkhorn # reg term - lambd=5e-4 + lambd = 1e-3 - Gs=ot.sinkhorn(a,b,M,lambd) + Gs = ot.sinkhorn(a, b, M, lambd) pl.figure(5) - pl.imshow(Gs,interpolation='nearest') + pl.imshow(Gs, interpolation='nearest') pl.title('OT matrix sinkhorn') pl.figure(6) - ot.plot.plot2D_samples_mat(xs,xt,Gs,color=[.5,.5,1]) - pl.plot(xs[:,0],xs[:,1],'+b',label='Source samples') - pl.plot(xt[:,0],xt[:,1],'xr',label='Target samples') + ot.plot.plot2D_samples_mat(xs, xt, Gs, color=[.5, .5, 1]) + pl.plot(xs[:, 0], xs[:, 1], '+b', label='Source samples') + pl.plot(xt[:, 0], xt[:, 1], 'xr', label='Target samples') pl.legend(loc=0) pl.title('OT matrix Sinkhorn with samples') -**Total running time of the script:** ( 0 minutes 0.623 seconds) + pl.show() + + + +.. rst-class:: sphx-glr-horizontal + + + * + + .. image:: /auto_examples/images/sphx_glr_plot_OT_2D_samples_009.png + :scale: 47 + + * + + .. image:: /auto_examples/images/sphx_glr_plot_OT_2D_samples_010.png + :scale: 47 + + + + +**Total running time of the script:** ( 0 minutes 1.743 seconds) @@ -150,4 +210,4 @@ .. rst-class:: sphx-glr-signature - `Generated by Sphinx-Gallery <http://sphinx-gallery.readthedocs.io>`_ + `Generated by Sphinx-Gallery <https://sphinx-gallery.readthedocs.io>`_ diff --git a/docs/source/auto_examples/plot_OT_L1_vs_L2.ipynb b/docs/source/auto_examples/plot_OT_L1_vs_L2.ipynb index 46283ac..2b9a364 100644 --- a/docs/source/auto_examples/plot_OT_L1_vs_L2.ipynb +++ b/docs/source/auto_examples/plot_OT_L1_vs_L2.ipynb @@ -15,7 +15,7 @@ }, { "source": [ - "\n# 2D Optimal transport for different metrics\n\n\nStole the figure idea from Fig. 1 and 2 in \nhttps://arxiv.org/pdf/1706.07650.pdf\n\n\n@author: rflamary\n\n" + "\n# 2D Optimal transport for different metrics\n\n\n2D OT on empirical distributio with different gound metric.\n\nStole the figure idea from Fig. 1 and 2 in\nhttps://arxiv.org/pdf/1706.07650.pdf\n\n\n\n" ], "cell_type": "markdown", "metadata": {} @@ -24,7 +24,79 @@ "execution_count": null, "cell_type": "code", "source": [ - "import numpy as np\nimport matplotlib.pylab as pl\nimport ot\n\n#%% parameters and data generation\n\nfor data in range(2):\n\n if data:\n n=20 # nb samples\n xs=np.zeros((n,2))\n xs[:,0]=np.arange(n)+1\n xs[:,1]=(np.arange(n)+1)*-0.001 # to make it strictly convex...\n \n xt=np.zeros((n,2))\n xt[:,1]=np.arange(n)+1\n else:\n \n n=50 # nb samples\n xtot=np.zeros((n+1,2))\n xtot[:,0]=np.cos((np.arange(n+1)+1.0)*0.9/(n+2)*2*np.pi)\n xtot[:,1]=np.sin((np.arange(n+1)+1.0)*0.9/(n+2)*2*np.pi)\n \n xs=xtot[:n,:]\n xt=xtot[1:,:]\n \n \n \n a,b = ot.unif(n),ot.unif(n) # uniform distribution on samples\n \n # loss matrix\n M1=ot.dist(xs,xt,metric='euclidean')\n M1/=M1.max()\n \n # loss matrix\n M2=ot.dist(xs,xt,metric='sqeuclidean')\n M2/=M2.max()\n \n # loss matrix\n Mp=np.sqrt(ot.dist(xs,xt,metric='euclidean'))\n Mp/=Mp.max()\n \n #%% plot samples\n \n pl.figure(1+3*data)\n pl.clf()\n pl.plot(xs[:,0],xs[:,1],'+b',label='Source samples')\n pl.plot(xt[:,0],xt[:,1],'xr',label='Target samples')\n pl.axis('equal')\n pl.title('Source and traget distributions')\n \n pl.figure(2+3*data,(15,5))\n pl.subplot(1,3,1)\n pl.imshow(M1,interpolation='nearest')\n pl.title('Eucidean cost')\n pl.subplot(1,3,2)\n pl.imshow(M2,interpolation='nearest')\n pl.title('Squared Euclidean cost')\n \n pl.subplot(1,3,3)\n pl.imshow(Mp,interpolation='nearest')\n pl.title('Sqrt Euclidean cost')\n #%% EMD\n \n G1=ot.emd(a,b,M1)\n G2=ot.emd(a,b,M2)\n Gp=ot.emd(a,b,Mp)\n \n pl.figure(3+3*data,(15,5))\n \n pl.subplot(1,3,1)\n ot.plot.plot2D_samples_mat(xs,xt,G1,c=[.5,.5,1])\n pl.plot(xs[:,0],xs[:,1],'+b',label='Source samples')\n pl.plot(xt[:,0],xt[:,1],'xr',label='Target samples')\n pl.axis('equal')\n #pl.legend(loc=0)\n pl.title('OT Euclidean')\n \n pl.subplot(1,3,2)\n \n ot.plot.plot2D_samples_mat(xs,xt,G2,c=[.5,.5,1])\n pl.plot(xs[:,0],xs[:,1],'+b',label='Source samples')\n pl.plot(xt[:,0],xt[:,1],'xr',label='Target samples')\n pl.axis('equal')\n #pl.legend(loc=0)\n pl.title('OT squared Euclidean')\n \n pl.subplot(1,3,3)\n \n ot.plot.plot2D_samples_mat(xs,xt,Gp,c=[.5,.5,1])\n pl.plot(xs[:,0],xs[:,1],'+b',label='Source samples')\n pl.plot(xt[:,0],xt[:,1],'xr',label='Target samples')\n pl.axis('equal')\n #pl.legend(loc=0)\n pl.title('OT sqrt Euclidean')" + "# Author: Remi Flamary <remi.flamary@unice.fr>\n#\n# License: MIT License\n\nimport numpy as np\nimport matplotlib.pylab as pl\nimport ot" + ], + "outputs": [], + "metadata": { + "collapsed": false + } + }, + { + "source": [ + "Dataset 1 : uniform sampling\n----------------------------\n\n" + ], + "cell_type": "markdown", + "metadata": {} + }, + { + "execution_count": null, + "cell_type": "code", + "source": [ + "n = 20 # nb samples\nxs = np.zeros((n, 2))\nxs[:, 0] = np.arange(n) + 1\nxs[:, 1] = (np.arange(n) + 1) * -0.001 # to make it strictly convex...\n\nxt = np.zeros((n, 2))\nxt[:, 1] = np.arange(n) + 1\n\na, b = ot.unif(n), ot.unif(n) # uniform distribution on samples\n\n# loss matrix\nM1 = ot.dist(xs, xt, metric='euclidean')\nM1 /= M1.max()\n\n# loss matrix\nM2 = ot.dist(xs, xt, metric='sqeuclidean')\nM2 /= M2.max()\n\n# loss matrix\nMp = np.sqrt(ot.dist(xs, xt, metric='euclidean'))\nMp /= Mp.max()\n\n# Data\npl.figure(1, figsize=(7, 3))\npl.clf()\npl.plot(xs[:, 0], xs[:, 1], '+b', label='Source samples')\npl.plot(xt[:, 0], xt[:, 1], 'xr', label='Target samples')\npl.axis('equal')\npl.title('Source and traget distributions')\n\n\n# Cost matrices\npl.figure(2, figsize=(7, 3))\n\npl.subplot(1, 3, 1)\npl.imshow(M1, interpolation='nearest')\npl.title('Euclidean cost')\n\npl.subplot(1, 3, 2)\npl.imshow(M2, interpolation='nearest')\npl.title('Squared Euclidean cost')\n\npl.subplot(1, 3, 3)\npl.imshow(Mp, interpolation='nearest')\npl.title('Sqrt Euclidean cost')\npl.tight_layout()" + ], + "outputs": [], + "metadata": { + "collapsed": false + } + }, + { + "source": [ + "Dataset 1 : Plot OT Matrices\n----------------------------\n\n" + ], + "cell_type": "markdown", + "metadata": {} + }, + { + "execution_count": null, + "cell_type": "code", + "source": [ + "#%% EMD\nG1 = ot.emd(a, b, M1)\nG2 = ot.emd(a, b, M2)\nGp = ot.emd(a, b, Mp)\n\n# OT matrices\npl.figure(3, figsize=(7, 3))\n\npl.subplot(1, 3, 1)\not.plot.plot2D_samples_mat(xs, xt, G1, c=[.5, .5, 1])\npl.plot(xs[:, 0], xs[:, 1], '+b', label='Source samples')\npl.plot(xt[:, 0], xt[:, 1], 'xr', label='Target samples')\npl.axis('equal')\n# pl.legend(loc=0)\npl.title('OT Euclidean')\n\npl.subplot(1, 3, 2)\not.plot.plot2D_samples_mat(xs, xt, G2, c=[.5, .5, 1])\npl.plot(xs[:, 0], xs[:, 1], '+b', label='Source samples')\npl.plot(xt[:, 0], xt[:, 1], 'xr', label='Target samples')\npl.axis('equal')\n# pl.legend(loc=0)\npl.title('OT squared Euclidean')\n\npl.subplot(1, 3, 3)\not.plot.plot2D_samples_mat(xs, xt, Gp, c=[.5, .5, 1])\npl.plot(xs[:, 0], xs[:, 1], '+b', label='Source samples')\npl.plot(xt[:, 0], xt[:, 1], 'xr', label='Target samples')\npl.axis('equal')\n# pl.legend(loc=0)\npl.title('OT sqrt Euclidean')\npl.tight_layout()\n\npl.show()" + ], + "outputs": [], + "metadata": { + "collapsed": false + } + }, + { + "source": [ + "Dataset 2 : Partial circle\n--------------------------\n\n" + ], + "cell_type": "markdown", + "metadata": {} + }, + { + "execution_count": null, + "cell_type": "code", + "source": [ + "n = 50 # nb samples\nxtot = np.zeros((n + 1, 2))\nxtot[:, 0] = np.cos(\n (np.arange(n + 1) + 1.0) * 0.9 / (n + 2) * 2 * np.pi)\nxtot[:, 1] = np.sin(\n (np.arange(n + 1) + 1.0) * 0.9 / (n + 2) * 2 * np.pi)\n\nxs = xtot[:n, :]\nxt = xtot[1:, :]\n\na, b = ot.unif(n), ot.unif(n) # uniform distribution on samples\n\n# loss matrix\nM1 = ot.dist(xs, xt, metric='euclidean')\nM1 /= M1.max()\n\n# loss matrix\nM2 = ot.dist(xs, xt, metric='sqeuclidean')\nM2 /= M2.max()\n\n# loss matrix\nMp = np.sqrt(ot.dist(xs, xt, metric='euclidean'))\nMp /= Mp.max()\n\n\n# Data\npl.figure(4, figsize=(7, 3))\npl.clf()\npl.plot(xs[:, 0], xs[:, 1], '+b', label='Source samples')\npl.plot(xt[:, 0], xt[:, 1], 'xr', label='Target samples')\npl.axis('equal')\npl.title('Source and traget distributions')\n\n\n# Cost matrices\npl.figure(5, figsize=(7, 3))\n\npl.subplot(1, 3, 1)\npl.imshow(M1, interpolation='nearest')\npl.title('Euclidean cost')\n\npl.subplot(1, 3, 2)\npl.imshow(M2, interpolation='nearest')\npl.title('Squared Euclidean cost')\n\npl.subplot(1, 3, 3)\npl.imshow(Mp, interpolation='nearest')\npl.title('Sqrt Euclidean cost')\npl.tight_layout()" + ], + "outputs": [], + "metadata": { + "collapsed": false + } + }, + { + "source": [ + "Dataset 2 : Plot OT Matrices\n-----------------------------\n\n" + ], + "cell_type": "markdown", + "metadata": {} + }, + { + "execution_count": null, + "cell_type": "code", + "source": [ + "#%% EMD\nG1 = ot.emd(a, b, M1)\nG2 = ot.emd(a, b, M2)\nGp = ot.emd(a, b, Mp)\n\n# OT matrices\npl.figure(6, figsize=(7, 3))\n\npl.subplot(1, 3, 1)\not.plot.plot2D_samples_mat(xs, xt, G1, c=[.5, .5, 1])\npl.plot(xs[:, 0], xs[:, 1], '+b', label='Source samples')\npl.plot(xt[:, 0], xt[:, 1], 'xr', label='Target samples')\npl.axis('equal')\n# pl.legend(loc=0)\npl.title('OT Euclidean')\n\npl.subplot(1, 3, 2)\not.plot.plot2D_samples_mat(xs, xt, G2, c=[.5, .5, 1])\npl.plot(xs[:, 0], xs[:, 1], '+b', label='Source samples')\npl.plot(xt[:, 0], xt[:, 1], 'xr', label='Target samples')\npl.axis('equal')\n# pl.legend(loc=0)\npl.title('OT squared Euclidean')\n\npl.subplot(1, 3, 3)\not.plot.plot2D_samples_mat(xs, xt, Gp, c=[.5, .5, 1])\npl.plot(xs[:, 0], xs[:, 1], '+b', label='Source samples')\npl.plot(xt[:, 0], xt[:, 1], 'xr', label='Target samples')\npl.axis('equal')\n# pl.legend(loc=0)\npl.title('OT sqrt Euclidean')\npl.tight_layout()\n\npl.show()" ], "outputs": [], "metadata": { diff --git a/docs/source/auto_examples/plot_OT_L1_vs_L2.py b/docs/source/auto_examples/plot_OT_L1_vs_L2.py index 9bb92fe..090e809 100644 --- a/docs/source/auto_examples/plot_OT_L1_vs_L2.py +++ b/docs/source/auto_examples/plot_OT_L1_vs_L2.py @@ -4,105 +4,204 @@ 2D Optimal transport for different metrics ========================================== -Stole the figure idea from Fig. 1 and 2 in +2D OT on empirical distributio with different gound metric. + +Stole the figure idea from Fig. 1 and 2 in https://arxiv.org/pdf/1706.07650.pdf -@author: rflamary """ +# Author: Remi Flamary <remi.flamary@unice.fr> +# +# License: MIT License + import numpy as np import matplotlib.pylab as pl import ot -#%% parameters and data generation - -for data in range(2): - - if data: - n=20 # nb samples - xs=np.zeros((n,2)) - xs[:,0]=np.arange(n)+1 - xs[:,1]=(np.arange(n)+1)*-0.001 # to make it strictly convex... - - xt=np.zeros((n,2)) - xt[:,1]=np.arange(n)+1 - else: - - n=50 # nb samples - xtot=np.zeros((n+1,2)) - xtot[:,0]=np.cos((np.arange(n+1)+1.0)*0.9/(n+2)*2*np.pi) - xtot[:,1]=np.sin((np.arange(n+1)+1.0)*0.9/(n+2)*2*np.pi) - - xs=xtot[:n,:] - xt=xtot[1:,:] - - - - a,b = ot.unif(n),ot.unif(n) # uniform distribution on samples - - # loss matrix - M1=ot.dist(xs,xt,metric='euclidean') - M1/=M1.max() - - # loss matrix - M2=ot.dist(xs,xt,metric='sqeuclidean') - M2/=M2.max() - - # loss matrix - Mp=np.sqrt(ot.dist(xs,xt,metric='euclidean')) - Mp/=Mp.max() - - #%% plot samples - - pl.figure(1+3*data) - pl.clf() - pl.plot(xs[:,0],xs[:,1],'+b',label='Source samples') - pl.plot(xt[:,0],xt[:,1],'xr',label='Target samples') - pl.axis('equal') - pl.title('Source and traget distributions') - - pl.figure(2+3*data,(15,5)) - pl.subplot(1,3,1) - pl.imshow(M1,interpolation='nearest') - pl.title('Eucidean cost') - pl.subplot(1,3,2) - pl.imshow(M2,interpolation='nearest') - pl.title('Squared Euclidean cost') - - pl.subplot(1,3,3) - pl.imshow(Mp,interpolation='nearest') - pl.title('Sqrt Euclidean cost') - #%% EMD - - G1=ot.emd(a,b,M1) - G2=ot.emd(a,b,M2) - Gp=ot.emd(a,b,Mp) - - pl.figure(3+3*data,(15,5)) - - pl.subplot(1,3,1) - ot.plot.plot2D_samples_mat(xs,xt,G1,c=[.5,.5,1]) - pl.plot(xs[:,0],xs[:,1],'+b',label='Source samples') - pl.plot(xt[:,0],xt[:,1],'xr',label='Target samples') - pl.axis('equal') - #pl.legend(loc=0) - pl.title('OT Euclidean') - - pl.subplot(1,3,2) - - ot.plot.plot2D_samples_mat(xs,xt,G2,c=[.5,.5,1]) - pl.plot(xs[:,0],xs[:,1],'+b',label='Source samples') - pl.plot(xt[:,0],xt[:,1],'xr',label='Target samples') - pl.axis('equal') - #pl.legend(loc=0) - pl.title('OT squared Euclidean') - - pl.subplot(1,3,3) - - ot.plot.plot2D_samples_mat(xs,xt,Gp,c=[.5,.5,1]) - pl.plot(xs[:,0],xs[:,1],'+b',label='Source samples') - pl.plot(xt[:,0],xt[:,1],'xr',label='Target samples') - pl.axis('equal') - #pl.legend(loc=0) - pl.title('OT sqrt Euclidean') +############################################################################## +# Dataset 1 : uniform sampling +# ---------------------------- + +n = 20 # nb samples +xs = np.zeros((n, 2)) +xs[:, 0] = np.arange(n) + 1 +xs[:, 1] = (np.arange(n) + 1) * -0.001 # to make it strictly convex... + +xt = np.zeros((n, 2)) +xt[:, 1] = np.arange(n) + 1 + +a, b = ot.unif(n), ot.unif(n) # uniform distribution on samples + +# loss matrix +M1 = ot.dist(xs, xt, metric='euclidean') +M1 /= M1.max() + +# loss matrix +M2 = ot.dist(xs, xt, metric='sqeuclidean') +M2 /= M2.max() + +# loss matrix +Mp = np.sqrt(ot.dist(xs, xt, metric='euclidean')) +Mp /= Mp.max() + +# Data +pl.figure(1, figsize=(7, 3)) +pl.clf() +pl.plot(xs[:, 0], xs[:, 1], '+b', label='Source samples') +pl.plot(xt[:, 0], xt[:, 1], 'xr', label='Target samples') +pl.axis('equal') +pl.title('Source and traget distributions') + + +# Cost matrices +pl.figure(2, figsize=(7, 3)) + +pl.subplot(1, 3, 1) +pl.imshow(M1, interpolation='nearest') +pl.title('Euclidean cost') + +pl.subplot(1, 3, 2) +pl.imshow(M2, interpolation='nearest') +pl.title('Squared Euclidean cost') + +pl.subplot(1, 3, 3) +pl.imshow(Mp, interpolation='nearest') +pl.title('Sqrt Euclidean cost') +pl.tight_layout() + +############################################################################## +# Dataset 1 : Plot OT Matrices +# ---------------------------- + + +#%% EMD +G1 = ot.emd(a, b, M1) +G2 = ot.emd(a, b, M2) +Gp = ot.emd(a, b, Mp) + +# OT matrices +pl.figure(3, figsize=(7, 3)) + +pl.subplot(1, 3, 1) +ot.plot.plot2D_samples_mat(xs, xt, G1, c=[.5, .5, 1]) +pl.plot(xs[:, 0], xs[:, 1], '+b', label='Source samples') +pl.plot(xt[:, 0], xt[:, 1], 'xr', label='Target samples') +pl.axis('equal') +# pl.legend(loc=0) +pl.title('OT Euclidean') + +pl.subplot(1, 3, 2) +ot.plot.plot2D_samples_mat(xs, xt, G2, c=[.5, .5, 1]) +pl.plot(xs[:, 0], xs[:, 1], '+b', label='Source samples') +pl.plot(xt[:, 0], xt[:, 1], 'xr', label='Target samples') +pl.axis('equal') +# pl.legend(loc=0) +pl.title('OT squared Euclidean') + +pl.subplot(1, 3, 3) +ot.plot.plot2D_samples_mat(xs, xt, Gp, c=[.5, .5, 1]) +pl.plot(xs[:, 0], xs[:, 1], '+b', label='Source samples') +pl.plot(xt[:, 0], xt[:, 1], 'xr', label='Target samples') +pl.axis('equal') +# pl.legend(loc=0) +pl.title('OT sqrt Euclidean') +pl.tight_layout() + +pl.show() + + +############################################################################## +# Dataset 2 : Partial circle +# -------------------------- + +n = 50 # nb samples +xtot = np.zeros((n + 1, 2)) +xtot[:, 0] = np.cos( + (np.arange(n + 1) + 1.0) * 0.9 / (n + 2) * 2 * np.pi) +xtot[:, 1] = np.sin( + (np.arange(n + 1) + 1.0) * 0.9 / (n + 2) * 2 * np.pi) + +xs = xtot[:n, :] +xt = xtot[1:, :] + +a, b = ot.unif(n), ot.unif(n) # uniform distribution on samples + +# loss matrix +M1 = ot.dist(xs, xt, metric='euclidean') +M1 /= M1.max() + +# loss matrix +M2 = ot.dist(xs, xt, metric='sqeuclidean') +M2 /= M2.max() + +# loss matrix +Mp = np.sqrt(ot.dist(xs, xt, metric='euclidean')) +Mp /= Mp.max() + + +# Data +pl.figure(4, figsize=(7, 3)) +pl.clf() +pl.plot(xs[:, 0], xs[:, 1], '+b', label='Source samples') +pl.plot(xt[:, 0], xt[:, 1], 'xr', label='Target samples') +pl.axis('equal') +pl.title('Source and traget distributions') + + +# Cost matrices +pl.figure(5, figsize=(7, 3)) + +pl.subplot(1, 3, 1) +pl.imshow(M1, interpolation='nearest') +pl.title('Euclidean cost') + +pl.subplot(1, 3, 2) +pl.imshow(M2, interpolation='nearest') +pl.title('Squared Euclidean cost') + +pl.subplot(1, 3, 3) +pl.imshow(Mp, interpolation='nearest') +pl.title('Sqrt Euclidean cost') +pl.tight_layout() + +############################################################################## +# Dataset 2 : Plot OT Matrices +# ----------------------------- + + +#%% EMD +G1 = ot.emd(a, b, M1) +G2 = ot.emd(a, b, M2) +Gp = ot.emd(a, b, Mp) + +# OT matrices +pl.figure(6, figsize=(7, 3)) + +pl.subplot(1, 3, 1) +ot.plot.plot2D_samples_mat(xs, xt, G1, c=[.5, .5, 1]) +pl.plot(xs[:, 0], xs[:, 1], '+b', label='Source samples') +pl.plot(xt[:, 0], xt[:, 1], 'xr', label='Target samples') +pl.axis('equal') +# pl.legend(loc=0) +pl.title('OT Euclidean') + +pl.subplot(1, 3, 2) +ot.plot.plot2D_samples_mat(xs, xt, G2, c=[.5, .5, 1]) +pl.plot(xs[:, 0], xs[:, 1], '+b', label='Source samples') +pl.plot(xt[:, 0], xt[:, 1], 'xr', label='Target samples') +pl.axis('equal') +# pl.legend(loc=0) +pl.title('OT squared Euclidean') + +pl.subplot(1, 3, 3) +ot.plot.plot2D_samples_mat(xs, xt, Gp, c=[.5, .5, 1]) +pl.plot(xs[:, 0], xs[:, 1], '+b', label='Source samples') +pl.plot(xt[:, 0], xt[:, 1], 'xr', label='Target samples') +pl.axis('equal') +# pl.legend(loc=0) +pl.title('OT sqrt Euclidean') +pl.tight_layout() + +pl.show() diff --git a/docs/source/auto_examples/plot_OT_L1_vs_L2.rst b/docs/source/auto_examples/plot_OT_L1_vs_L2.rst index 4e94bef..f97b373 100644 --- a/docs/source/auto_examples/plot_OT_L1_vs_L2.rst +++ b/docs/source/auto_examples/plot_OT_L1_vs_L2.rst @@ -7,11 +7,86 @@ 2D Optimal transport for different metrics ========================================== -Stole the figure idea from Fig. 1 and 2 in +2D OT on empirical distributio with different gound metric. + +Stole the figure idea from Fig. 1 and 2 in https://arxiv.org/pdf/1706.07650.pdf -@author: rflamary + + + +.. code-block:: python + + + # Author: Remi Flamary <remi.flamary@unice.fr> + # + # License: MIT License + + import numpy as np + import matplotlib.pylab as pl + import ot + + + + + + + +Dataset 1 : uniform sampling +---------------------------- + + + +.. code-block:: python + + + n = 20 # nb samples + xs = np.zeros((n, 2)) + xs[:, 0] = np.arange(n) + 1 + xs[:, 1] = (np.arange(n) + 1) * -0.001 # to make it strictly convex... + + xt = np.zeros((n, 2)) + xt[:, 1] = np.arange(n) + 1 + + a, b = ot.unif(n), ot.unif(n) # uniform distribution on samples + + # loss matrix + M1 = ot.dist(xs, xt, metric='euclidean') + M1 /= M1.max() + + # loss matrix + M2 = ot.dist(xs, xt, metric='sqeuclidean') + M2 /= M2.max() + + # loss matrix + Mp = np.sqrt(ot.dist(xs, xt, metric='euclidean')) + Mp /= Mp.max() + + # Data + pl.figure(1, figsize=(7, 3)) + pl.clf() + pl.plot(xs[:, 0], xs[:, 1], '+b', label='Source samples') + pl.plot(xt[:, 0], xt[:, 1], 'xr', label='Target samples') + pl.axis('equal') + pl.title('Source and traget distributions') + + + # Cost matrices + pl.figure(2, figsize=(7, 3)) + + pl.subplot(1, 3, 1) + pl.imshow(M1, interpolation='nearest') + pl.title('Euclidean cost') + + pl.subplot(1, 3, 2) + pl.imshow(M2, interpolation='nearest') + pl.title('Squared Euclidean cost') + + pl.subplot(1, 3, 3) + pl.imshow(Mp, interpolation='nearest') + pl.title('Sqrt Euclidean cost') + pl.tight_layout() @@ -29,130 +104,193 @@ https://arxiv.org/pdf/1706.07650.pdf .. image:: /auto_examples/images/sphx_glr_plot_OT_L1_vs_L2_002.png :scale: 47 - * - .. image:: /auto_examples/images/sphx_glr_plot_OT_L1_vs_L2_003.png - :scale: 47 - * - .. image:: /auto_examples/images/sphx_glr_plot_OT_L1_vs_L2_004.png - :scale: 47 +Dataset 1 : Plot OT Matrices +---------------------------- + + + +.. code-block:: python + + + + #%% EMD + G1 = ot.emd(a, b, M1) + G2 = ot.emd(a, b, M2) + Gp = ot.emd(a, b, Mp) + + # OT matrices + pl.figure(3, figsize=(7, 3)) + + pl.subplot(1, 3, 1) + ot.plot.plot2D_samples_mat(xs, xt, G1, c=[.5, .5, 1]) + pl.plot(xs[:, 0], xs[:, 1], '+b', label='Source samples') + pl.plot(xt[:, 0], xt[:, 1], 'xr', label='Target samples') + pl.axis('equal') + # pl.legend(loc=0) + pl.title('OT Euclidean') + + pl.subplot(1, 3, 2) + ot.plot.plot2D_samples_mat(xs, xt, G2, c=[.5, .5, 1]) + pl.plot(xs[:, 0], xs[:, 1], '+b', label='Source samples') + pl.plot(xt[:, 0], xt[:, 1], 'xr', label='Target samples') + pl.axis('equal') + # pl.legend(loc=0) + pl.title('OT squared Euclidean') + + pl.subplot(1, 3, 3) + ot.plot.plot2D_samples_mat(xs, xt, Gp, c=[.5, .5, 1]) + pl.plot(xs[:, 0], xs[:, 1], '+b', label='Source samples') + pl.plot(xt[:, 0], xt[:, 1], 'xr', label='Target samples') + pl.axis('equal') + # pl.legend(loc=0) + pl.title('OT sqrt Euclidean') + pl.tight_layout() + + pl.show() + + + + + +.. image:: /auto_examples/images/sphx_glr_plot_OT_L1_vs_L2_005.png + :align: center + + + + +Dataset 2 : Partial circle +-------------------------- + + + +.. code-block:: python + + + n = 50 # nb samples + xtot = np.zeros((n + 1, 2)) + xtot[:, 0] = np.cos( + (np.arange(n + 1) + 1.0) * 0.9 / (n + 2) * 2 * np.pi) + xtot[:, 1] = np.sin( + (np.arange(n + 1) + 1.0) * 0.9 / (n + 2) * 2 * np.pi) + + xs = xtot[:n, :] + xt = xtot[1:, :] + + a, b = ot.unif(n), ot.unif(n) # uniform distribution on samples + + # loss matrix + M1 = ot.dist(xs, xt, metric='euclidean') + M1 /= M1.max() + + # loss matrix + M2 = ot.dist(xs, xt, metric='sqeuclidean') + M2 /= M2.max() + + # loss matrix + Mp = np.sqrt(ot.dist(xs, xt, metric='euclidean')) + Mp /= Mp.max() + + + # Data + pl.figure(4, figsize=(7, 3)) + pl.clf() + pl.plot(xs[:, 0], xs[:, 1], '+b', label='Source samples') + pl.plot(xt[:, 0], xt[:, 1], 'xr', label='Target samples') + pl.axis('equal') + pl.title('Source and traget distributions') + + + # Cost matrices + pl.figure(5, figsize=(7, 3)) + + pl.subplot(1, 3, 1) + pl.imshow(M1, interpolation='nearest') + pl.title('Euclidean cost') + + pl.subplot(1, 3, 2) + pl.imshow(M2, interpolation='nearest') + pl.title('Squared Euclidean cost') + + pl.subplot(1, 3, 3) + pl.imshow(Mp, interpolation='nearest') + pl.title('Sqrt Euclidean cost') + pl.tight_layout() + + + + +.. rst-class:: sphx-glr-horizontal + * - .. image:: /auto_examples/images/sphx_glr_plot_OT_L1_vs_L2_005.png + .. image:: /auto_examples/images/sphx_glr_plot_OT_L1_vs_L2_007.png :scale: 47 * - .. image:: /auto_examples/images/sphx_glr_plot_OT_L1_vs_L2_006.png + .. image:: /auto_examples/images/sphx_glr_plot_OT_L1_vs_L2_008.png :scale: 47 +Dataset 2 : Plot OT Matrices +----------------------------- + + .. code-block:: python - import numpy as np - import matplotlib.pylab as pl - import ot - #%% parameters and data generation - - for data in range(2): - - if data: - n=20 # nb samples - xs=np.zeros((n,2)) - xs[:,0]=np.arange(n)+1 - xs[:,1]=(np.arange(n)+1)*-0.001 # to make it strictly convex... - - xt=np.zeros((n,2)) - xt[:,1]=np.arange(n)+1 - else: - - n=50 # nb samples - xtot=np.zeros((n+1,2)) - xtot[:,0]=np.cos((np.arange(n+1)+1.0)*0.9/(n+2)*2*np.pi) - xtot[:,1]=np.sin((np.arange(n+1)+1.0)*0.9/(n+2)*2*np.pi) - - xs=xtot[:n,:] - xt=xtot[1:,:] - - - - a,b = ot.unif(n),ot.unif(n) # uniform distribution on samples - - # loss matrix - M1=ot.dist(xs,xt,metric='euclidean') - M1/=M1.max() - - # loss matrix - M2=ot.dist(xs,xt,metric='sqeuclidean') - M2/=M2.max() - - # loss matrix - Mp=np.sqrt(ot.dist(xs,xt,metric='euclidean')) - Mp/=Mp.max() - - #%% plot samples - - pl.figure(1+3*data) - pl.clf() - pl.plot(xs[:,0],xs[:,1],'+b',label='Source samples') - pl.plot(xt[:,0],xt[:,1],'xr',label='Target samples') - pl.axis('equal') - pl.title('Source and traget distributions') - - pl.figure(2+3*data,(15,5)) - pl.subplot(1,3,1) - pl.imshow(M1,interpolation='nearest') - pl.title('Eucidean cost') - pl.subplot(1,3,2) - pl.imshow(M2,interpolation='nearest') - pl.title('Squared Euclidean cost') - - pl.subplot(1,3,3) - pl.imshow(Mp,interpolation='nearest') - pl.title('Sqrt Euclidean cost') - #%% EMD - - G1=ot.emd(a,b,M1) - G2=ot.emd(a,b,M2) - Gp=ot.emd(a,b,Mp) - - pl.figure(3+3*data,(15,5)) - - pl.subplot(1,3,1) - ot.plot.plot2D_samples_mat(xs,xt,G1,c=[.5,.5,1]) - pl.plot(xs[:,0],xs[:,1],'+b',label='Source samples') - pl.plot(xt[:,0],xt[:,1],'xr',label='Target samples') - pl.axis('equal') - #pl.legend(loc=0) - pl.title('OT Euclidean') - - pl.subplot(1,3,2) - - ot.plot.plot2D_samples_mat(xs,xt,G2,c=[.5,.5,1]) - pl.plot(xs[:,0],xs[:,1],'+b',label='Source samples') - pl.plot(xt[:,0],xt[:,1],'xr',label='Target samples') - pl.axis('equal') - #pl.legend(loc=0) - pl.title('OT squared Euclidean') - - pl.subplot(1,3,3) - - ot.plot.plot2D_samples_mat(xs,xt,Gp,c=[.5,.5,1]) - pl.plot(xs[:,0],xs[:,1],'+b',label='Source samples') - pl.plot(xt[:,0],xt[:,1],'xr',label='Target samples') - pl.axis('equal') - #pl.legend(loc=0) - pl.title('OT sqrt Euclidean') - -**Total running time of the script:** ( 0 minutes 1.417 seconds) + #%% EMD + G1 = ot.emd(a, b, M1) + G2 = ot.emd(a, b, M2) + Gp = ot.emd(a, b, Mp) + + # OT matrices + pl.figure(6, figsize=(7, 3)) + + pl.subplot(1, 3, 1) + ot.plot.plot2D_samples_mat(xs, xt, G1, c=[.5, .5, 1]) + pl.plot(xs[:, 0], xs[:, 1], '+b', label='Source samples') + pl.plot(xt[:, 0], xt[:, 1], 'xr', label='Target samples') + pl.axis('equal') + # pl.legend(loc=0) + pl.title('OT Euclidean') + + pl.subplot(1, 3, 2) + ot.plot.plot2D_samples_mat(xs, xt, G2, c=[.5, .5, 1]) + pl.plot(xs[:, 0], xs[:, 1], '+b', label='Source samples') + pl.plot(xt[:, 0], xt[:, 1], 'xr', label='Target samples') + pl.axis('equal') + # pl.legend(loc=0) + pl.title('OT squared Euclidean') + + pl.subplot(1, 3, 3) + ot.plot.plot2D_samples_mat(xs, xt, Gp, c=[.5, .5, 1]) + pl.plot(xs[:, 0], xs[:, 1], '+b', label='Source samples') + pl.plot(xt[:, 0], xt[:, 1], 'xr', label='Target samples') + pl.axis('equal') + # pl.legend(loc=0) + pl.title('OT sqrt Euclidean') + pl.tight_layout() + + pl.show() + + + +.. image:: /auto_examples/images/sphx_glr_plot_OT_L1_vs_L2_011.png + :align: center + + + + +**Total running time of the script:** ( 0 minutes 1.134 seconds) @@ -171,4 +309,4 @@ https://arxiv.org/pdf/1706.07650.pdf .. rst-class:: sphx-glr-signature - `Generated by Sphinx-Gallery <http://sphinx-gallery.readthedocs.io>`_ + `Generated by Sphinx-Gallery <https://sphinx-gallery.readthedocs.io>`_ diff --git a/docs/source/auto_examples/plot_OT_conv.ipynb b/docs/source/auto_examples/plot_OT_conv.ipynb deleted file mode 100644 index 7fc4af0..0000000 --- a/docs/source/auto_examples/plot_OT_conv.ipynb +++ /dev/null @@ -1,54 +0,0 @@ -{ - "nbformat_minor": 0, - "nbformat": 4, - "cells": [ - { - "execution_count": null, - "cell_type": "code", - "source": [ - "%matplotlib inline" - ], - "outputs": [], - "metadata": { - "collapsed": false - } - }, - { - "source": [ - "\n# 1D Wasserstein barycenter demo\n\n\n\n@author: rflamary\n\n" - ], - "cell_type": "markdown", - "metadata": {} - }, - { - "execution_count": null, - "cell_type": "code", - "source": [ - "import numpy as np\nimport matplotlib.pylab as pl\nimport ot\nfrom mpl_toolkits.mplot3d import Axes3D #necessary for 3d plot even if not used\nimport scipy as sp\nimport scipy.signal as sps\n#%% parameters\n\nn=10 # nb bins\n\n# bin positions\nx=np.arange(n,dtype=np.float64)\n\nxx,yy=np.meshgrid(x,x)\n\n\nxpos=np.hstack((xx.reshape(-1,1),yy.reshape(-1,1)))\n\nM=ot.dist(xpos)\n\n\nI0=((xx-5)**2+(yy-5)**2<3**2)*1.0\nI1=((xx-7)**2+(yy-7)**2<3**2)*1.0\n\nI0/=I0.sum()\nI1/=I1.sum()\n\ni0=I0.ravel()\ni1=I1.ravel()\n\nM=M[i0>0,:][:,i1>0].copy()\ni0=i0[i0>0]\ni1=i1[i1>0]\nItot=np.concatenate((I0[:,:,np.newaxis],I1[:,:,np.newaxis]),2)\n\n\n#%% plot the distributions\n\npl.figure(1)\npl.subplot(2,2,1)\npl.imshow(I0)\npl.subplot(2,2,2)\npl.imshow(I1)\n\n\n#%% barycenter computation\n\nalpha=0.5 # 0<=alpha<=1\nweights=np.array([1-alpha,alpha])\n\n\ndef conv2(I,k):\n return sp.ndimage.convolve1d(sp.ndimage.convolve1d(I,k,axis=1),k,axis=0)\n\ndef conv2n(I,k):\n res=np.zeros_like(I)\n for i in range(I.shape[2]):\n res[:,:,i]=conv2(I[:,:,i],k)\n return res\n\n\ndef get_1Dkernel(reg,thr=1e-16,wmax=1024):\n w=max(min(wmax,2*int((-np.log(thr)*reg)**(.5))),3)\n x=np.arange(w,dtype=np.float64)\n return np.exp(-((x-w/2)**2)/reg)\n \nthr=1e-16\nreg=1e0\n\nk=get_1Dkernel(reg)\npl.figure(2)\npl.plot(k)\n\nI05=conv2(I0,k)\n\npl.figure(1)\npl.subplot(2,2,1)\npl.imshow(I0)\npl.subplot(2,2,2)\npl.imshow(I05)\n\n#%%\n\nG=ot.emd(i0,i1,M)\nr0=np.sum(M*G)\n\nreg=1e-1\nGs=ot.bregman.sinkhorn_knopp(i0,i1,M,reg=reg)\nrs=np.sum(M*Gs)\n\n#%%\n\ndef mylog(u):\n tmp=np.log(u)\n tmp[np.isnan(tmp)]=0\n return tmp\n\ndef sinkhorn_conv(a,b, reg, numItermax = 1000, stopThr=1e-9, verbose=False, log=False,**kwargs):\n\n\n a=np.asarray(a,dtype=np.float64)\n b=np.asarray(b,dtype=np.float64)\n \n \n if len(b.shape)>2:\n nbb=b.shape[2]\n a=a[:,:,np.newaxis]\n else:\n nbb=0\n \n\n if log:\n log={'err':[]}\n\n # we assume that no distances are null except those of the diagonal of distances\n if nbb:\n u = np.ones((a.shape[0],a.shape[1],nbb))/(np.prod(a.shape[:2]))\n v = np.ones((a.shape[0],a.shape[1],nbb))/(np.prod(b.shape[:2]))\n a0=1.0/(np.prod(b.shape[:2]))\n else:\n u = np.ones((a.shape[0],a.shape[1]))/(np.prod(a.shape[:2]))\n v = np.ones((a.shape[0],a.shape[1]))/(np.prod(b.shape[:2]))\n a0=1.0/(np.prod(b.shape[:2]))\n \n \n k=get_1Dkernel(reg)\n \n if nbb:\n K=lambda I: conv2n(I,k)\n else:\n K=lambda I: conv2(I,k)\n\n cpt = 0\n err=1\n while (err>stopThr and cpt<numItermax):\n uprev = u\n vprev = v\n \n v = np.divide(b, K(u))\n u = np.divide(a, K(v))\n\n if (np.any(np.isnan(u)) or np.any(np.isnan(v)) \n or np.any(np.isinf(u)) or np.any(np.isinf(v))):\n # we have reached the machine precision\n # come back to previous solution and quit loop\n print('Warning: numerical errors at iteration', cpt)\n u = uprev\n v = vprev\n break\n if cpt%10==0:\n # we can speed up the process by checking for the error only all the 10th iterations\n\n err = np.sum((u-uprev)**2)/np.sum((u)**2)+np.sum((v-vprev)**2)/np.sum((v)**2)\n\n if log:\n log['err'].append(err)\n\n if verbose:\n if cpt%200 ==0:\n print('{:5s}|{:12s}'.format('It.','Err')+'\\n'+'-'*19)\n print('{:5d}|{:8e}|'.format(cpt,err))\n cpt = cpt +1\n if log:\n log['u']=u\n log['v']=v\n \n if nbb: #return only loss \n res=np.zeros((nbb))\n for i in range(nbb):\n res[i]=np.sum(u[:,i].reshape((-1,1))*K*v[:,i].reshape((1,-1))*M)\n if log:\n return res,log\n else:\n return res \n \n else: # return OT matrix\n res=reg*a0*np.sum(a*mylog(u+(u==0))+b*mylog(v+(v==0)))\n if log:\n \n return res,log\n else:\n return res\n\nreg=1e0\nr,log=sinkhorn_conv(I0,I1,reg,verbose=True,log=True)\na=I0\nb=I1\nu=log['u']\nv=log['v']\n#%% barycenter interpolation" - ], - "outputs": [], - "metadata": { - "collapsed": false - } - } - ], - "metadata": { - "kernelspec": { - "display_name": "Python 2", - "name": "python2", - "language": "python" - }, - "language_info": { - "mimetype": "text/x-python", - "nbconvert_exporter": "python", - "name": "python", - "file_extension": ".py", - "version": "2.7.12", - "pygments_lexer": "ipython2", - "codemirror_mode": { - "version": 2, - "name": "ipython" - } - } - } -}
\ No newline at end of file diff --git a/docs/source/auto_examples/plot_OT_conv.py b/docs/source/auto_examples/plot_OT_conv.py deleted file mode 100644 index a86e7a2..0000000 --- a/docs/source/auto_examples/plot_OT_conv.py +++ /dev/null @@ -1,200 +0,0 @@ -# -*- coding: utf-8 -*- -""" -============================== -1D Wasserstein barycenter demo -============================== - - -@author: rflamary -""" - -import numpy as np -import matplotlib.pylab as pl -import ot -from mpl_toolkits.mplot3d import Axes3D #necessary for 3d plot even if not used -import scipy as sp -import scipy.signal as sps -#%% parameters - -n=10 # nb bins - -# bin positions -x=np.arange(n,dtype=np.float64) - -xx,yy=np.meshgrid(x,x) - - -xpos=np.hstack((xx.reshape(-1,1),yy.reshape(-1,1))) - -M=ot.dist(xpos) - - -I0=((xx-5)**2+(yy-5)**2<3**2)*1.0 -I1=((xx-7)**2+(yy-7)**2<3**2)*1.0 - -I0/=I0.sum() -I1/=I1.sum() - -i0=I0.ravel() -i1=I1.ravel() - -M=M[i0>0,:][:,i1>0].copy() -i0=i0[i0>0] -i1=i1[i1>0] -Itot=np.concatenate((I0[:,:,np.newaxis],I1[:,:,np.newaxis]),2) - - -#%% plot the distributions - -pl.figure(1) -pl.subplot(2,2,1) -pl.imshow(I0) -pl.subplot(2,2,2) -pl.imshow(I1) - - -#%% barycenter computation - -alpha=0.5 # 0<=alpha<=1 -weights=np.array([1-alpha,alpha]) - - -def conv2(I,k): - return sp.ndimage.convolve1d(sp.ndimage.convolve1d(I,k,axis=1),k,axis=0) - -def conv2n(I,k): - res=np.zeros_like(I) - for i in range(I.shape[2]): - res[:,:,i]=conv2(I[:,:,i],k) - return res - - -def get_1Dkernel(reg,thr=1e-16,wmax=1024): - w=max(min(wmax,2*int((-np.log(thr)*reg)**(.5))),3) - x=np.arange(w,dtype=np.float64) - return np.exp(-((x-w/2)**2)/reg) - -thr=1e-16 -reg=1e0 - -k=get_1Dkernel(reg) -pl.figure(2) -pl.plot(k) - -I05=conv2(I0,k) - -pl.figure(1) -pl.subplot(2,2,1) -pl.imshow(I0) -pl.subplot(2,2,2) -pl.imshow(I05) - -#%% - -G=ot.emd(i0,i1,M) -r0=np.sum(M*G) - -reg=1e-1 -Gs=ot.bregman.sinkhorn_knopp(i0,i1,M,reg=reg) -rs=np.sum(M*Gs) - -#%% - -def mylog(u): - tmp=np.log(u) - tmp[np.isnan(tmp)]=0 - return tmp - -def sinkhorn_conv(a,b, reg, numItermax = 1000, stopThr=1e-9, verbose=False, log=False,**kwargs): - - - a=np.asarray(a,dtype=np.float64) - b=np.asarray(b,dtype=np.float64) - - - if len(b.shape)>2: - nbb=b.shape[2] - a=a[:,:,np.newaxis] - else: - nbb=0 - - - if log: - log={'err':[]} - - # we assume that no distances are null except those of the diagonal of distances - if nbb: - u = np.ones((a.shape[0],a.shape[1],nbb))/(np.prod(a.shape[:2])) - v = np.ones((a.shape[0],a.shape[1],nbb))/(np.prod(b.shape[:2])) - a0=1.0/(np.prod(b.shape[:2])) - else: - u = np.ones((a.shape[0],a.shape[1]))/(np.prod(a.shape[:2])) - v = np.ones((a.shape[0],a.shape[1]))/(np.prod(b.shape[:2])) - a0=1.0/(np.prod(b.shape[:2])) - - - k=get_1Dkernel(reg) - - if nbb: - K=lambda I: conv2n(I,k) - else: - K=lambda I: conv2(I,k) - - cpt = 0 - err=1 - while (err>stopThr and cpt<numItermax): - uprev = u - vprev = v - - v = np.divide(b, K(u)) - u = np.divide(a, K(v)) - - if (np.any(np.isnan(u)) or np.any(np.isnan(v)) - or np.any(np.isinf(u)) or np.any(np.isinf(v))): - # we have reached the machine precision - # come back to previous solution and quit loop - print('Warning: numerical errors at iteration', cpt) - u = uprev - v = vprev - break - if cpt%10==0: - # we can speed up the process by checking for the error only all the 10th iterations - - err = np.sum((u-uprev)**2)/np.sum((u)**2)+np.sum((v-vprev)**2)/np.sum((v)**2) - - if log: - log['err'].append(err) - - if verbose: - if cpt%200 ==0: - print('{:5s}|{:12s}'.format('It.','Err')+'\n'+'-'*19) - print('{:5d}|{:8e}|'.format(cpt,err)) - cpt = cpt +1 - if log: - log['u']=u - log['v']=v - - if nbb: #return only loss - res=np.zeros((nbb)) - for i in range(nbb): - res[i]=np.sum(u[:,i].reshape((-1,1))*K*v[:,i].reshape((1,-1))*M) - if log: - return res,log - else: - return res - - else: # return OT matrix - res=reg*a0*np.sum(a*mylog(u+(u==0))+b*mylog(v+(v==0))) - if log: - - return res,log - else: - return res - -reg=1e0 -r,log=sinkhorn_conv(I0,I1,reg,verbose=True,log=True) -a=I0 -b=I1 -u=log['u'] -v=log['v'] -#%% barycenter interpolation diff --git a/docs/source/auto_examples/plot_OT_conv.rst b/docs/source/auto_examples/plot_OT_conv.rst deleted file mode 100644 index 039bbdb..0000000 --- a/docs/source/auto_examples/plot_OT_conv.rst +++ /dev/null @@ -1,241 +0,0 @@ - - -.. _sphx_glr_auto_examples_plot_OT_conv.py: - - -============================== -1D Wasserstein barycenter demo -============================== - - -@author: rflamary - - - - -.. code-block:: pytb - - Traceback (most recent call last): - File "/home/rflamary/.local/lib/python2.7/site-packages/sphinx_gallery/gen_rst.py", line 518, in execute_code_block - exec(code_block, example_globals) - File "<string>", line 86, in <module> - TypeError: unsupported operand type(s) for *: 'float' and 'Mock' - - - - - -.. code-block:: python - - - import numpy as np - import matplotlib.pylab as pl - import ot - from mpl_toolkits.mplot3d import Axes3D #necessary for 3d plot even if not used - import scipy as sp - import scipy.signal as sps - #%% parameters - - n=10 # nb bins - - # bin positions - x=np.arange(n,dtype=np.float64) - - xx,yy=np.meshgrid(x,x) - - - xpos=np.hstack((xx.reshape(-1,1),yy.reshape(-1,1))) - - M=ot.dist(xpos) - - - I0=((xx-5)**2+(yy-5)**2<3**2)*1.0 - I1=((xx-7)**2+(yy-7)**2<3**2)*1.0 - - I0/=I0.sum() - I1/=I1.sum() - - i0=I0.ravel() - i1=I1.ravel() - - M=M[i0>0,:][:,i1>0].copy() - i0=i0[i0>0] - i1=i1[i1>0] - Itot=np.concatenate((I0[:,:,np.newaxis],I1[:,:,np.newaxis]),2) - - - #%% plot the distributions - - pl.figure(1) - pl.subplot(2,2,1) - pl.imshow(I0) - pl.subplot(2,2,2) - pl.imshow(I1) - - - #%% barycenter computation - - alpha=0.5 # 0<=alpha<=1 - weights=np.array([1-alpha,alpha]) - - - def conv2(I,k): - return sp.ndimage.convolve1d(sp.ndimage.convolve1d(I,k,axis=1),k,axis=0) - - def conv2n(I,k): - res=np.zeros_like(I) - for i in range(I.shape[2]): - res[:,:,i]=conv2(I[:,:,i],k) - return res - - - def get_1Dkernel(reg,thr=1e-16,wmax=1024): - w=max(min(wmax,2*int((-np.log(thr)*reg)**(.5))),3) - x=np.arange(w,dtype=np.float64) - return np.exp(-((x-w/2)**2)/reg) - - thr=1e-16 - reg=1e0 - - k=get_1Dkernel(reg) - pl.figure(2) - pl.plot(k) - - I05=conv2(I0,k) - - pl.figure(1) - pl.subplot(2,2,1) - pl.imshow(I0) - pl.subplot(2,2,2) - pl.imshow(I05) - - #%% - - G=ot.emd(i0,i1,M) - r0=np.sum(M*G) - - reg=1e-1 - Gs=ot.bregman.sinkhorn_knopp(i0,i1,M,reg=reg) - rs=np.sum(M*Gs) - - #%% - - def mylog(u): - tmp=np.log(u) - tmp[np.isnan(tmp)]=0 - return tmp - - def sinkhorn_conv(a,b, reg, numItermax = 1000, stopThr=1e-9, verbose=False, log=False,**kwargs): - - - a=np.asarray(a,dtype=np.float64) - b=np.asarray(b,dtype=np.float64) - - - if len(b.shape)>2: - nbb=b.shape[2] - a=a[:,:,np.newaxis] - else: - nbb=0 - - - if log: - log={'err':[]} - - # we assume that no distances are null except those of the diagonal of distances - if nbb: - u = np.ones((a.shape[0],a.shape[1],nbb))/(np.prod(a.shape[:2])) - v = np.ones((a.shape[0],a.shape[1],nbb))/(np.prod(b.shape[:2])) - a0=1.0/(np.prod(b.shape[:2])) - else: - u = np.ones((a.shape[0],a.shape[1]))/(np.prod(a.shape[:2])) - v = np.ones((a.shape[0],a.shape[1]))/(np.prod(b.shape[:2])) - a0=1.0/(np.prod(b.shape[:2])) - - - k=get_1Dkernel(reg) - - if nbb: - K=lambda I: conv2n(I,k) - else: - K=lambda I: conv2(I,k) - - cpt = 0 - err=1 - while (err>stopThr and cpt<numItermax): - uprev = u - vprev = v - - v = np.divide(b, K(u)) - u = np.divide(a, K(v)) - - if (np.any(np.isnan(u)) or np.any(np.isnan(v)) - or np.any(np.isinf(u)) or np.any(np.isinf(v))): - # we have reached the machine precision - # come back to previous solution and quit loop - print('Warning: numerical errors at iteration', cpt) - u = uprev - v = vprev - break - if cpt%10==0: - # we can speed up the process by checking for the error only all the 10th iterations - - err = np.sum((u-uprev)**2)/np.sum((u)**2)+np.sum((v-vprev)**2)/np.sum((v)**2) - - if log: - log['err'].append(err) - - if verbose: - if cpt%200 ==0: - print('{:5s}|{:12s}'.format('It.','Err')+'\n'+'-'*19) - print('{:5d}|{:8e}|'.format(cpt,err)) - cpt = cpt +1 - if log: - log['u']=u - log['v']=v - - if nbb: #return only loss - res=np.zeros((nbb)) - for i in range(nbb): - res[i]=np.sum(u[:,i].reshape((-1,1))*K*v[:,i].reshape((1,-1))*M) - if log: - return res,log - else: - return res - - else: # return OT matrix - res=reg*a0*np.sum(a*mylog(u+(u==0))+b*mylog(v+(v==0))) - if log: - - return res,log - else: - return res - - reg=1e0 - r,log=sinkhorn_conv(I0,I1,reg,verbose=True,log=True) - a=I0 - b=I1 - u=log['u'] - v=log['v'] - #%% barycenter interpolation - -**Total running time of the script:** ( 0 minutes 0.000 seconds) - - - -.. container:: sphx-glr-footer - - - .. container:: sphx-glr-download - - :download:`Download Python source code: plot_OT_conv.py <plot_OT_conv.py>` - - - - .. container:: sphx-glr-download - - :download:`Download Jupyter notebook: plot_OT_conv.ipynb <plot_OT_conv.ipynb>` - -.. rst-class:: sphx-glr-signature - - `Generated by Sphinx-Gallery <http://sphinx-gallery.readthedocs.io>`_ diff --git a/docs/source/auto_examples/plot_WDA.ipynb b/docs/source/auto_examples/plot_WDA.ipynb index 408a605..1661c53 100644 --- a/docs/source/auto_examples/plot_WDA.ipynb +++ b/docs/source/auto_examples/plot_WDA.ipynb @@ -15,7 +15,7 @@ }, { "source": [ - "\n# Wasserstein Discriminant Analysis\n\n\n@author: rflamary\n\n" + "\n# Wasserstein Discriminant Analysis\n\n\nThis example illustrate the use of WDA as proposed in [11].\n\n\n[11] Flamary, R., Cuturi, M., Courty, N., & Rakotomamonjy, A. (2016).\nWasserstein Discriminant Analysis.\n\n\n" ], "cell_type": "markdown", "metadata": {} @@ -24,7 +24,97 @@ "execution_count": null, "cell_type": "code", "source": [ - "import numpy as np\nimport matplotlib.pylab as pl\nimport ot\nfrom ot.datasets import get_1D_gauss as gauss\nfrom ot.dr import wda\n\n\n#%% parameters\n\nn=1000 # nb samples in source and target datasets\nnz=0.2\nxs,ys=ot.datasets.get_data_classif('3gauss',n,nz)\nxt,yt=ot.datasets.get_data_classif('3gauss',n,nz)\n\nnbnoise=8\n\nxs=np.hstack((xs,np.random.randn(n,nbnoise)))\nxt=np.hstack((xt,np.random.randn(n,nbnoise)))\n\n#%% plot samples\n\npl.figure(1)\n\n\npl.scatter(xt[:,0],xt[:,1],c=ys,marker='+',label='Source samples')\npl.legend(loc=0)\npl.title('Discriminant dimensions')\n\n\n#%% plot distributions and loss matrix\np=2\nreg=1\nk=10\nmaxiter=100\n\nP,proj = wda(xs,ys,p,reg,k,maxiter=maxiter)\n\n#%% plot samples\n\nxsp=proj(xs)\nxtp=proj(xt)\n\npl.figure(1,(10,5))\n\npl.subplot(1,2,1)\npl.scatter(xsp[:,0],xsp[:,1],c=ys,marker='+',label='Projected samples')\npl.legend(loc=0)\npl.title('Projected training samples')\n\n\npl.subplot(1,2,2)\npl.scatter(xtp[:,0],xtp[:,1],c=ys,marker='+',label='Projected samples')\npl.legend(loc=0)\npl.title('Projected test samples')" + "# Author: Remi Flamary <remi.flamary@unice.fr>\n#\n# License: MIT License\n\nimport numpy as np\nimport matplotlib.pylab as pl\n\nfrom ot.dr import wda, fda" + ], + "outputs": [], + "metadata": { + "collapsed": false + } + }, + { + "source": [ + "Generate data\n-------------\n\n" + ], + "cell_type": "markdown", + "metadata": {} + }, + { + "execution_count": null, + "cell_type": "code", + "source": [ + "#%% parameters\n\nn = 1000 # nb samples in source and target datasets\nnz = 0.2\n\n# generate circle dataset\nt = np.random.rand(n) * 2 * np.pi\nys = np.floor((np.arange(n) * 1.0 / n * 3)) + 1\nxs = np.concatenate(\n (np.cos(t).reshape((-1, 1)), np.sin(t).reshape((-1, 1))), 1)\nxs = xs * ys.reshape(-1, 1) + nz * np.random.randn(n, 2)\n\nt = np.random.rand(n) * 2 * np.pi\nyt = np.floor((np.arange(n) * 1.0 / n * 3)) + 1\nxt = np.concatenate(\n (np.cos(t).reshape((-1, 1)), np.sin(t).reshape((-1, 1))), 1)\nxt = xt * yt.reshape(-1, 1) + nz * np.random.randn(n, 2)\n\nnbnoise = 8\n\nxs = np.hstack((xs, np.random.randn(n, nbnoise)))\nxt = np.hstack((xt, np.random.randn(n, nbnoise)))" + ], + "outputs": [], + "metadata": { + "collapsed": false + } + }, + { + "source": [ + "Plot data\n---------\n\n" + ], + "cell_type": "markdown", + "metadata": {} + }, + { + "execution_count": null, + "cell_type": "code", + "source": [ + "#%% plot samples\npl.figure(1, figsize=(6.4, 3.5))\n\npl.subplot(1, 2, 1)\npl.scatter(xt[:, 0], xt[:, 1], c=ys, marker='+', label='Source samples')\npl.legend(loc=0)\npl.title('Discriminant dimensions')\n\npl.subplot(1, 2, 2)\npl.scatter(xt[:, 2], xt[:, 3], c=ys, marker='+', label='Source samples')\npl.legend(loc=0)\npl.title('Other dimensions')\npl.tight_layout()" + ], + "outputs": [], + "metadata": { + "collapsed": false + } + }, + { + "source": [ + "Compute Fisher Discriminant Analysis\n------------------------------------\n\n" + ], + "cell_type": "markdown", + "metadata": {} + }, + { + "execution_count": null, + "cell_type": "code", + "source": [ + "#%% Compute FDA\np = 2\n\nPfda, projfda = fda(xs, ys, p)" + ], + "outputs": [], + "metadata": { + "collapsed": false + } + }, + { + "source": [ + "Compute Wasserstein Discriminant Analysis\n-----------------------------------------\n\n" + ], + "cell_type": "markdown", + "metadata": {} + }, + { + "execution_count": null, + "cell_type": "code", + "source": [ + "#%% Compute WDA\np = 2\nreg = 1e0\nk = 10\nmaxiter = 100\n\nPwda, projwda = wda(xs, ys, p, reg, k, maxiter=maxiter)" + ], + "outputs": [], + "metadata": { + "collapsed": false + } + }, + { + "source": [ + "Plot 2D projections\n-------------------\n\n" + ], + "cell_type": "markdown", + "metadata": {} + }, + { + "execution_count": null, + "cell_type": "code", + "source": [ + "#%% plot samples\n\nxsp = projfda(xs)\nxtp = projfda(xt)\n\nxspw = projwda(xs)\nxtpw = projwda(xt)\n\npl.figure(2)\n\npl.subplot(2, 2, 1)\npl.scatter(xsp[:, 0], xsp[:, 1], c=ys, marker='+', label='Projected samples')\npl.legend(loc=0)\npl.title('Projected training samples FDA')\n\npl.subplot(2, 2, 2)\npl.scatter(xtp[:, 0], xtp[:, 1], c=ys, marker='+', label='Projected samples')\npl.legend(loc=0)\npl.title('Projected test samples FDA')\n\npl.subplot(2, 2, 3)\npl.scatter(xspw[:, 0], xspw[:, 1], c=ys, marker='+', label='Projected samples')\npl.legend(loc=0)\npl.title('Projected training samples WDA')\n\npl.subplot(2, 2, 4)\npl.scatter(xtpw[:, 0], xtpw[:, 1], c=ys, marker='+', label='Projected samples')\npl.legend(loc=0)\npl.title('Projected test samples WDA')\npl.tight_layout()\n\npl.show()" ], "outputs": [], "metadata": { diff --git a/docs/source/auto_examples/plot_WDA.py b/docs/source/auto_examples/plot_WDA.py index bbe3888..93cc237 100644 --- a/docs/source/auto_examples/plot_WDA.py +++ b/docs/source/auto_examples/plot_WDA.py @@ -4,60 +4,124 @@ Wasserstein Discriminant Analysis ================================= -@author: rflamary +This example illustrate the use of WDA as proposed in [11]. + + +[11] Flamary, R., Cuturi, M., Courty, N., & Rakotomamonjy, A. (2016). +Wasserstein Discriminant Analysis. + """ +# Author: Remi Flamary <remi.flamary@unice.fr> +# +# License: MIT License + import numpy as np import matplotlib.pylab as pl -import ot -from ot.datasets import get_1D_gauss as gauss -from ot.dr import wda +from ot.dr import wda, fda + + +############################################################################## +# Generate data +# ------------- #%% parameters -n=1000 # nb samples in source and target datasets -nz=0.2 -xs,ys=ot.datasets.get_data_classif('3gauss',n,nz) -xt,yt=ot.datasets.get_data_classif('3gauss',n,nz) +n = 1000 # nb samples in source and target datasets +nz = 0.2 -nbnoise=8 +# generate circle dataset +t = np.random.rand(n) * 2 * np.pi +ys = np.floor((np.arange(n) * 1.0 / n * 3)) + 1 +xs = np.concatenate( + (np.cos(t).reshape((-1, 1)), np.sin(t).reshape((-1, 1))), 1) +xs = xs * ys.reshape(-1, 1) + nz * np.random.randn(n, 2) -xs=np.hstack((xs,np.random.randn(n,nbnoise))) -xt=np.hstack((xt,np.random.randn(n,nbnoise))) +t = np.random.rand(n) * 2 * np.pi +yt = np.floor((np.arange(n) * 1.0 / n * 3)) + 1 +xt = np.concatenate( + (np.cos(t).reshape((-1, 1)), np.sin(t).reshape((-1, 1))), 1) +xt = xt * yt.reshape(-1, 1) + nz * np.random.randn(n, 2) -#%% plot samples +nbnoise = 8 + +xs = np.hstack((xs, np.random.randn(n, nbnoise))) +xt = np.hstack((xt, np.random.randn(n, nbnoise))) -pl.figure(1) +############################################################################## +# Plot data +# --------- +#%% plot samples +pl.figure(1, figsize=(6.4, 3.5)) -pl.scatter(xt[:,0],xt[:,1],c=ys,marker='+',label='Source samples') +pl.subplot(1, 2, 1) +pl.scatter(xt[:, 0], xt[:, 1], c=ys, marker='+', label='Source samples') pl.legend(loc=0) pl.title('Discriminant dimensions') +pl.subplot(1, 2, 2) +pl.scatter(xt[:, 2], xt[:, 3], c=ys, marker='+', label='Source samples') +pl.legend(loc=0) +pl.title('Other dimensions') +pl.tight_layout() + +############################################################################## +# Compute Fisher Discriminant Analysis +# ------------------------------------ -#%% plot distributions and loss matrix -p=2 -reg=1 -k=10 -maxiter=100 +#%% Compute FDA +p = 2 -P,proj = wda(xs,ys,p,reg,k,maxiter=maxiter) +Pfda, projfda = fda(xs, ys, p) + +############################################################################## +# Compute Wasserstein Discriminant Analysis +# ----------------------------------------- + +#%% Compute WDA +p = 2 +reg = 1e0 +k = 10 +maxiter = 100 + +Pwda, projwda = wda(xs, ys, p, reg, k, maxiter=maxiter) + + +############################################################################## +# Plot 2D projections +# ------------------- #%% plot samples -xsp=proj(xs) -xtp=proj(xt) +xsp = projfda(xs) +xtp = projfda(xt) -pl.figure(1,(10,5)) +xspw = projwda(xs) +xtpw = projwda(xt) -pl.subplot(1,2,1) -pl.scatter(xsp[:,0],xsp[:,1],c=ys,marker='+',label='Projected samples') +pl.figure(2) + +pl.subplot(2, 2, 1) +pl.scatter(xsp[:, 0], xsp[:, 1], c=ys, marker='+', label='Projected samples') pl.legend(loc=0) -pl.title('Projected training samples') +pl.title('Projected training samples FDA') +pl.subplot(2, 2, 2) +pl.scatter(xtp[:, 0], xtp[:, 1], c=ys, marker='+', label='Projected samples') +pl.legend(loc=0) +pl.title('Projected test samples FDA') -pl.subplot(1,2,2) -pl.scatter(xtp[:,0],xtp[:,1],c=ys,marker='+',label='Projected samples') +pl.subplot(2, 2, 3) +pl.scatter(xspw[:, 0], xspw[:, 1], c=ys, marker='+', label='Projected samples') pl.legend(loc=0) -pl.title('Projected test samples') +pl.title('Projected training samples WDA') + +pl.subplot(2, 2, 4) +pl.scatter(xtpw[:, 0], xtpw[:, 1], c=ys, marker='+', label='Projected samples') +pl.legend(loc=0) +pl.title('Projected test samples WDA') +pl.tight_layout() + +pl.show() diff --git a/docs/source/auto_examples/plot_WDA.rst b/docs/source/auto_examples/plot_WDA.rst index 540555d..64ddb47 100644 --- a/docs/source/auto_examples/plot_WDA.rst +++ b/docs/source/auto_examples/plot_WDA.rst @@ -7,108 +7,216 @@ Wasserstein Discriminant Analysis ================================= -@author: rflamary +This example illustrate the use of WDA as proposed in [11]. +[11] Flamary, R., Cuturi, M., Courty, N., & Rakotomamonjy, A. (2016). +Wasserstein Discriminant Analysis. -.. image:: /auto_examples/images/sphx_glr_plot_WDA_001.png - :align: center -.. rst-class:: sphx-glr-script-out +.. code-block:: python - Out:: - Compiling cost function... - Computing gradient of cost function... - iter cost val grad. norm - 1 +5.2427396265941129e-01 8.16627951e-01 - 2 +1.7904850059627236e-01 1.91366819e-01 - 3 +1.6985797253002377e-01 1.70940682e-01 - 4 +1.3903474972292729e-01 1.28606342e-01 - 5 +7.4961734618782416e-02 6.41973980e-02 - 6 +7.1900245222486239e-02 4.25693592e-02 - 7 +7.0472023318269614e-02 2.34599232e-02 - 8 +6.9917568641317152e-02 5.66542766e-03 - 9 +6.9885086242452696e-02 4.05756115e-04 - 10 +6.9884967432653489e-02 2.16836017e-04 - 11 +6.9884923649884148e-02 5.74961622e-05 - 12 +6.9884921818258436e-02 3.83257203e-05 - 13 +6.9884920459612282e-02 9.97486224e-06 - 14 +6.9884920414414409e-02 7.33567875e-06 - 15 +6.9884920388431387e-02 5.23889187e-06 - 16 +6.9884920385183902e-02 4.91959084e-06 - 17 +6.9884920373983223e-02 3.56451669e-06 - 18 +6.9884920369701245e-02 2.88858709e-06 - 19 +6.9884920361621208e-02 1.82294279e-07 - Terminated - min grad norm reached after 19 iterations, 9.65 seconds. + # Author: Remi Flamary <remi.flamary@unice.fr> + # + # License: MIT License + import numpy as np + import matplotlib.pylab as pl + from ot.dr import wda, fda -| -.. code-block:: python - import numpy as np - import matplotlib.pylab as pl - import ot - from ot.datasets import get_1D_gauss as gauss - from ot.dr import wda + + +Generate data +------------- + + + +.. code-block:: python #%% parameters - n=1000 # nb samples in source and target datasets - nz=0.2 - xs,ys=ot.datasets.get_data_classif('3gauss',n,nz) - xt,yt=ot.datasets.get_data_classif('3gauss',n,nz) + n = 1000 # nb samples in source and target datasets + nz = 0.2 + + # generate circle dataset + t = np.random.rand(n) * 2 * np.pi + ys = np.floor((np.arange(n) * 1.0 / n * 3)) + 1 + xs = np.concatenate( + (np.cos(t).reshape((-1, 1)), np.sin(t).reshape((-1, 1))), 1) + xs = xs * ys.reshape(-1, 1) + nz * np.random.randn(n, 2) + + t = np.random.rand(n) * 2 * np.pi + yt = np.floor((np.arange(n) * 1.0 / n * 3)) + 1 + xt = np.concatenate( + (np.cos(t).reshape((-1, 1)), np.sin(t).reshape((-1, 1))), 1) + xt = xt * yt.reshape(-1, 1) + nz * np.random.randn(n, 2) + + nbnoise = 8 + + xs = np.hstack((xs, np.random.randn(n, nbnoise))) + xt = np.hstack((xt, np.random.randn(n, nbnoise))) - nbnoise=8 - xs=np.hstack((xs,np.random.randn(n,nbnoise))) - xt=np.hstack((xt,np.random.randn(n,nbnoise))) - #%% plot samples - pl.figure(1) - pl.scatter(xt[:,0],xt[:,1],c=ys,marker='+',label='Source samples') + +Plot data +--------- + + + +.. code-block:: python + + + #%% plot samples + pl.figure(1, figsize=(6.4, 3.5)) + + pl.subplot(1, 2, 1) + pl.scatter(xt[:, 0], xt[:, 1], c=ys, marker='+', label='Source samples') pl.legend(loc=0) pl.title('Discriminant dimensions') + pl.subplot(1, 2, 2) + pl.scatter(xt[:, 2], xt[:, 3], c=ys, marker='+', label='Source samples') + pl.legend(loc=0) + pl.title('Other dimensions') + pl.tight_layout() + + + + +.. image:: /auto_examples/images/sphx_glr_plot_WDA_001.png + :align: center + + + + +Compute Fisher Discriminant Analysis +------------------------------------ + + + +.. code-block:: python - #%% plot distributions and loss matrix - p=2 - reg=1 - k=10 - maxiter=100 - P,proj = wda(xs,ys,p,reg,k,maxiter=maxiter) + #%% Compute FDA + p = 2 + + Pfda, projfda = fda(xs, ys, p) + + + + + + + +Compute Wasserstein Discriminant Analysis +----------------------------------------- + + + +.. code-block:: python + + + #%% Compute WDA + p = 2 + reg = 1e0 + k = 10 + maxiter = 100 + + Pwda, projwda = wda(xs, ys, p, reg, k, maxiter=maxiter) + + + + + + +.. rst-class:: sphx-glr-script-out + + Out:: + + Compiling cost function... + Computing gradient of cost function... + iter cost val grad. norm + 1 +5.4993226050368416e-01 5.18285173e-01 + 2 +3.4883000507542844e-01 1.96795818e-01 + 3 +2.9841234004693890e-01 2.33029475e-01 + 4 +2.3976476757548179e-01 1.38593951e-01 + 5 +2.3614468346177828e-01 1.19615394e-01 + 6 +2.2586536502789240e-01 4.82430685e-02 + 7 +2.2451030967794622e-01 2.56564039e-02 + 8 +2.2421446331083625e-01 1.47932578e-02 + 9 +2.2407441444450052e-01 1.12040327e-03 + 10 +2.2407365923337522e-01 3.78899763e-04 + 11 +2.2407356874011675e-01 1.79740810e-05 + 12 +2.2407356862959993e-01 1.25643005e-05 + 13 +2.2407356853043561e-01 1.40415001e-06 + 14 +2.2407356852925220e-01 3.41183585e-07 + Terminated - min grad norm reached after 14 iterations, 6.78 seconds. + + +Plot 2D projections +------------------- + + + +.. code-block:: python + #%% plot samples - xsp=proj(xs) - xtp=proj(xt) + xsp = projfda(xs) + xtp = projfda(xt) + + xspw = projwda(xs) + xtpw = projwda(xt) - pl.figure(1,(10,5)) + pl.figure(2) - pl.subplot(1,2,1) - pl.scatter(xsp[:,0],xsp[:,1],c=ys,marker='+',label='Projected samples') + pl.subplot(2, 2, 1) + pl.scatter(xsp[:, 0], xsp[:, 1], c=ys, marker='+', label='Projected samples') pl.legend(loc=0) - pl.title('Projected training samples') + pl.title('Projected training samples FDA') + pl.subplot(2, 2, 2) + pl.scatter(xtp[:, 0], xtp[:, 1], c=ys, marker='+', label='Projected samples') + pl.legend(loc=0) + pl.title('Projected test samples FDA') + + pl.subplot(2, 2, 3) + pl.scatter(xspw[:, 0], xspw[:, 1], c=ys, marker='+', label='Projected samples') + pl.legend(loc=0) + pl.title('Projected training samples WDA') - pl.subplot(1,2,2) - pl.scatter(xtp[:,0],xtp[:,1],c=ys,marker='+',label='Projected samples') + pl.subplot(2, 2, 4) + pl.scatter(xtpw[:, 0], xtpw[:, 1], c=ys, marker='+', label='Projected samples') pl.legend(loc=0) - pl.title('Projected test samples') + pl.title('Projected test samples WDA') + pl.tight_layout() + + pl.show() + + + +.. image:: /auto_examples/images/sphx_glr_plot_WDA_003.png + :align: center + + + -**Total running time of the script:** ( 0 minutes 16.902 seconds) +**Total running time of the script:** ( 0 minutes 7.637 seconds) @@ -127,4 +235,4 @@ Wasserstein Discriminant Analysis .. rst-class:: sphx-glr-signature - `Generated by Sphinx-Gallery <http://sphinx-gallery.readthedocs.io>`_ + `Generated by Sphinx-Gallery <https://sphinx-gallery.readthedocs.io>`_ diff --git a/docs/source/auto_examples/plot_barycenter_1D.ipynb b/docs/source/auto_examples/plot_barycenter_1D.ipynb index 36f3975..a19e0fd 100644 --- a/docs/source/auto_examples/plot_barycenter_1D.ipynb +++ b/docs/source/auto_examples/plot_barycenter_1D.ipynb @@ -15,7 +15,7 @@ }, { "source": [ - "\n# 1D Wasserstein barycenter demo\n\n\n\n@author: rflamary\n\n" + "\n# 1D Wasserstein barycenter demo\n\n\nThis example illustrates the computation of regularized Wassersyein Barycenter\nas proposed in [3].\n\n\n[3] Benamou, J. D., Carlier, G., Cuturi, M., Nenna, L., & Peyr\u00e9, G. (2015).\nIterative Bregman projections for regularized transportation problems\nSIAM Journal on Scientific Computing, 37(2), A1111-A1138.\n\n\n" ], "cell_type": "markdown", "metadata": {} @@ -24,7 +24,79 @@ "execution_count": null, "cell_type": "code", "source": [ - "import numpy as np\nimport matplotlib.pylab as pl\nimport ot\nfrom mpl_toolkits.mplot3d import Axes3D #necessary for 3d plot even if not used\nfrom matplotlib.collections import PolyCollection\n\n\n#%% parameters\n\nn=100 # nb bins\n\n# bin positions\nx=np.arange(n,dtype=np.float64)\n\n# Gaussian distributions\na1=ot.datasets.get_1D_gauss(n,m=20,s=5) # m= mean, s= std\na2=ot.datasets.get_1D_gauss(n,m=60,s=8)\n\n# creating matrix A containing all distributions\nA=np.vstack((a1,a2)).T\nnbd=A.shape[1]\n\n# loss matrix + normalization\nM=ot.utils.dist0(n)\nM/=M.max()\n\n#%% plot the distributions\n\npl.figure(1)\nfor i in range(nbd):\n pl.plot(x,A[:,i])\npl.title('Distributions')\n\n#%% barycenter computation\n\nalpha=0.2 # 0<=alpha<=1\nweights=np.array([1-alpha,alpha])\n\n# l2bary\nbary_l2=A.dot(weights)\n\n# wasserstein\nreg=1e-3\nbary_wass=ot.bregman.barycenter(A,M,reg,weights)\n\npl.figure(2)\npl.clf()\npl.subplot(2,1,1)\nfor i in range(nbd):\n pl.plot(x,A[:,i])\npl.title('Distributions')\n\npl.subplot(2,1,2)\npl.plot(x,bary_l2,'r',label='l2')\npl.plot(x,bary_wass,'g',label='Wasserstein')\npl.legend()\npl.title('Barycenters')\n\n\n#%% barycenter interpolation\n\nnbalpha=11\nalphalist=np.linspace(0,1,nbalpha)\n\n\nB_l2=np.zeros((n,nbalpha))\n\nB_wass=np.copy(B_l2)\n\nfor i in range(0,nbalpha):\n alpha=alphalist[i]\n weights=np.array([1-alpha,alpha])\n B_l2[:,i]=A.dot(weights)\n B_wass[:,i]=ot.bregman.barycenter(A,M,reg,weights)\n\n#%% plot interpolation\n\npl.figure(3,(10,5))\n\n#pl.subplot(1,2,1)\ncmap=pl.cm.get_cmap('viridis')\nverts = []\nzs = alphalist\nfor i,z in enumerate(zs):\n ys = B_l2[:,i]\n verts.append(list(zip(x, ys)))\n\nax = pl.gcf().gca(projection='3d')\n\npoly = PolyCollection(verts,facecolors=[cmap(a) for a in alphalist])\npoly.set_alpha(0.7)\nax.add_collection3d(poly, zs=zs, zdir='y')\n\nax.set_xlabel('x')\nax.set_xlim3d(0, n)\nax.set_ylabel('$\\\\alpha$')\nax.set_ylim3d(0,1)\nax.set_zlabel('')\nax.set_zlim3d(0, B_l2.max()*1.01)\npl.title('Barycenter interpolation with l2')\n\npl.show()\n\npl.figure(4,(10,5))\n\n#pl.subplot(1,2,1)\ncmap=pl.cm.get_cmap('viridis')\nverts = []\nzs = alphalist\nfor i,z in enumerate(zs):\n ys = B_wass[:,i]\n verts.append(list(zip(x, ys)))\n\nax = pl.gcf().gca(projection='3d')\n\npoly = PolyCollection(verts,facecolors=[cmap(a) for a in alphalist])\npoly.set_alpha(0.7)\nax.add_collection3d(poly, zs=zs, zdir='y')\n\nax.set_xlabel('x')\nax.set_xlim3d(0, n)\nax.set_ylabel('$\\\\alpha$')\nax.set_ylim3d(0,1)\nax.set_zlabel('')\nax.set_zlim3d(0, B_l2.max()*1.01)\npl.title('Barycenter interpolation with Wasserstein')\n\npl.show()" + "# Author: Remi Flamary <remi.flamary@unice.fr>\n#\n# License: MIT License\n\nimport numpy as np\nimport matplotlib.pylab as pl\nimport ot\n# necessary for 3d plot even if not used\nfrom mpl_toolkits.mplot3d import Axes3D # noqa\nfrom matplotlib.collections import PolyCollection" + ], + "outputs": [], + "metadata": { + "collapsed": false + } + }, + { + "source": [ + "Generate data\n-------------\n\n" + ], + "cell_type": "markdown", + "metadata": {} + }, + { + "execution_count": null, + "cell_type": "code", + "source": [ + "#%% parameters\n\nn = 100 # nb bins\n\n# bin positions\nx = np.arange(n, dtype=np.float64)\n\n# Gaussian distributions\na1 = ot.datasets.get_1D_gauss(n, m=20, s=5) # m= mean, s= std\na2 = ot.datasets.get_1D_gauss(n, m=60, s=8)\n\n# creating matrix A containing all distributions\nA = np.vstack((a1, a2)).T\nn_distributions = A.shape[1]\n\n# loss matrix + normalization\nM = ot.utils.dist0(n)\nM /= M.max()" + ], + "outputs": [], + "metadata": { + "collapsed": false + } + }, + { + "source": [ + "Plot data\n---------\n\n" + ], + "cell_type": "markdown", + "metadata": {} + }, + { + "execution_count": null, + "cell_type": "code", + "source": [ + "#%% plot the distributions\n\npl.figure(1, figsize=(6.4, 3))\nfor i in range(n_distributions):\n pl.plot(x, A[:, i])\npl.title('Distributions')\npl.tight_layout()" + ], + "outputs": [], + "metadata": { + "collapsed": false + } + }, + { + "source": [ + "Barycenter computation\n----------------------\n\n" + ], + "cell_type": "markdown", + "metadata": {} + }, + { + "execution_count": null, + "cell_type": "code", + "source": [ + "#%% barycenter computation\n\nalpha = 0.2 # 0<=alpha<=1\nweights = np.array([1 - alpha, alpha])\n\n# l2bary\nbary_l2 = A.dot(weights)\n\n# wasserstein\nreg = 1e-3\nbary_wass = ot.bregman.barycenter(A, M, reg, weights)\n\npl.figure(2)\npl.clf()\npl.subplot(2, 1, 1)\nfor i in range(n_distributions):\n pl.plot(x, A[:, i])\npl.title('Distributions')\n\npl.subplot(2, 1, 2)\npl.plot(x, bary_l2, 'r', label='l2')\npl.plot(x, bary_wass, 'g', label='Wasserstein')\npl.legend()\npl.title('Barycenters')\npl.tight_layout()" + ], + "outputs": [], + "metadata": { + "collapsed": false + } + }, + { + "source": [ + "Barycentric interpolation\n-------------------------\n\n" + ], + "cell_type": "markdown", + "metadata": {} + }, + { + "execution_count": null, + "cell_type": "code", + "source": [ + "#%% barycenter interpolation\n\nn_alpha = 11\nalpha_list = np.linspace(0, 1, n_alpha)\n\n\nB_l2 = np.zeros((n, n_alpha))\n\nB_wass = np.copy(B_l2)\n\nfor i in range(0, n_alpha):\n alpha = alpha_list[i]\n weights = np.array([1 - alpha, alpha])\n B_l2[:, i] = A.dot(weights)\n B_wass[:, i] = ot.bregman.barycenter(A, M, reg, weights)\n\n#%% plot interpolation\n\npl.figure(3)\n\ncmap = pl.cm.get_cmap('viridis')\nverts = []\nzs = alpha_list\nfor i, z in enumerate(zs):\n ys = B_l2[:, i]\n verts.append(list(zip(x, ys)))\n\nax = pl.gcf().gca(projection='3d')\n\npoly = PolyCollection(verts, facecolors=[cmap(a) for a in alpha_list])\npoly.set_alpha(0.7)\nax.add_collection3d(poly, zs=zs, zdir='y')\nax.set_xlabel('x')\nax.set_xlim3d(0, n)\nax.set_ylabel('$\\\\alpha$')\nax.set_ylim3d(0, 1)\nax.set_zlabel('')\nax.set_zlim3d(0, B_l2.max() * 1.01)\npl.title('Barycenter interpolation with l2')\npl.tight_layout()\n\npl.figure(4)\ncmap = pl.cm.get_cmap('viridis')\nverts = []\nzs = alpha_list\nfor i, z in enumerate(zs):\n ys = B_wass[:, i]\n verts.append(list(zip(x, ys)))\n\nax = pl.gcf().gca(projection='3d')\n\npoly = PolyCollection(verts, facecolors=[cmap(a) for a in alpha_list])\npoly.set_alpha(0.7)\nax.add_collection3d(poly, zs=zs, zdir='y')\nax.set_xlabel('x')\nax.set_xlim3d(0, n)\nax.set_ylabel('$\\\\alpha$')\nax.set_ylim3d(0, 1)\nax.set_zlabel('')\nax.set_zlim3d(0, B_l2.max() * 1.01)\npl.title('Barycenter interpolation with Wasserstein')\npl.tight_layout()\n\npl.show()" ], "outputs": [], "metadata": { diff --git a/docs/source/auto_examples/plot_barycenter_1D.py b/docs/source/auto_examples/plot_barycenter_1D.py index 30eecbf..620936b 100644 --- a/docs/source/auto_examples/plot_barycenter_1D.py +++ b/docs/source/auto_examples/plot_barycenter_1D.py @@ -4,135 +4,157 @@ 1D Wasserstein barycenter demo ============================== +This example illustrates the computation of regularized Wassersyein Barycenter +as proposed in [3]. + + +[3] Benamou, J. D., Carlier, G., Cuturi, M., Nenna, L., & Peyré, G. (2015). +Iterative Bregman projections for regularized transportation problems +SIAM Journal on Scientific Computing, 37(2), A1111-A1138. -@author: rflamary """ +# Author: Remi Flamary <remi.flamary@unice.fr> +# +# License: MIT License + import numpy as np import matplotlib.pylab as pl import ot -from mpl_toolkits.mplot3d import Axes3D #necessary for 3d plot even if not used +# necessary for 3d plot even if not used +from mpl_toolkits.mplot3d import Axes3D # noqa from matplotlib.collections import PolyCollection +############################################################################## +# Generate data +# ------------- #%% parameters -n=100 # nb bins +n = 100 # nb bins # bin positions -x=np.arange(n,dtype=np.float64) +x = np.arange(n, dtype=np.float64) # Gaussian distributions -a1=ot.datasets.get_1D_gauss(n,m=20,s=5) # m= mean, s= std -a2=ot.datasets.get_1D_gauss(n,m=60,s=8) +a1 = ot.datasets.get_1D_gauss(n, m=20, s=5) # m= mean, s= std +a2 = ot.datasets.get_1D_gauss(n, m=60, s=8) # creating matrix A containing all distributions -A=np.vstack((a1,a2)).T -nbd=A.shape[1] +A = np.vstack((a1, a2)).T +n_distributions = A.shape[1] # loss matrix + normalization -M=ot.utils.dist0(n) -M/=M.max() +M = ot.utils.dist0(n) +M /= M.max() + +############################################################################## +# Plot data +# --------- #%% plot the distributions -pl.figure(1) -for i in range(nbd): - pl.plot(x,A[:,i]) +pl.figure(1, figsize=(6.4, 3)) +for i in range(n_distributions): + pl.plot(x, A[:, i]) pl.title('Distributions') +pl.tight_layout() + +############################################################################## +# Barycenter computation +# ---------------------- #%% barycenter computation -alpha=0.2 # 0<=alpha<=1 -weights=np.array([1-alpha,alpha]) +alpha = 0.2 # 0<=alpha<=1 +weights = np.array([1 - alpha, alpha]) # l2bary -bary_l2=A.dot(weights) +bary_l2 = A.dot(weights) # wasserstein -reg=1e-3 -bary_wass=ot.bregman.barycenter(A,M,reg,weights) +reg = 1e-3 +bary_wass = ot.bregman.barycenter(A, M, reg, weights) pl.figure(2) pl.clf() -pl.subplot(2,1,1) -for i in range(nbd): - pl.plot(x,A[:,i]) +pl.subplot(2, 1, 1) +for i in range(n_distributions): + pl.plot(x, A[:, i]) pl.title('Distributions') -pl.subplot(2,1,2) -pl.plot(x,bary_l2,'r',label='l2') -pl.plot(x,bary_wass,'g',label='Wasserstein') +pl.subplot(2, 1, 2) +pl.plot(x, bary_l2, 'r', label='l2') +pl.plot(x, bary_wass, 'g', label='Wasserstein') pl.legend() pl.title('Barycenters') +pl.tight_layout() +############################################################################## +# Barycentric interpolation +# ------------------------- #%% barycenter interpolation -nbalpha=11 -alphalist=np.linspace(0,1,nbalpha) +n_alpha = 11 +alpha_list = np.linspace(0, 1, n_alpha) -B_l2=np.zeros((n,nbalpha)) +B_l2 = np.zeros((n, n_alpha)) -B_wass=np.copy(B_l2) +B_wass = np.copy(B_l2) -for i in range(0,nbalpha): - alpha=alphalist[i] - weights=np.array([1-alpha,alpha]) - B_l2[:,i]=A.dot(weights) - B_wass[:,i]=ot.bregman.barycenter(A,M,reg,weights) +for i in range(0, n_alpha): + alpha = alpha_list[i] + weights = np.array([1 - alpha, alpha]) + B_l2[:, i] = A.dot(weights) + B_wass[:, i] = ot.bregman.barycenter(A, M, reg, weights) #%% plot interpolation -pl.figure(3,(10,5)) +pl.figure(3) -#pl.subplot(1,2,1) -cmap=pl.cm.get_cmap('viridis') +cmap = pl.cm.get_cmap('viridis') verts = [] -zs = alphalist -for i,z in enumerate(zs): - ys = B_l2[:,i] +zs = alpha_list +for i, z in enumerate(zs): + ys = B_l2[:, i] verts.append(list(zip(x, ys))) ax = pl.gcf().gca(projection='3d') -poly = PolyCollection(verts,facecolors=[cmap(a) for a in alphalist]) +poly = PolyCollection(verts, facecolors=[cmap(a) for a in alpha_list]) poly.set_alpha(0.7) ax.add_collection3d(poly, zs=zs, zdir='y') - ax.set_xlabel('x') ax.set_xlim3d(0, n) ax.set_ylabel('$\\alpha$') -ax.set_ylim3d(0,1) +ax.set_ylim3d(0, 1) ax.set_zlabel('') -ax.set_zlim3d(0, B_l2.max()*1.01) +ax.set_zlim3d(0, B_l2.max() * 1.01) pl.title('Barycenter interpolation with l2') +pl.tight_layout() -pl.show() - -pl.figure(4,(10,5)) - -#pl.subplot(1,2,1) -cmap=pl.cm.get_cmap('viridis') +pl.figure(4) +cmap = pl.cm.get_cmap('viridis') verts = [] -zs = alphalist -for i,z in enumerate(zs): - ys = B_wass[:,i] +zs = alpha_list +for i, z in enumerate(zs): + ys = B_wass[:, i] verts.append(list(zip(x, ys))) ax = pl.gcf().gca(projection='3d') -poly = PolyCollection(verts,facecolors=[cmap(a) for a in alphalist]) +poly = PolyCollection(verts, facecolors=[cmap(a) for a in alpha_list]) poly.set_alpha(0.7) ax.add_collection3d(poly, zs=zs, zdir='y') - ax.set_xlabel('x') ax.set_xlim3d(0, n) ax.set_ylabel('$\\alpha$') -ax.set_ylim3d(0,1) +ax.set_ylim3d(0, 1) ax.set_zlabel('') -ax.set_zlim3d(0, B_l2.max()*1.01) +ax.set_zlim3d(0, B_l2.max() * 1.01) pl.title('Barycenter interpolation with Wasserstein') +pl.tight_layout() -pl.show()
\ No newline at end of file +pl.show() diff --git a/docs/source/auto_examples/plot_barycenter_1D.rst b/docs/source/auto_examples/plot_barycenter_1D.rst index 1b15c77..413fae3 100644 --- a/docs/source/auto_examples/plot_barycenter_1D.rst +++ b/docs/source/auto_examples/plot_barycenter_1D.rst @@ -7,171 +7,230 @@ 1D Wasserstein barycenter demo ============================== +This example illustrates the computation of regularized Wassersyein Barycenter +as proposed in [3]. -@author: rflamary +[3] Benamou, J. D., Carlier, G., Cuturi, M., Nenna, L., & Peyré, G. (2015). +Iterative Bregman projections for regularized transportation problems +SIAM Journal on Scientific Computing, 37(2), A1111-A1138. -.. rst-class:: sphx-glr-horizontal +.. code-block:: python - * - .. image:: /auto_examples/images/sphx_glr_plot_barycenter_1D_001.png - :scale: 47 + # Author: Remi Flamary <remi.flamary@unice.fr> + # + # License: MIT License - * + import numpy as np + import matplotlib.pylab as pl + import ot + # necessary for 3d plot even if not used + from mpl_toolkits.mplot3d import Axes3D # noqa + from matplotlib.collections import PolyCollection - .. image:: /auto_examples/images/sphx_glr_plot_barycenter_1D_002.png - :scale: 47 - * - .. image:: /auto_examples/images/sphx_glr_plot_barycenter_1D_003.png - :scale: 47 - * - .. image:: /auto_examples/images/sphx_glr_plot_barycenter_1D_004.png - :scale: 47 +Generate data +------------- .. code-block:: python - import numpy as np - import matplotlib.pylab as pl - import ot - from mpl_toolkits.mplot3d import Axes3D #necessary for 3d plot even if not used - from matplotlib.collections import PolyCollection - - #%% parameters - n=100 # nb bins + n = 100 # nb bins # bin positions - x=np.arange(n,dtype=np.float64) + x = np.arange(n, dtype=np.float64) # Gaussian distributions - a1=ot.datasets.get_1D_gauss(n,m=20,s=5) # m= mean, s= std - a2=ot.datasets.get_1D_gauss(n,m=60,s=8) + a1 = ot.datasets.get_1D_gauss(n, m=20, s=5) # m= mean, s= std + a2 = ot.datasets.get_1D_gauss(n, m=60, s=8) # creating matrix A containing all distributions - A=np.vstack((a1,a2)).T - nbd=A.shape[1] + A = np.vstack((a1, a2)).T + n_distributions = A.shape[1] # loss matrix + normalization - M=ot.utils.dist0(n) - M/=M.max() + M = ot.utils.dist0(n) + M /= M.max() + + + + + + + +Plot data +--------- + + + +.. code-block:: python + #%% plot the distributions - pl.figure(1) - for i in range(nbd): - pl.plot(x,A[:,i]) + pl.figure(1, figsize=(6.4, 3)) + for i in range(n_distributions): + pl.plot(x, A[:, i]) pl.title('Distributions') + pl.tight_layout() + + + + +.. image:: /auto_examples/images/sphx_glr_plot_barycenter_1D_001.png + :align: center + + + + +Barycenter computation +---------------------- + + + +.. code-block:: python + #%% barycenter computation - alpha=0.2 # 0<=alpha<=1 - weights=np.array([1-alpha,alpha]) + alpha = 0.2 # 0<=alpha<=1 + weights = np.array([1 - alpha, alpha]) # l2bary - bary_l2=A.dot(weights) + bary_l2 = A.dot(weights) # wasserstein - reg=1e-3 - bary_wass=ot.bregman.barycenter(A,M,reg,weights) + reg = 1e-3 + bary_wass = ot.bregman.barycenter(A, M, reg, weights) pl.figure(2) pl.clf() - pl.subplot(2,1,1) - for i in range(nbd): - pl.plot(x,A[:,i]) + pl.subplot(2, 1, 1) + for i in range(n_distributions): + pl.plot(x, A[:, i]) pl.title('Distributions') - pl.subplot(2,1,2) - pl.plot(x,bary_l2,'r',label='l2') - pl.plot(x,bary_wass,'g',label='Wasserstein') + pl.subplot(2, 1, 2) + pl.plot(x, bary_l2, 'r', label='l2') + pl.plot(x, bary_wass, 'g', label='Wasserstein') pl.legend() pl.title('Barycenters') + pl.tight_layout() + + + + +.. image:: /auto_examples/images/sphx_glr_plot_barycenter_1D_003.png + :align: center + + + + +Barycentric interpolation +------------------------- + + + +.. code-block:: python #%% barycenter interpolation - nbalpha=11 - alphalist=np.linspace(0,1,nbalpha) + n_alpha = 11 + alpha_list = np.linspace(0, 1, n_alpha) - B_l2=np.zeros((n,nbalpha)) + B_l2 = np.zeros((n, n_alpha)) - B_wass=np.copy(B_l2) + B_wass = np.copy(B_l2) - for i in range(0,nbalpha): - alpha=alphalist[i] - weights=np.array([1-alpha,alpha]) - B_l2[:,i]=A.dot(weights) - B_wass[:,i]=ot.bregman.barycenter(A,M,reg,weights) + for i in range(0, n_alpha): + alpha = alpha_list[i] + weights = np.array([1 - alpha, alpha]) + B_l2[:, i] = A.dot(weights) + B_wass[:, i] = ot.bregman.barycenter(A, M, reg, weights) #%% plot interpolation - pl.figure(3,(10,5)) + pl.figure(3) - #pl.subplot(1,2,1) - cmap=pl.cm.get_cmap('viridis') + cmap = pl.cm.get_cmap('viridis') verts = [] - zs = alphalist - for i,z in enumerate(zs): - ys = B_l2[:,i] + zs = alpha_list + for i, z in enumerate(zs): + ys = B_l2[:, i] verts.append(list(zip(x, ys))) ax = pl.gcf().gca(projection='3d') - poly = PolyCollection(verts,facecolors=[cmap(a) for a in alphalist]) + poly = PolyCollection(verts, facecolors=[cmap(a) for a in alpha_list]) poly.set_alpha(0.7) ax.add_collection3d(poly, zs=zs, zdir='y') - ax.set_xlabel('x') ax.set_xlim3d(0, n) ax.set_ylabel('$\\alpha$') - ax.set_ylim3d(0,1) + ax.set_ylim3d(0, 1) ax.set_zlabel('') - ax.set_zlim3d(0, B_l2.max()*1.01) + ax.set_zlim3d(0, B_l2.max() * 1.01) pl.title('Barycenter interpolation with l2') + pl.tight_layout() - pl.show() - - pl.figure(4,(10,5)) - - #pl.subplot(1,2,1) - cmap=pl.cm.get_cmap('viridis') + pl.figure(4) + cmap = pl.cm.get_cmap('viridis') verts = [] - zs = alphalist - for i,z in enumerate(zs): - ys = B_wass[:,i] + zs = alpha_list + for i, z in enumerate(zs): + ys = B_wass[:, i] verts.append(list(zip(x, ys))) ax = pl.gcf().gca(projection='3d') - poly = PolyCollection(verts,facecolors=[cmap(a) for a in alphalist]) + poly = PolyCollection(verts, facecolors=[cmap(a) for a in alpha_list]) poly.set_alpha(0.7) ax.add_collection3d(poly, zs=zs, zdir='y') - ax.set_xlabel('x') ax.set_xlim3d(0, n) ax.set_ylabel('$\\alpha$') - ax.set_ylim3d(0,1) + ax.set_ylim3d(0, 1) ax.set_zlabel('') - ax.set_zlim3d(0, B_l2.max()*1.01) + ax.set_zlim3d(0, B_l2.max() * 1.01) pl.title('Barycenter interpolation with Wasserstein') + pl.tight_layout() pl.show() -**Total running time of the script:** ( 0 minutes 2.274 seconds) + + + +.. rst-class:: sphx-glr-horizontal + + + * + + .. image:: /auto_examples/images/sphx_glr_plot_barycenter_1D_005.png + :scale: 47 + + * + + .. image:: /auto_examples/images/sphx_glr_plot_barycenter_1D_006.png + :scale: 47 + + + + +**Total running time of the script:** ( 0 minutes 0.431 seconds) @@ -190,4 +249,4 @@ .. rst-class:: sphx-glr-signature - `Generated by Sphinx-Gallery <http://sphinx-gallery.readthedocs.io>`_ + `Generated by Sphinx-Gallery <https://sphinx-gallery.readthedocs.io>`_ diff --git a/docs/source/auto_examples/plot_compute_emd.ipynb b/docs/source/auto_examples/plot_compute_emd.ipynb index 4162144..b9b8bc5 100644 --- a/docs/source/auto_examples/plot_compute_emd.ipynb +++ b/docs/source/auto_examples/plot_compute_emd.ipynb @@ -15,7 +15,7 @@ }, { "source": [ - "\n# 1D optimal transport\n\n\n@author: rflamary\n\n" + "\n# Plot multiple EMD\n\n\nShows how to compute multiple EMD and Sinkhorn with two differnt\nground metrics and plot their values for diffeent distributions.\n\n\n\n" ], "cell_type": "markdown", "metadata": {} @@ -24,7 +24,79 @@ "execution_count": null, "cell_type": "code", "source": [ - "import numpy as np\nimport matplotlib.pylab as pl\nimport ot\nfrom ot.datasets import get_1D_gauss as gauss\n\n\n#%% parameters\n\nn=100 # nb bins\nn_target=50 # nb target distributions\n\n\n# bin positions\nx=np.arange(n,dtype=np.float64)\n\nlst_m=np.linspace(20,90,n_target)\n\n# Gaussian distributions\na=gauss(n,m=20,s=5) # m= mean, s= std\n\nB=np.zeros((n,n_target))\n\nfor i,m in enumerate(lst_m):\n B[:,i]=gauss(n,m=m,s=5)\n\n# loss matrix and normalization\nM=ot.dist(x.reshape((n,1)),x.reshape((n,1)),'euclidean')\nM/=M.max()\nM2=ot.dist(x.reshape((n,1)),x.reshape((n,1)),'sqeuclidean')\nM2/=M2.max()\n#%% plot the distributions\n\npl.figure(1)\npl.subplot(2,1,1)\npl.plot(x,a,'b',label='Source distribution')\npl.title('Source distribution')\npl.subplot(2,1,2)\npl.plot(x,B,label='Target distributions')\npl.title('Target distributions')\n\n#%% Compute and plot distributions and loss matrix\n\nd_emd=ot.emd2(a,B,M) # direct computation of EMD\nd_emd2=ot.emd2(a,B,M2) # direct computation of EMD with loss M3\n\n\npl.figure(2)\npl.plot(d_emd,label='Euclidean EMD')\npl.plot(d_emd2,label='Squared Euclidean EMD')\npl.title('EMD distances')\npl.legend()\n\n#%%\nreg=1e-2\nd_sinkhorn=ot.sinkhorn(a,B,M,reg)\nd_sinkhorn2=ot.sinkhorn(a,B,M2,reg)\n\npl.figure(2)\npl.clf()\npl.plot(d_emd,label='Euclidean EMD')\npl.plot(d_emd2,label='Squared Euclidean EMD')\npl.plot(d_sinkhorn,'+',label='Euclidean Sinkhorn')\npl.plot(d_sinkhorn2,'+',label='Squared Euclidean Sinkhorn')\npl.title('EMD distances')\npl.legend()" + "# Author: Remi Flamary <remi.flamary@unice.fr>\n#\n# License: MIT License\n\nimport numpy as np\nimport matplotlib.pylab as pl\nimport ot\nfrom ot.datasets import get_1D_gauss as gauss" + ], + "outputs": [], + "metadata": { + "collapsed": false + } + }, + { + "source": [ + "Generate data\n-------------\n\n" + ], + "cell_type": "markdown", + "metadata": {} + }, + { + "execution_count": null, + "cell_type": "code", + "source": [ + "#%% parameters\n\nn = 100 # nb bins\nn_target = 50 # nb target distributions\n\n\n# bin positions\nx = np.arange(n, dtype=np.float64)\n\nlst_m = np.linspace(20, 90, n_target)\n\n# Gaussian distributions\na = gauss(n, m=20, s=5) # m= mean, s= std\n\nB = np.zeros((n, n_target))\n\nfor i, m in enumerate(lst_m):\n B[:, i] = gauss(n, m=m, s=5)\n\n# loss matrix and normalization\nM = ot.dist(x.reshape((n, 1)), x.reshape((n, 1)), 'euclidean')\nM /= M.max()\nM2 = ot.dist(x.reshape((n, 1)), x.reshape((n, 1)), 'sqeuclidean')\nM2 /= M2.max()" + ], + "outputs": [], + "metadata": { + "collapsed": false + } + }, + { + "source": [ + "Plot data\n---------\n\n" + ], + "cell_type": "markdown", + "metadata": {} + }, + { + "execution_count": null, + "cell_type": "code", + "source": [ + "#%% plot the distributions\n\npl.figure(1)\npl.subplot(2, 1, 1)\npl.plot(x, a, 'b', label='Source distribution')\npl.title('Source distribution')\npl.subplot(2, 1, 2)\npl.plot(x, B, label='Target distributions')\npl.title('Target distributions')\npl.tight_layout()" + ], + "outputs": [], + "metadata": { + "collapsed": false + } + }, + { + "source": [ + "Compute EMD for the different losses\n------------------------------------\n\n" + ], + "cell_type": "markdown", + "metadata": {} + }, + { + "execution_count": null, + "cell_type": "code", + "source": [ + "#%% Compute and plot distributions and loss matrix\n\nd_emd = ot.emd2(a, B, M) # direct computation of EMD\nd_emd2 = ot.emd2(a, B, M2) # direct computation of EMD with loss M2\n\n\npl.figure(2)\npl.plot(d_emd, label='Euclidean EMD')\npl.plot(d_emd2, label='Squared Euclidean EMD')\npl.title('EMD distances')\npl.legend()" + ], + "outputs": [], + "metadata": { + "collapsed": false + } + }, + { + "source": [ + "Compute Sinkhorn for the different losses\n-----------------------------------------\n\n" + ], + "cell_type": "markdown", + "metadata": {} + }, + { + "execution_count": null, + "cell_type": "code", + "source": [ + "#%%\nreg = 1e-2\nd_sinkhorn = ot.sinkhorn2(a, B, M, reg)\nd_sinkhorn2 = ot.sinkhorn2(a, B, M2, reg)\n\npl.figure(2)\npl.clf()\npl.plot(d_emd, label='Euclidean EMD')\npl.plot(d_emd2, label='Squared Euclidean EMD')\npl.plot(d_sinkhorn, '+', label='Euclidean Sinkhorn')\npl.plot(d_sinkhorn2, '+', label='Squared Euclidean Sinkhorn')\npl.title('EMD distances')\npl.legend()\n\npl.show()" ], "outputs": [], "metadata": { diff --git a/docs/source/auto_examples/plot_compute_emd.py b/docs/source/auto_examples/plot_compute_emd.py index c7063e8..73b42c3 100644 --- a/docs/source/auto_examples/plot_compute_emd.py +++ b/docs/source/auto_examples/plot_compute_emd.py @@ -1,74 +1,102 @@ # -*- coding: utf-8 -*- """ -==================== -1D optimal transport -==================== +================= +Plot multiple EMD +================= + +Shows how to compute multiple EMD and Sinkhorn with two differnt +ground metrics and plot their values for diffeent distributions. + -@author: rflamary """ +# Author: Remi Flamary <remi.flamary@unice.fr> +# +# License: MIT License + import numpy as np import matplotlib.pylab as pl import ot from ot.datasets import get_1D_gauss as gauss +############################################################################## +# Generate data +# ------------- + #%% parameters -n=100 # nb bins -n_target=50 # nb target distributions +n = 100 # nb bins +n_target = 50 # nb target distributions # bin positions -x=np.arange(n,dtype=np.float64) +x = np.arange(n, dtype=np.float64) -lst_m=np.linspace(20,90,n_target) +lst_m = np.linspace(20, 90, n_target) # Gaussian distributions -a=gauss(n,m=20,s=5) # m= mean, s= std +a = gauss(n, m=20, s=5) # m= mean, s= std -B=np.zeros((n,n_target)) +B = np.zeros((n, n_target)) -for i,m in enumerate(lst_m): - B[:,i]=gauss(n,m=m,s=5) +for i, m in enumerate(lst_m): + B[:, i] = gauss(n, m=m, s=5) # loss matrix and normalization -M=ot.dist(x.reshape((n,1)),x.reshape((n,1)),'euclidean') -M/=M.max() -M2=ot.dist(x.reshape((n,1)),x.reshape((n,1)),'sqeuclidean') -M2/=M2.max() +M = ot.dist(x.reshape((n, 1)), x.reshape((n, 1)), 'euclidean') +M /= M.max() +M2 = ot.dist(x.reshape((n, 1)), x.reshape((n, 1)), 'sqeuclidean') +M2 /= M2.max() + +############################################################################## +# Plot data +# --------- + #%% plot the distributions pl.figure(1) -pl.subplot(2,1,1) -pl.plot(x,a,'b',label='Source distribution') +pl.subplot(2, 1, 1) +pl.plot(x, a, 'b', label='Source distribution') pl.title('Source distribution') -pl.subplot(2,1,2) -pl.plot(x,B,label='Target distributions') +pl.subplot(2, 1, 2) +pl.plot(x, B, label='Target distributions') pl.title('Target distributions') +pl.tight_layout() + + +############################################################################## +# Compute EMD for the different losses +# ------------------------------------ #%% Compute and plot distributions and loss matrix -d_emd=ot.emd2(a,B,M) # direct computation of EMD -d_emd2=ot.emd2(a,B,M2) # direct computation of EMD with loss M3 +d_emd = ot.emd2(a, B, M) # direct computation of EMD +d_emd2 = ot.emd2(a, B, M2) # direct computation of EMD with loss M2 pl.figure(2) -pl.plot(d_emd,label='Euclidean EMD') -pl.plot(d_emd2,label='Squared Euclidean EMD') +pl.plot(d_emd, label='Euclidean EMD') +pl.plot(d_emd2, label='Squared Euclidean EMD') pl.title('EMD distances') pl.legend() +############################################################################## +# Compute Sinkhorn for the different losses +# ----------------------------------------- + #%% -reg=1e-2 -d_sinkhorn=ot.sinkhorn(a,B,M,reg) -d_sinkhorn2=ot.sinkhorn(a,B,M2,reg) +reg = 1e-2 +d_sinkhorn = ot.sinkhorn2(a, B, M, reg) +d_sinkhorn2 = ot.sinkhorn2(a, B, M2, reg) pl.figure(2) pl.clf() -pl.plot(d_emd,label='Euclidean EMD') -pl.plot(d_emd2,label='Squared Euclidean EMD') -pl.plot(d_sinkhorn,'+',label='Euclidean Sinkhorn') -pl.plot(d_sinkhorn2,'+',label='Squared Euclidean Sinkhorn') +pl.plot(d_emd, label='Euclidean EMD') +pl.plot(d_emd2, label='Squared Euclidean EMD') +pl.plot(d_sinkhorn, '+', label='Euclidean Sinkhorn') +pl.plot(d_sinkhorn2, '+', label='Squared Euclidean Sinkhorn') pl.title('EMD distances') -pl.legend()
\ No newline at end of file +pl.legend() + +pl.show() diff --git a/docs/source/auto_examples/plot_compute_emd.rst b/docs/source/auto_examples/plot_compute_emd.rst index 4c7445b..ce79e20 100644 --- a/docs/source/auto_examples/plot_compute_emd.rst +++ b/docs/source/auto_examples/plot_compute_emd.rst @@ -3,101 +3,166 @@ .. _sphx_glr_auto_examples_plot_compute_emd.py: -==================== -1D optimal transport -==================== +================= +Plot multiple EMD +================= -@author: rflamary +Shows how to compute multiple EMD and Sinkhorn with two differnt +ground metrics and plot their values for diffeent distributions. -.. rst-class:: sphx-glr-horizontal +.. code-block:: python - * - .. image:: /auto_examples/images/sphx_glr_plot_compute_emd_001.png - :scale: 47 + # Author: Remi Flamary <remi.flamary@unice.fr> + # + # License: MIT License - * + import numpy as np + import matplotlib.pylab as pl + import ot + from ot.datasets import get_1D_gauss as gauss - .. image:: /auto_examples/images/sphx_glr_plot_compute_emd_002.png - :scale: 47 -.. code-block:: python - import numpy as np - import matplotlib.pylab as pl - import ot - from ot.datasets import get_1D_gauss as gauss +Generate data +------------- + + + +.. code-block:: python #%% parameters - n=100 # nb bins - n_target=50 # nb target distributions + n = 100 # nb bins + n_target = 50 # nb target distributions # bin positions - x=np.arange(n,dtype=np.float64) + x = np.arange(n, dtype=np.float64) - lst_m=np.linspace(20,90,n_target) + lst_m = np.linspace(20, 90, n_target) # Gaussian distributions - a=gauss(n,m=20,s=5) # m= mean, s= std + a = gauss(n, m=20, s=5) # m= mean, s= std - B=np.zeros((n,n_target)) + B = np.zeros((n, n_target)) - for i,m in enumerate(lst_m): - B[:,i]=gauss(n,m=m,s=5) + for i, m in enumerate(lst_m): + B[:, i] = gauss(n, m=m, s=5) # loss matrix and normalization - M=ot.dist(x.reshape((n,1)),x.reshape((n,1)),'euclidean') - M/=M.max() - M2=ot.dist(x.reshape((n,1)),x.reshape((n,1)),'sqeuclidean') - M2/=M2.max() + M = ot.dist(x.reshape((n, 1)), x.reshape((n, 1)), 'euclidean') + M /= M.max() + M2 = ot.dist(x.reshape((n, 1)), x.reshape((n, 1)), 'sqeuclidean') + M2 /= M2.max() + + + + + + + +Plot data +--------- + + + +.. code-block:: python + + #%% plot the distributions pl.figure(1) - pl.subplot(2,1,1) - pl.plot(x,a,'b',label='Source distribution') + pl.subplot(2, 1, 1) + pl.plot(x, a, 'b', label='Source distribution') pl.title('Source distribution') - pl.subplot(2,1,2) - pl.plot(x,B,label='Target distributions') + pl.subplot(2, 1, 2) + pl.plot(x, B, label='Target distributions') pl.title('Target distributions') + pl.tight_layout() + + + + + +.. image:: /auto_examples/images/sphx_glr_plot_compute_emd_001.png + :align: center + + + + +Compute EMD for the different losses +------------------------------------ + + + +.. code-block:: python + #%% Compute and plot distributions and loss matrix - d_emd=ot.emd2(a,B,M) # direct computation of EMD - d_emd2=ot.emd2(a,B,M2) # direct computation of EMD with loss M3 + d_emd = ot.emd2(a, B, M) # direct computation of EMD + d_emd2 = ot.emd2(a, B, M2) # direct computation of EMD with loss M2 pl.figure(2) - pl.plot(d_emd,label='Euclidean EMD') - pl.plot(d_emd2,label='Squared Euclidean EMD') + pl.plot(d_emd, label='Euclidean EMD') + pl.plot(d_emd2, label='Squared Euclidean EMD') pl.title('EMD distances') pl.legend() + + + +.. image:: /auto_examples/images/sphx_glr_plot_compute_emd_003.png + :align: center + + + + +Compute Sinkhorn for the different losses +----------------------------------------- + + + +.. code-block:: python + + #%% - reg=1e-2 - d_sinkhorn=ot.sinkhorn(a,B,M,reg) - d_sinkhorn2=ot.sinkhorn(a,B,M2,reg) + reg = 1e-2 + d_sinkhorn = ot.sinkhorn2(a, B, M, reg) + d_sinkhorn2 = ot.sinkhorn2(a, B, M2, reg) pl.figure(2) pl.clf() - pl.plot(d_emd,label='Euclidean EMD') - pl.plot(d_emd2,label='Squared Euclidean EMD') - pl.plot(d_sinkhorn,'+',label='Euclidean Sinkhorn') - pl.plot(d_sinkhorn2,'+',label='Squared Euclidean Sinkhorn') + pl.plot(d_emd, label='Euclidean EMD') + pl.plot(d_emd2, label='Squared Euclidean EMD') + pl.plot(d_sinkhorn, '+', label='Euclidean Sinkhorn') + pl.plot(d_sinkhorn2, '+', label='Squared Euclidean Sinkhorn') pl.title('EMD distances') pl.legend() -**Total running time of the script:** ( 0 minutes 0.521 seconds) + + pl.show() + + + +.. image:: /auto_examples/images/sphx_glr_plot_compute_emd_004.png + :align: center + + + + +**Total running time of the script:** ( 0 minutes 0.441 seconds) @@ -116,4 +181,4 @@ .. rst-class:: sphx-glr-signature - `Generated by Sphinx-Gallery <http://sphinx-gallery.readthedocs.io>`_ + `Generated by Sphinx-Gallery <https://sphinx-gallery.readthedocs.io>`_ diff --git a/docs/source/auto_examples/plot_optim_OTreg.ipynb b/docs/source/auto_examples/plot_optim_OTreg.ipynb index 5ded922..333331b 100644 --- a/docs/source/auto_examples/plot_optim_OTreg.ipynb +++ b/docs/source/auto_examples/plot_optim_OTreg.ipynb @@ -15,7 +15,7 @@ }, { "source": [ - "\n# Regularized OT with generic solver\n\n\n\n\n" + "\n# Regularized OT with generic solver\n\n\nIllustrates the use of the generic solver for regularized OT with\nuser-designed regularization term. It uses Conditional gradient as in [6] and\ngeneralized Conditional Gradient as proposed in [5][7].\n\n\n[5] N. Courty; R. Flamary; D. Tuia; A. Rakotomamonjy, Optimal Transport for\nDomain Adaptation, in IEEE Transactions on Pattern Analysis and Machine\nIntelligence , vol.PP, no.99, pp.1-1.\n\n[6] Ferradans, S., Papadakis, N., Peyr\u00e9, G., & Aujol, J. F. (2014).\nRegularized discrete optimal transport. SIAM Journal on Imaging Sciences,\n7(3), 1853-1882.\n\n[7] Rakotomamonjy, A., Flamary, R., & Courty, N. (2015). Generalized\nconditional gradient: analysis of convergence and applications.\narXiv preprint arXiv:1510.06567.\n\n\n\n\n" ], "cell_type": "markdown", "metadata": {} @@ -24,7 +24,97 @@ "execution_count": null, "cell_type": "code", "source": [ - "import numpy as np\nimport matplotlib.pylab as pl\nimport ot\n\n\n\n#%% parameters\n\nn=100 # nb bins\n\n# bin positions\nx=np.arange(n,dtype=np.float64)\n\n# Gaussian distributions\na=ot.datasets.get_1D_gauss(n,m=20,s=5) # m= mean, s= std\nb=ot.datasets.get_1D_gauss(n,m=60,s=10)\n\n# loss matrix\nM=ot.dist(x.reshape((n,1)),x.reshape((n,1)))\nM/=M.max()\n\n#%% EMD\n\nG0=ot.emd(a,b,M)\n\npl.figure(3)\not.plot.plot1D_mat(a,b,G0,'OT matrix G0')\n\n#%% Example with Frobenius norm regularization\n\ndef f(G): return 0.5*np.sum(G**2)\ndef df(G): return G\n\nreg=1e-1\n\nGl2=ot.optim.cg(a,b,M,reg,f,df,verbose=True)\n\npl.figure(3)\not.plot.plot1D_mat(a,b,Gl2,'OT matrix Frob. reg')\n\n#%% Example with entropic regularization\n\ndef f(G): return np.sum(G*np.log(G))\ndef df(G): return np.log(G)+1\n\nreg=1e-3\n\nGe=ot.optim.cg(a,b,M,reg,f,df,verbose=True)\n\npl.figure(4)\not.plot.plot1D_mat(a,b,Ge,'OT matrix Entrop. reg')\n\n#%% Example with Frobenius norm + entropic regularization with gcg\n\ndef f(G): return 0.5*np.sum(G**2)\ndef df(G): return G\n\nreg1=1e-3\nreg2=1e-1\n\nGel2=ot.optim.gcg(a,b,M,reg1,reg2,f,df,verbose=True)\n\npl.figure(5)\not.plot.plot1D_mat(a,b,Gel2,'OT entropic + matrix Frob. reg')\npl.show()" + "import numpy as np\nimport matplotlib.pylab as pl\nimport ot" + ], + "outputs": [], + "metadata": { + "collapsed": false + } + }, + { + "source": [ + "Generate data\n-------------\n\n" + ], + "cell_type": "markdown", + "metadata": {} + }, + { + "execution_count": null, + "cell_type": "code", + "source": [ + "#%% parameters\n\nn = 100 # nb bins\n\n# bin positions\nx = np.arange(n, dtype=np.float64)\n\n# Gaussian distributions\na = ot.datasets.get_1D_gauss(n, m=20, s=5) # m= mean, s= std\nb = ot.datasets.get_1D_gauss(n, m=60, s=10)\n\n# loss matrix\nM = ot.dist(x.reshape((n, 1)), x.reshape((n, 1)))\nM /= M.max()" + ], + "outputs": [], + "metadata": { + "collapsed": false + } + }, + { + "source": [ + "Solve EMD\n---------\n\n" + ], + "cell_type": "markdown", + "metadata": {} + }, + { + "execution_count": null, + "cell_type": "code", + "source": [ + "#%% EMD\n\nG0 = ot.emd(a, b, M)\n\npl.figure(3, figsize=(5, 5))\not.plot.plot1D_mat(a, b, G0, 'OT matrix G0')" + ], + "outputs": [], + "metadata": { + "collapsed": false + } + }, + { + "source": [ + "Solve EMD with Frobenius norm regularization\n--------------------------------------------\n\n" + ], + "cell_type": "markdown", + "metadata": {} + }, + { + "execution_count": null, + "cell_type": "code", + "source": [ + "#%% Example with Frobenius norm regularization\n\n\ndef f(G):\n return 0.5 * np.sum(G**2)\n\n\ndef df(G):\n return G\n\n\nreg = 1e-1\n\nGl2 = ot.optim.cg(a, b, M, reg, f, df, verbose=True)\n\npl.figure(3)\not.plot.plot1D_mat(a, b, Gl2, 'OT matrix Frob. reg')" + ], + "outputs": [], + "metadata": { + "collapsed": false + } + }, + { + "source": [ + "Solve EMD with entropic regularization\n--------------------------------------\n\n" + ], + "cell_type": "markdown", + "metadata": {} + }, + { + "execution_count": null, + "cell_type": "code", + "source": [ + "#%% Example with entropic regularization\n\n\ndef f(G):\n return np.sum(G * np.log(G))\n\n\ndef df(G):\n return np.log(G) + 1.\n\n\nreg = 1e-3\n\nGe = ot.optim.cg(a, b, M, reg, f, df, verbose=True)\n\npl.figure(4, figsize=(5, 5))\not.plot.plot1D_mat(a, b, Ge, 'OT matrix Entrop. reg')" + ], + "outputs": [], + "metadata": { + "collapsed": false + } + }, + { + "source": [ + "Solve EMD with Frobenius norm + entropic regularization\n-------------------------------------------------------\n\n" + ], + "cell_type": "markdown", + "metadata": {} + }, + { + "execution_count": null, + "cell_type": "code", + "source": [ + "#%% Example with Frobenius norm + entropic regularization with gcg\n\n\ndef f(G):\n return 0.5 * np.sum(G**2)\n\n\ndef df(G):\n return G\n\n\nreg1 = 1e-3\nreg2 = 1e-1\n\nGel2 = ot.optim.gcg(a, b, M, reg1, reg2, f, df, verbose=True)\n\npl.figure(5, figsize=(5, 5))\not.plot.plot1D_mat(a, b, Gel2, 'OT entropic + matrix Frob. reg')\npl.show()" ], "outputs": [], "metadata": { diff --git a/docs/source/auto_examples/plot_optim_OTreg.py b/docs/source/auto_examples/plot_optim_OTreg.py index 8abb426..e1a737e 100644 --- a/docs/source/auto_examples/plot_optim_OTreg.py +++ b/docs/source/auto_examples/plot_optim_OTreg.py @@ -4,6 +4,24 @@ Regularized OT with generic solver ================================== +Illustrates the use of the generic solver for regularized OT with +user-designed regularization term. It uses Conditional gradient as in [6] and +generalized Conditional Gradient as proposed in [5][7]. + + +[5] N. Courty; R. Flamary; D. Tuia; A. Rakotomamonjy, Optimal Transport for +Domain Adaptation, in IEEE Transactions on Pattern Analysis and Machine +Intelligence , vol.PP, no.99, pp.1-1. + +[6] Ferradans, S., Papadakis, N., Peyré, G., & Aujol, J. F. (2014). +Regularized discrete optimal transport. SIAM Journal on Imaging Sciences, +7(3), 1853-1882. + +[7] Rakotomamonjy, A., Flamary, R., & Courty, N. (2015). Generalized +conditional gradient: analysis of convergence and applications. +arXiv preprint arXiv:1510.06567. + + """ @@ -12,63 +30,100 @@ import matplotlib.pylab as pl import ot +############################################################################## +# Generate data +# ------------- #%% parameters -n=100 # nb bins +n = 100 # nb bins # bin positions -x=np.arange(n,dtype=np.float64) +x = np.arange(n, dtype=np.float64) # Gaussian distributions -a=ot.datasets.get_1D_gauss(n,m=20,s=5) # m= mean, s= std -b=ot.datasets.get_1D_gauss(n,m=60,s=10) +a = ot.datasets.get_1D_gauss(n, m=20, s=5) # m= mean, s= std +b = ot.datasets.get_1D_gauss(n, m=60, s=10) # loss matrix -M=ot.dist(x.reshape((n,1)),x.reshape((n,1))) -M/=M.max() +M = ot.dist(x.reshape((n, 1)), x.reshape((n, 1))) +M /= M.max() + +############################################################################## +# Solve EMD +# --------- #%% EMD -G0=ot.emd(a,b,M) +G0 = ot.emd(a, b, M) -pl.figure(3) -ot.plot.plot1D_mat(a,b,G0,'OT matrix G0') +pl.figure(3, figsize=(5, 5)) +ot.plot.plot1D_mat(a, b, G0, 'OT matrix G0') + +############################################################################## +# Solve EMD with Frobenius norm regularization +# -------------------------------------------- #%% Example with Frobenius norm regularization -def f(G): return 0.5*np.sum(G**2) -def df(G): return G -reg=1e-1 +def f(G): + return 0.5 * np.sum(G**2) + + +def df(G): + return G + -Gl2=ot.optim.cg(a,b,M,reg,f,df,verbose=True) +reg = 1e-1 + +Gl2 = ot.optim.cg(a, b, M, reg, f, df, verbose=True) pl.figure(3) -ot.plot.plot1D_mat(a,b,Gl2,'OT matrix Frob. reg') +ot.plot.plot1D_mat(a, b, Gl2, 'OT matrix Frob. reg') + +############################################################################## +# Solve EMD with entropic regularization +# -------------------------------------- #%% Example with entropic regularization -def f(G): return np.sum(G*np.log(G)) -def df(G): return np.log(G)+1 -reg=1e-3 +def f(G): + return np.sum(G * np.log(G)) + + +def df(G): + return np.log(G) + 1. + + +reg = 1e-3 -Ge=ot.optim.cg(a,b,M,reg,f,df,verbose=True) +Ge = ot.optim.cg(a, b, M, reg, f, df, verbose=True) -pl.figure(4) -ot.plot.plot1D_mat(a,b,Ge,'OT matrix Entrop. reg') +pl.figure(4, figsize=(5, 5)) +ot.plot.plot1D_mat(a, b, Ge, 'OT matrix Entrop. reg') + +############################################################################## +# Solve EMD with Frobenius norm + entropic regularization +# ------------------------------------------------------- #%% Example with Frobenius norm + entropic regularization with gcg -def f(G): return 0.5*np.sum(G**2) -def df(G): return G -reg1=1e-3 -reg2=1e-1 +def f(G): + return 0.5 * np.sum(G**2) + + +def df(G): + return G + + +reg1 = 1e-3 +reg2 = 1e-1 -Gel2=ot.optim.gcg(a,b,M,reg1,reg2,f,df,verbose=True) +Gel2 = ot.optim.gcg(a, b, M, reg1, reg2, f, df, verbose=True) -pl.figure(5) -ot.plot.plot1D_mat(a,b,Gel2,'OT entropic + matrix Frob. reg') -pl.show()
\ No newline at end of file +pl.figure(5, figsize=(5, 5)) +ot.plot.plot1D_mat(a, b, Gel2, 'OT entropic + matrix Frob. reg') +pl.show() diff --git a/docs/source/auto_examples/plot_optim_OTreg.rst b/docs/source/auto_examples/plot_optim_OTreg.rst index 70cd26c..f628024 100644 --- a/docs/source/auto_examples/plot_optim_OTreg.rst +++ b/docs/source/auto_examples/plot_optim_OTreg.rst @@ -7,28 +7,126 @@ Regularized OT with generic solver ================================== +Illustrates the use of the generic solver for regularized OT with +user-designed regularization term. It uses Conditional gradient as in [6] and +generalized Conditional Gradient as proposed in [5][7]. +[5] N. Courty; R. Flamary; D. Tuia; A. Rakotomamonjy, Optimal Transport for +Domain Adaptation, in IEEE Transactions on Pattern Analysis and Machine +Intelligence , vol.PP, no.99, pp.1-1. +[6] Ferradans, S., Papadakis, N., Peyré, G., & Aujol, J. F. (2014). +Regularized discrete optimal transport. SIAM Journal on Imaging Sciences, +7(3), 1853-1882. +[7] Rakotomamonjy, A., Flamary, R., & Courty, N. (2015). Generalized +conditional gradient: analysis of convergence and applications. +arXiv preprint arXiv:1510.06567. -.. rst-class:: sphx-glr-horizontal - * - .. image:: /auto_examples/images/sphx_glr_plot_optim_OTreg_003.png - :scale: 47 - * - .. image:: /auto_examples/images/sphx_glr_plot_optim_OTreg_004.png - :scale: 47 +.. code-block:: python + + + import numpy as np + import matplotlib.pylab as pl + import ot + + + + + + + + +Generate data +------------- + + + +.. code-block:: python + + + #%% parameters + + n = 100 # nb bins + + # bin positions + x = np.arange(n, dtype=np.float64) + + # Gaussian distributions + a = ot.datasets.get_1D_gauss(n, m=20, s=5) # m= mean, s= std + b = ot.datasets.get_1D_gauss(n, m=60, s=10) + + # loss matrix + M = ot.dist(x.reshape((n, 1)), x.reshape((n, 1))) + M /= M.max() + + + + + + + +Solve EMD +--------- + + + +.. code-block:: python + + + #%% EMD + + G0 = ot.emd(a, b, M) + + pl.figure(3, figsize=(5, 5)) + ot.plot.plot1D_mat(a, b, G0, 'OT matrix G0') + + + + +.. image:: /auto_examples/images/sphx_glr_plot_optim_OTreg_003.png + :align: center + + + + +Solve EMD with Frobenius norm regularization +-------------------------------------------- + + + +.. code-block:: python + + + #%% Example with Frobenius norm regularization + + + def f(G): + return 0.5 * np.sum(G**2) + + + def df(G): + return G + + + reg = 1e-1 + + Gl2 = ot.optim.cg(a, b, M, reg, f, df, verbose=True) + + pl.figure(3) + ot.plot.plot1D_mat(a, b, Gl2, 'OT matrix Frob. reg') - * - .. image:: /auto_examples/images/sphx_glr_plot_optim_OTreg_005.png - :scale: 47 + + +.. image:: /auto_examples/images/sphx_glr_plot_optim_OTreg_004.png + :align: center .. rst-class:: sphx-glr-script-out @@ -258,6 +356,45 @@ Regularized OT with generic solver It. |Loss |Delta loss -------------------------------- 200|1.663543e-01|-8.737134e-08 + + +Solve EMD with entropic regularization +-------------------------------------- + + + +.. code-block:: python + + + #%% Example with entropic regularization + + + def f(G): + return np.sum(G * np.log(G)) + + + def df(G): + return np.log(G) + 1. + + + reg = 1e-3 + + Ge = ot.optim.cg(a, b, M, reg, f, df, verbose=True) + + pl.figure(4, figsize=(5, 5)) + ot.plot.plot1D_mat(a, b, Ge, 'OT matrix Entrop. reg') + + + + +.. image:: /auto_examples/images/sphx_glr_plot_optim_OTreg_006.png + :align: center + + +.. rst-class:: sphx-glr-script-out + + Out:: + It. |Loss |Delta loss -------------------------------- 0|1.692289e-01|0.000000e+00 @@ -481,89 +618,56 @@ Regularized OT with generic solver It. |Loss |Delta loss -------------------------------- 200|1.607143e-01|-2.151971e-10 - It. |Loss |Delta loss - -------------------------------- - 0|1.693084e-01|0.000000e+00 - 1|1.610121e-01|-5.152589e-02 - 2|1.609378e-01|-4.622297e-04 - 3|1.609284e-01|-5.830043e-05 - 4|1.609284e-01|-1.111580e-12 - +Solve EMD with Frobenius norm + entropic regularization +------------------------------------------------------- -| .. code-block:: python - import numpy as np - import matplotlib.pylab as pl - import ot - - - - #%% parameters - - n=100 # nb bins - - # bin positions - x=np.arange(n,dtype=np.float64) - - # Gaussian distributions - a=ot.datasets.get_1D_gauss(n,m=20,s=5) # m= mean, s= std - b=ot.datasets.get_1D_gauss(n,m=60,s=10) - - # loss matrix - M=ot.dist(x.reshape((n,1)),x.reshape((n,1))) - M/=M.max() - - #%% EMD + #%% Example with Frobenius norm + entropic regularization with gcg - G0=ot.emd(a,b,M) - pl.figure(3) - ot.plot.plot1D_mat(a,b,G0,'OT matrix G0') + def f(G): + return 0.5 * np.sum(G**2) - #%% Example with Frobenius norm regularization - def f(G): return 0.5*np.sum(G**2) - def df(G): return G + def df(G): + return G - reg=1e-1 - Gl2=ot.optim.cg(a,b,M,reg,f,df,verbose=True) + reg1 = 1e-3 + reg2 = 1e-1 - pl.figure(3) - ot.plot.plot1D_mat(a,b,Gl2,'OT matrix Frob. reg') + Gel2 = ot.optim.gcg(a, b, M, reg1, reg2, f, df, verbose=True) - #%% Example with entropic regularization + pl.figure(5, figsize=(5, 5)) + ot.plot.plot1D_mat(a, b, Gel2, 'OT entropic + matrix Frob. reg') + pl.show() - def f(G): return np.sum(G*np.log(G)) - def df(G): return np.log(G)+1 - reg=1e-3 - Ge=ot.optim.cg(a,b,M,reg,f,df,verbose=True) +.. image:: /auto_examples/images/sphx_glr_plot_optim_OTreg_008.png + :align: center - pl.figure(4) - ot.plot.plot1D_mat(a,b,Ge,'OT matrix Entrop. reg') - #%% Example with Frobenius norm + entropic regularization with gcg +.. rst-class:: sphx-glr-script-out - def f(G): return 0.5*np.sum(G**2) - def df(G): return G + Out:: - reg1=1e-3 - reg2=1e-1 + It. |Loss |Delta loss + -------------------------------- + 0|1.693084e-01|0.000000e+00 + 1|1.610121e-01|-5.152589e-02 + 2|1.609378e-01|-4.622297e-04 + 3|1.609284e-01|-5.830043e-05 + 4|1.609284e-01|-1.111407e-12 - Gel2=ot.optim.gcg(a,b,M,reg1,reg2,f,df,verbose=True) - pl.figure(5) - ot.plot.plot1D_mat(a,b,Gel2,'OT entropic + matrix Frob. reg') - pl.show() -**Total running time of the script:** ( 0 minutes 2.319 seconds) +**Total running time of the script:** ( 0 minutes 1.809 seconds) @@ -582,4 +686,4 @@ Regularized OT with generic solver .. rst-class:: sphx-glr-signature - `Generated by Sphinx-Gallery <http://sphinx-gallery.readthedocs.io>`_ + `Generated by Sphinx-Gallery <https://sphinx-gallery.readthedocs.io>`_ diff --git a/docs/source/auto_examples/plot_otda_classes.ipynb b/docs/source/auto_examples/plot_otda_classes.ipynb new file mode 100644 index 0000000..6754fa5 --- /dev/null +++ b/docs/source/auto_examples/plot_otda_classes.ipynb @@ -0,0 +1,126 @@ +{ + "nbformat_minor": 0, + "nbformat": 4, + "cells": [ + { + "execution_count": null, + "cell_type": "code", + "source": [ + "%matplotlib inline" + ], + "outputs": [], + "metadata": { + "collapsed": false + } + }, + { + "source": [ + "\n# OT for domain adaptation\n\n\nThis example introduces a domain adaptation in a 2D setting and the 4 OTDA\napproaches currently supported in POT.\n\n\n" + ], + "cell_type": "markdown", + "metadata": {} + }, + { + "execution_count": null, + "cell_type": "code", + "source": [ + "# Authors: Remi Flamary <remi.flamary@unice.fr>\n# Stanislas Chambon <stan.chambon@gmail.com>\n#\n# License: MIT License\n\nimport matplotlib.pylab as pl\nimport ot" + ], + "outputs": [], + "metadata": { + "collapsed": false + } + }, + { + "source": [ + "Generate data\n-------------\n\n" + ], + "cell_type": "markdown", + "metadata": {} + }, + { + "execution_count": null, + "cell_type": "code", + "source": [ + "n_source_samples = 150\nn_target_samples = 150\n\nXs, ys = ot.datasets.get_data_classif('3gauss', n_source_samples)\nXt, yt = ot.datasets.get_data_classif('3gauss2', n_target_samples)" + ], + "outputs": [], + "metadata": { + "collapsed": false + } + }, + { + "source": [ + "Instantiate the different transport algorithms and fit them\n-----------------------------------------------------------\n\n" + ], + "cell_type": "markdown", + "metadata": {} + }, + { + "execution_count": null, + "cell_type": "code", + "source": [ + "# EMD Transport\not_emd = ot.da.EMDTransport()\not_emd.fit(Xs=Xs, Xt=Xt)\n\n# Sinkhorn Transport\not_sinkhorn = ot.da.SinkhornTransport(reg_e=1e-1)\not_sinkhorn.fit(Xs=Xs, Xt=Xt)\n\n# Sinkhorn Transport with Group lasso regularization\not_lpl1 = ot.da.SinkhornLpl1Transport(reg_e=1e-1, reg_cl=1e0)\not_lpl1.fit(Xs=Xs, ys=ys, Xt=Xt)\n\n# Sinkhorn Transport with Group lasso regularization l1l2\not_l1l2 = ot.da.SinkhornL1l2Transport(reg_e=1e-1, reg_cl=2e0, max_iter=20,\n verbose=True)\not_l1l2.fit(Xs=Xs, ys=ys, Xt=Xt)\n\n# transport source samples onto target samples\ntransp_Xs_emd = ot_emd.transform(Xs=Xs)\ntransp_Xs_sinkhorn = ot_sinkhorn.transform(Xs=Xs)\ntransp_Xs_lpl1 = ot_lpl1.transform(Xs=Xs)\ntransp_Xs_l1l2 = ot_l1l2.transform(Xs=Xs)" + ], + "outputs": [], + "metadata": { + "collapsed": false + } + }, + { + "source": [ + "Fig 1 : plots source and target samples\n---------------------------------------\n\n" + ], + "cell_type": "markdown", + "metadata": {} + }, + { + "execution_count": null, + "cell_type": "code", + "source": [ + "pl.figure(1, figsize=(10, 5))\npl.subplot(1, 2, 1)\npl.scatter(Xs[:, 0], Xs[:, 1], c=ys, marker='+', label='Source samples')\npl.xticks([])\npl.yticks([])\npl.legend(loc=0)\npl.title('Source samples')\n\npl.subplot(1, 2, 2)\npl.scatter(Xt[:, 0], Xt[:, 1], c=yt, marker='o', label='Target samples')\npl.xticks([])\npl.yticks([])\npl.legend(loc=0)\npl.title('Target samples')\npl.tight_layout()" + ], + "outputs": [], + "metadata": { + "collapsed": false + } + }, + { + "source": [ + "Fig 2 : plot optimal couplings and transported samples\n------------------------------------------------------\n\n" + ], + "cell_type": "markdown", + "metadata": {} + }, + { + "execution_count": null, + "cell_type": "code", + "source": [ + "param_img = {'interpolation': 'nearest', 'cmap': 'spectral'}\n\npl.figure(2, figsize=(15, 8))\npl.subplot(2, 4, 1)\npl.imshow(ot_emd.coupling_, **param_img)\npl.xticks([])\npl.yticks([])\npl.title('Optimal coupling\\nEMDTransport')\n\npl.subplot(2, 4, 2)\npl.imshow(ot_sinkhorn.coupling_, **param_img)\npl.xticks([])\npl.yticks([])\npl.title('Optimal coupling\\nSinkhornTransport')\n\npl.subplot(2, 4, 3)\npl.imshow(ot_lpl1.coupling_, **param_img)\npl.xticks([])\npl.yticks([])\npl.title('Optimal coupling\\nSinkhornLpl1Transport')\n\npl.subplot(2, 4, 4)\npl.imshow(ot_l1l2.coupling_, **param_img)\npl.xticks([])\npl.yticks([])\npl.title('Optimal coupling\\nSinkhornL1l2Transport')\n\npl.subplot(2, 4, 5)\npl.scatter(Xt[:, 0], Xt[:, 1], c=yt, marker='o',\n label='Target samples', alpha=0.3)\npl.scatter(transp_Xs_emd[:, 0], transp_Xs_emd[:, 1], c=ys,\n marker='+', label='Transp samples', s=30)\npl.xticks([])\npl.yticks([])\npl.title('Transported samples\\nEmdTransport')\npl.legend(loc=\"lower left\")\n\npl.subplot(2, 4, 6)\npl.scatter(Xt[:, 0], Xt[:, 1], c=yt, marker='o',\n label='Target samples', alpha=0.3)\npl.scatter(transp_Xs_sinkhorn[:, 0], transp_Xs_sinkhorn[:, 1], c=ys,\n marker='+', label='Transp samples', s=30)\npl.xticks([])\npl.yticks([])\npl.title('Transported samples\\nSinkhornTransport')\n\npl.subplot(2, 4, 7)\npl.scatter(Xt[:, 0], Xt[:, 1], c=yt, marker='o',\n label='Target samples', alpha=0.3)\npl.scatter(transp_Xs_lpl1[:, 0], transp_Xs_lpl1[:, 1], c=ys,\n marker='+', label='Transp samples', s=30)\npl.xticks([])\npl.yticks([])\npl.title('Transported samples\\nSinkhornLpl1Transport')\n\npl.subplot(2, 4, 8)\npl.scatter(Xt[:, 0], Xt[:, 1], c=yt, marker='o',\n label='Target samples', alpha=0.3)\npl.scatter(transp_Xs_l1l2[:, 0], transp_Xs_l1l2[:, 1], c=ys,\n marker='+', label='Transp samples', s=30)\npl.xticks([])\npl.yticks([])\npl.title('Transported samples\\nSinkhornL1l2Transport')\npl.tight_layout()\n\npl.show()" + ], + "outputs": [], + "metadata": { + "collapsed": false + } + } + ], + "metadata": { + "kernelspec": { + "display_name": "Python 2", + "name": "python2", + "language": "python" + }, + "language_info": { + "mimetype": "text/x-python", + "nbconvert_exporter": "python", + "name": "python", + "file_extension": ".py", + "version": "2.7.12", + "pygments_lexer": "ipython2", + "codemirror_mode": { + "version": 2, + "name": "ipython" + } + } + } +}
\ No newline at end of file diff --git a/docs/source/auto_examples/plot_otda_classes.py b/docs/source/auto_examples/plot_otda_classes.py new file mode 100644 index 0000000..b14c11a --- /dev/null +++ b/docs/source/auto_examples/plot_otda_classes.py @@ -0,0 +1,150 @@ +# -*- coding: utf-8 -*- +""" +======================== +OT for domain adaptation +======================== + +This example introduces a domain adaptation in a 2D setting and the 4 OTDA +approaches currently supported in POT. + +""" + +# Authors: Remi Flamary <remi.flamary@unice.fr> +# Stanislas Chambon <stan.chambon@gmail.com> +# +# License: MIT License + +import matplotlib.pylab as pl +import ot + + +############################################################################## +# Generate data +# ------------- + +n_source_samples = 150 +n_target_samples = 150 + +Xs, ys = ot.datasets.get_data_classif('3gauss', n_source_samples) +Xt, yt = ot.datasets.get_data_classif('3gauss2', n_target_samples) + + +############################################################################## +# Instantiate the different transport algorithms and fit them +# ----------------------------------------------------------- + +# EMD Transport +ot_emd = ot.da.EMDTransport() +ot_emd.fit(Xs=Xs, Xt=Xt) + +# Sinkhorn Transport +ot_sinkhorn = ot.da.SinkhornTransport(reg_e=1e-1) +ot_sinkhorn.fit(Xs=Xs, Xt=Xt) + +# Sinkhorn Transport with Group lasso regularization +ot_lpl1 = ot.da.SinkhornLpl1Transport(reg_e=1e-1, reg_cl=1e0) +ot_lpl1.fit(Xs=Xs, ys=ys, Xt=Xt) + +# Sinkhorn Transport with Group lasso regularization l1l2 +ot_l1l2 = ot.da.SinkhornL1l2Transport(reg_e=1e-1, reg_cl=2e0, max_iter=20, + verbose=True) +ot_l1l2.fit(Xs=Xs, ys=ys, Xt=Xt) + +# transport source samples onto target samples +transp_Xs_emd = ot_emd.transform(Xs=Xs) +transp_Xs_sinkhorn = ot_sinkhorn.transform(Xs=Xs) +transp_Xs_lpl1 = ot_lpl1.transform(Xs=Xs) +transp_Xs_l1l2 = ot_l1l2.transform(Xs=Xs) + + +############################################################################## +# Fig 1 : plots source and target samples +# --------------------------------------- + +pl.figure(1, figsize=(10, 5)) +pl.subplot(1, 2, 1) +pl.scatter(Xs[:, 0], Xs[:, 1], c=ys, marker='+', label='Source samples') +pl.xticks([]) +pl.yticks([]) +pl.legend(loc=0) +pl.title('Source samples') + +pl.subplot(1, 2, 2) +pl.scatter(Xt[:, 0], Xt[:, 1], c=yt, marker='o', label='Target samples') +pl.xticks([]) +pl.yticks([]) +pl.legend(loc=0) +pl.title('Target samples') +pl.tight_layout() + + +############################################################################## +# Fig 2 : plot optimal couplings and transported samples +# ------------------------------------------------------ + +param_img = {'interpolation': 'nearest', 'cmap': 'spectral'} + +pl.figure(2, figsize=(15, 8)) +pl.subplot(2, 4, 1) +pl.imshow(ot_emd.coupling_, **param_img) +pl.xticks([]) +pl.yticks([]) +pl.title('Optimal coupling\nEMDTransport') + +pl.subplot(2, 4, 2) +pl.imshow(ot_sinkhorn.coupling_, **param_img) +pl.xticks([]) +pl.yticks([]) +pl.title('Optimal coupling\nSinkhornTransport') + +pl.subplot(2, 4, 3) +pl.imshow(ot_lpl1.coupling_, **param_img) +pl.xticks([]) +pl.yticks([]) +pl.title('Optimal coupling\nSinkhornLpl1Transport') + +pl.subplot(2, 4, 4) +pl.imshow(ot_l1l2.coupling_, **param_img) +pl.xticks([]) +pl.yticks([]) +pl.title('Optimal coupling\nSinkhornL1l2Transport') + +pl.subplot(2, 4, 5) +pl.scatter(Xt[:, 0], Xt[:, 1], c=yt, marker='o', + label='Target samples', alpha=0.3) +pl.scatter(transp_Xs_emd[:, 0], transp_Xs_emd[:, 1], c=ys, + marker='+', label='Transp samples', s=30) +pl.xticks([]) +pl.yticks([]) +pl.title('Transported samples\nEmdTransport') +pl.legend(loc="lower left") + +pl.subplot(2, 4, 6) +pl.scatter(Xt[:, 0], Xt[:, 1], c=yt, marker='o', + label='Target samples', alpha=0.3) +pl.scatter(transp_Xs_sinkhorn[:, 0], transp_Xs_sinkhorn[:, 1], c=ys, + marker='+', label='Transp samples', s=30) +pl.xticks([]) +pl.yticks([]) +pl.title('Transported samples\nSinkhornTransport') + +pl.subplot(2, 4, 7) +pl.scatter(Xt[:, 0], Xt[:, 1], c=yt, marker='o', + label='Target samples', alpha=0.3) +pl.scatter(transp_Xs_lpl1[:, 0], transp_Xs_lpl1[:, 1], c=ys, + marker='+', label='Transp samples', s=30) +pl.xticks([]) +pl.yticks([]) +pl.title('Transported samples\nSinkhornLpl1Transport') + +pl.subplot(2, 4, 8) +pl.scatter(Xt[:, 0], Xt[:, 1], c=yt, marker='o', + label='Target samples', alpha=0.3) +pl.scatter(transp_Xs_l1l2[:, 0], transp_Xs_l1l2[:, 1], c=ys, + marker='+', label='Transp samples', s=30) +pl.xticks([]) +pl.yticks([]) +pl.title('Transported samples\nSinkhornL1l2Transport') +pl.tight_layout() + +pl.show() diff --git a/docs/source/auto_examples/plot_otda_classes.rst b/docs/source/auto_examples/plot_otda_classes.rst new file mode 100644 index 0000000..f19a99f --- /dev/null +++ b/docs/source/auto_examples/plot_otda_classes.rst @@ -0,0 +1,258 @@ + + +.. _sphx_glr_auto_examples_plot_otda_classes.py: + + +======================== +OT for domain adaptation +======================== + +This example introduces a domain adaptation in a 2D setting and the 4 OTDA +approaches currently supported in POT. + + + + +.. code-block:: python + + + # Authors: Remi Flamary <remi.flamary@unice.fr> + # Stanislas Chambon <stan.chambon@gmail.com> + # + # License: MIT License + + import matplotlib.pylab as pl + import ot + + + + + + + + +Generate data +------------- + + + +.. code-block:: python + + + n_source_samples = 150 + n_target_samples = 150 + + Xs, ys = ot.datasets.get_data_classif('3gauss', n_source_samples) + Xt, yt = ot.datasets.get_data_classif('3gauss2', n_target_samples) + + + + + + + + +Instantiate the different transport algorithms and fit them +----------------------------------------------------------- + + + +.. code-block:: python + + + # EMD Transport + ot_emd = ot.da.EMDTransport() + ot_emd.fit(Xs=Xs, Xt=Xt) + + # Sinkhorn Transport + ot_sinkhorn = ot.da.SinkhornTransport(reg_e=1e-1) + ot_sinkhorn.fit(Xs=Xs, Xt=Xt) + + # Sinkhorn Transport with Group lasso regularization + ot_lpl1 = ot.da.SinkhornLpl1Transport(reg_e=1e-1, reg_cl=1e0) + ot_lpl1.fit(Xs=Xs, ys=ys, Xt=Xt) + + # Sinkhorn Transport with Group lasso regularization l1l2 + ot_l1l2 = ot.da.SinkhornL1l2Transport(reg_e=1e-1, reg_cl=2e0, max_iter=20, + verbose=True) + ot_l1l2.fit(Xs=Xs, ys=ys, Xt=Xt) + + # transport source samples onto target samples + transp_Xs_emd = ot_emd.transform(Xs=Xs) + transp_Xs_sinkhorn = ot_sinkhorn.transform(Xs=Xs) + transp_Xs_lpl1 = ot_lpl1.transform(Xs=Xs) + transp_Xs_l1l2 = ot_l1l2.transform(Xs=Xs) + + + + + + +.. rst-class:: sphx-glr-script-out + + Out:: + + It. |Loss |Delta loss + -------------------------------- + 0|9.552437e+00|0.000000e+00 + 1|1.921833e+00|-3.970483e+00 + 2|1.671022e+00|-1.500942e-01 + 3|1.615147e+00|-3.459458e-02 + 4|1.594289e+00|-1.308252e-02 + 5|1.587287e+00|-4.411254e-03 + 6|1.581665e+00|-3.554702e-03 + 7|1.577022e+00|-2.943809e-03 + 8|1.573870e+00|-2.002870e-03 + 9|1.571645e+00|-1.415696e-03 + 10|1.569342e+00|-1.467590e-03 + 11|1.567863e+00|-9.432233e-04 + 12|1.566558e+00|-8.329769e-04 + 13|1.565414e+00|-7.311320e-04 + 14|1.564425e+00|-6.319985e-04 + 15|1.563955e+00|-3.007604e-04 + 16|1.563658e+00|-1.894627e-04 + 17|1.562886e+00|-4.941143e-04 + 18|1.562578e+00|-1.974031e-04 + 19|1.562445e+00|-8.468825e-05 + It. |Loss |Delta loss + -------------------------------- + 20|1.562007e+00|-2.805136e-04 + + +Fig 1 : plots source and target samples +--------------------------------------- + + + +.. code-block:: python + + + pl.figure(1, figsize=(10, 5)) + pl.subplot(1, 2, 1) + pl.scatter(Xs[:, 0], Xs[:, 1], c=ys, marker='+', label='Source samples') + pl.xticks([]) + pl.yticks([]) + pl.legend(loc=0) + pl.title('Source samples') + + pl.subplot(1, 2, 2) + pl.scatter(Xt[:, 0], Xt[:, 1], c=yt, marker='o', label='Target samples') + pl.xticks([]) + pl.yticks([]) + pl.legend(loc=0) + pl.title('Target samples') + pl.tight_layout() + + + + + +.. image:: /auto_examples/images/sphx_glr_plot_otda_classes_001.png + :align: center + + + + +Fig 2 : plot optimal couplings and transported samples +------------------------------------------------------ + + + +.. code-block:: python + + + param_img = {'interpolation': 'nearest', 'cmap': 'spectral'} + + pl.figure(2, figsize=(15, 8)) + pl.subplot(2, 4, 1) + pl.imshow(ot_emd.coupling_, **param_img) + pl.xticks([]) + pl.yticks([]) + pl.title('Optimal coupling\nEMDTransport') + + pl.subplot(2, 4, 2) + pl.imshow(ot_sinkhorn.coupling_, **param_img) + pl.xticks([]) + pl.yticks([]) + pl.title('Optimal coupling\nSinkhornTransport') + + pl.subplot(2, 4, 3) + pl.imshow(ot_lpl1.coupling_, **param_img) + pl.xticks([]) + pl.yticks([]) + pl.title('Optimal coupling\nSinkhornLpl1Transport') + + pl.subplot(2, 4, 4) + pl.imshow(ot_l1l2.coupling_, **param_img) + pl.xticks([]) + pl.yticks([]) + pl.title('Optimal coupling\nSinkhornL1l2Transport') + + pl.subplot(2, 4, 5) + pl.scatter(Xt[:, 0], Xt[:, 1], c=yt, marker='o', + label='Target samples', alpha=0.3) + pl.scatter(transp_Xs_emd[:, 0], transp_Xs_emd[:, 1], c=ys, + marker='+', label='Transp samples', s=30) + pl.xticks([]) + pl.yticks([]) + pl.title('Transported samples\nEmdTransport') + pl.legend(loc="lower left") + + pl.subplot(2, 4, 6) + pl.scatter(Xt[:, 0], Xt[:, 1], c=yt, marker='o', + label='Target samples', alpha=0.3) + pl.scatter(transp_Xs_sinkhorn[:, 0], transp_Xs_sinkhorn[:, 1], c=ys, + marker='+', label='Transp samples', s=30) + pl.xticks([]) + pl.yticks([]) + pl.title('Transported samples\nSinkhornTransport') + + pl.subplot(2, 4, 7) + pl.scatter(Xt[:, 0], Xt[:, 1], c=yt, marker='o', + label='Target samples', alpha=0.3) + pl.scatter(transp_Xs_lpl1[:, 0], transp_Xs_lpl1[:, 1], c=ys, + marker='+', label='Transp samples', s=30) + pl.xticks([]) + pl.yticks([]) + pl.title('Transported samples\nSinkhornLpl1Transport') + + pl.subplot(2, 4, 8) + pl.scatter(Xt[:, 0], Xt[:, 1], c=yt, marker='o', + label='Target samples', alpha=0.3) + pl.scatter(transp_Xs_l1l2[:, 0], transp_Xs_l1l2[:, 1], c=ys, + marker='+', label='Transp samples', s=30) + pl.xticks([]) + pl.yticks([]) + pl.title('Transported samples\nSinkhornL1l2Transport') + pl.tight_layout() + + pl.show() + + + +.. image:: /auto_examples/images/sphx_glr_plot_otda_classes_003.png + :align: center + + + + +**Total running time of the script:** ( 0 minutes 1.596 seconds) + + + +.. container:: sphx-glr-footer + + + .. container:: sphx-glr-download + + :download:`Download Python source code: plot_otda_classes.py <plot_otda_classes.py>` + + + + .. container:: sphx-glr-download + + :download:`Download Jupyter notebook: plot_otda_classes.ipynb <plot_otda_classes.ipynb>` + +.. rst-class:: sphx-glr-signature + + `Generated by Sphinx-Gallery <https://sphinx-gallery.readthedocs.io>`_ diff --git a/docs/source/auto_examples/plot_otda_color_images.ipynb b/docs/source/auto_examples/plot_otda_color_images.ipynb new file mode 100644 index 0000000..2daf406 --- /dev/null +++ b/docs/source/auto_examples/plot_otda_color_images.ipynb @@ -0,0 +1,144 @@ +{ + "nbformat_minor": 0, + "nbformat": 4, + "cells": [ + { + "execution_count": null, + "cell_type": "code", + "source": [ + "%matplotlib inline" + ], + "outputs": [], + "metadata": { + "collapsed": false + } + }, + { + "source": [ + "\n# OT for image color adaptation\n\n\nThis example presents a way of transferring colors between two image\nwith Optimal Transport as introduced in [6]\n\n[6] Ferradans, S., Papadakis, N., Peyre, G., & Aujol, J. F. (2014).\nRegularized discrete optimal transport.\nSIAM Journal on Imaging Sciences, 7(3), 1853-1882.\n\n" + ], + "cell_type": "markdown", + "metadata": {} + }, + { + "execution_count": null, + "cell_type": "code", + "source": [ + "# Authors: Remi Flamary <remi.flamary@unice.fr>\n# Stanislas Chambon <stan.chambon@gmail.com>\n#\n# License: MIT License\n\nimport numpy as np\nfrom scipy import ndimage\nimport matplotlib.pylab as pl\nimport ot\n\n\nr = np.random.RandomState(42)\n\n\ndef im2mat(I):\n \"\"\"Converts and image to matrix (one pixel per line)\"\"\"\n return I.reshape((I.shape[0] * I.shape[1], I.shape[2]))\n\n\ndef mat2im(X, shape):\n \"\"\"Converts back a matrix to an image\"\"\"\n return X.reshape(shape)\n\n\ndef minmax(I):\n return np.clip(I, 0, 1)" + ], + "outputs": [], + "metadata": { + "collapsed": false + } + }, + { + "source": [ + "Generate data\n-------------\n\n" + ], + "cell_type": "markdown", + "metadata": {} + }, + { + "execution_count": null, + "cell_type": "code", + "source": [ + "# Loading images\nI1 = ndimage.imread('../data/ocean_day.jpg').astype(np.float64) / 256\nI2 = ndimage.imread('../data/ocean_sunset.jpg').astype(np.float64) / 256\n\nX1 = im2mat(I1)\nX2 = im2mat(I2)\n\n# training samples\nnb = 1000\nidx1 = r.randint(X1.shape[0], size=(nb,))\nidx2 = r.randint(X2.shape[0], size=(nb,))\n\nXs = X1[idx1, :]\nXt = X2[idx2, :]" + ], + "outputs": [], + "metadata": { + "collapsed": false + } + }, + { + "source": [ + "Plot original image\n-------------------\n\n" + ], + "cell_type": "markdown", + "metadata": {} + }, + { + "execution_count": null, + "cell_type": "code", + "source": [ + "pl.figure(1, figsize=(6.4, 3))\n\npl.subplot(1, 2, 1)\npl.imshow(I1)\npl.axis('off')\npl.title('Image 1')\n\npl.subplot(1, 2, 2)\npl.imshow(I2)\npl.axis('off')\npl.title('Image 2')" + ], + "outputs": [], + "metadata": { + "collapsed": false + } + }, + { + "source": [ + "Scatter plot of colors\n----------------------\n\n" + ], + "cell_type": "markdown", + "metadata": {} + }, + { + "execution_count": null, + "cell_type": "code", + "source": [ + "pl.figure(2, figsize=(6.4, 3))\n\npl.subplot(1, 2, 1)\npl.scatter(Xs[:, 0], Xs[:, 2], c=Xs)\npl.axis([0, 1, 0, 1])\npl.xlabel('Red')\npl.ylabel('Blue')\npl.title('Image 1')\n\npl.subplot(1, 2, 2)\npl.scatter(Xt[:, 0], Xt[:, 2], c=Xt)\npl.axis([0, 1, 0, 1])\npl.xlabel('Red')\npl.ylabel('Blue')\npl.title('Image 2')\npl.tight_layout()" + ], + "outputs": [], + "metadata": { + "collapsed": false + } + }, + { + "source": [ + "Instantiate the different transport algorithms and fit them\n-----------------------------------------------------------\n\n" + ], + "cell_type": "markdown", + "metadata": {} + }, + { + "execution_count": null, + "cell_type": "code", + "source": [ + "# EMDTransport\not_emd = ot.da.EMDTransport()\not_emd.fit(Xs=Xs, Xt=Xt)\n\n# SinkhornTransport\not_sinkhorn = ot.da.SinkhornTransport(reg_e=1e-1)\not_sinkhorn.fit(Xs=Xs, Xt=Xt)\n\n# prediction between images (using out of sample prediction as in [6])\ntransp_Xs_emd = ot_emd.transform(Xs=X1)\ntransp_Xt_emd = ot_emd.inverse_transform(Xt=X2)\n\ntransp_Xs_sinkhorn = ot_emd.transform(Xs=X1)\ntransp_Xt_sinkhorn = ot_emd.inverse_transform(Xt=X2)\n\nI1t = minmax(mat2im(transp_Xs_emd, I1.shape))\nI2t = minmax(mat2im(transp_Xt_emd, I2.shape))\n\nI1te = minmax(mat2im(transp_Xs_sinkhorn, I1.shape))\nI2te = minmax(mat2im(transp_Xt_sinkhorn, I2.shape))" + ], + "outputs": [], + "metadata": { + "collapsed": false + } + }, + { + "source": [ + "Plot new images\n---------------\n\n" + ], + "cell_type": "markdown", + "metadata": {} + }, + { + "execution_count": null, + "cell_type": "code", + "source": [ + "pl.figure(3, figsize=(8, 4))\n\npl.subplot(2, 3, 1)\npl.imshow(I1)\npl.axis('off')\npl.title('Image 1')\n\npl.subplot(2, 3, 2)\npl.imshow(I1t)\npl.axis('off')\npl.title('Image 1 Adapt')\n\npl.subplot(2, 3, 3)\npl.imshow(I1te)\npl.axis('off')\npl.title('Image 1 Adapt (reg)')\n\npl.subplot(2, 3, 4)\npl.imshow(I2)\npl.axis('off')\npl.title('Image 2')\n\npl.subplot(2, 3, 5)\npl.imshow(I2t)\npl.axis('off')\npl.title('Image 2 Adapt')\n\npl.subplot(2, 3, 6)\npl.imshow(I2te)\npl.axis('off')\npl.title('Image 2 Adapt (reg)')\npl.tight_layout()\n\npl.show()" + ], + "outputs": [], + "metadata": { + "collapsed": false + } + } + ], + "metadata": { + "kernelspec": { + "display_name": "Python 2", + "name": "python2", + "language": "python" + }, + "language_info": { + "mimetype": "text/x-python", + "nbconvert_exporter": "python", + "name": "python", + "file_extension": ".py", + "version": "2.7.12", + "pygments_lexer": "ipython2", + "codemirror_mode": { + "version": 2, + "name": "ipython" + } + } + } +}
\ No newline at end of file diff --git a/docs/source/auto_examples/plot_otda_color_images.py b/docs/source/auto_examples/plot_otda_color_images.py new file mode 100644 index 0000000..e77aec0 --- /dev/null +++ b/docs/source/auto_examples/plot_otda_color_images.py @@ -0,0 +1,165 @@ +# -*- coding: utf-8 -*- +""" +============================= +OT for image color adaptation +============================= + +This example presents a way of transferring colors between two image +with Optimal Transport as introduced in [6] + +[6] Ferradans, S., Papadakis, N., Peyre, G., & Aujol, J. F. (2014). +Regularized discrete optimal transport. +SIAM Journal on Imaging Sciences, 7(3), 1853-1882. +""" + +# Authors: Remi Flamary <remi.flamary@unice.fr> +# Stanislas Chambon <stan.chambon@gmail.com> +# +# License: MIT License + +import numpy as np +from scipy import ndimage +import matplotlib.pylab as pl +import ot + + +r = np.random.RandomState(42) + + +def im2mat(I): + """Converts and image to matrix (one pixel per line)""" + return I.reshape((I.shape[0] * I.shape[1], I.shape[2])) + + +def mat2im(X, shape): + """Converts back a matrix to an image""" + return X.reshape(shape) + + +def minmax(I): + return np.clip(I, 0, 1) + + +############################################################################## +# Generate data +# ------------- + +# Loading images +I1 = ndimage.imread('../data/ocean_day.jpg').astype(np.float64) / 256 +I2 = ndimage.imread('../data/ocean_sunset.jpg').astype(np.float64) / 256 + +X1 = im2mat(I1) +X2 = im2mat(I2) + +# training samples +nb = 1000 +idx1 = r.randint(X1.shape[0], size=(nb,)) +idx2 = r.randint(X2.shape[0], size=(nb,)) + +Xs = X1[idx1, :] +Xt = X2[idx2, :] + + +############################################################################## +# Plot original image +# ------------------- + +pl.figure(1, figsize=(6.4, 3)) + +pl.subplot(1, 2, 1) +pl.imshow(I1) +pl.axis('off') +pl.title('Image 1') + +pl.subplot(1, 2, 2) +pl.imshow(I2) +pl.axis('off') +pl.title('Image 2') + + +############################################################################## +# Scatter plot of colors +# ---------------------- + +pl.figure(2, figsize=(6.4, 3)) + +pl.subplot(1, 2, 1) +pl.scatter(Xs[:, 0], Xs[:, 2], c=Xs) +pl.axis([0, 1, 0, 1]) +pl.xlabel('Red') +pl.ylabel('Blue') +pl.title('Image 1') + +pl.subplot(1, 2, 2) +pl.scatter(Xt[:, 0], Xt[:, 2], c=Xt) +pl.axis([0, 1, 0, 1]) +pl.xlabel('Red') +pl.ylabel('Blue') +pl.title('Image 2') +pl.tight_layout() + + +############################################################################## +# Instantiate the different transport algorithms and fit them +# ----------------------------------------------------------- + +# EMDTransport +ot_emd = ot.da.EMDTransport() +ot_emd.fit(Xs=Xs, Xt=Xt) + +# SinkhornTransport +ot_sinkhorn = ot.da.SinkhornTransport(reg_e=1e-1) +ot_sinkhorn.fit(Xs=Xs, Xt=Xt) + +# prediction between images (using out of sample prediction as in [6]) +transp_Xs_emd = ot_emd.transform(Xs=X1) +transp_Xt_emd = ot_emd.inverse_transform(Xt=X2) + +transp_Xs_sinkhorn = ot_emd.transform(Xs=X1) +transp_Xt_sinkhorn = ot_emd.inverse_transform(Xt=X2) + +I1t = minmax(mat2im(transp_Xs_emd, I1.shape)) +I2t = minmax(mat2im(transp_Xt_emd, I2.shape)) + +I1te = minmax(mat2im(transp_Xs_sinkhorn, I1.shape)) +I2te = minmax(mat2im(transp_Xt_sinkhorn, I2.shape)) + + +############################################################################## +# Plot new images +# --------------- + +pl.figure(3, figsize=(8, 4)) + +pl.subplot(2, 3, 1) +pl.imshow(I1) +pl.axis('off') +pl.title('Image 1') + +pl.subplot(2, 3, 2) +pl.imshow(I1t) +pl.axis('off') +pl.title('Image 1 Adapt') + +pl.subplot(2, 3, 3) +pl.imshow(I1te) +pl.axis('off') +pl.title('Image 1 Adapt (reg)') + +pl.subplot(2, 3, 4) +pl.imshow(I2) +pl.axis('off') +pl.title('Image 2') + +pl.subplot(2, 3, 5) +pl.imshow(I2t) +pl.axis('off') +pl.title('Image 2 Adapt') + +pl.subplot(2, 3, 6) +pl.imshow(I2te) +pl.axis('off') +pl.title('Image 2 Adapt (reg)') +pl.tight_layout() + +pl.show() diff --git a/docs/source/auto_examples/plot_otda_color_images.rst b/docs/source/auto_examples/plot_otda_color_images.rst new file mode 100644 index 0000000..4772bed --- /dev/null +++ b/docs/source/auto_examples/plot_otda_color_images.rst @@ -0,0 +1,257 @@ + + +.. _sphx_glr_auto_examples_plot_otda_color_images.py: + + +============================= +OT for image color adaptation +============================= + +This example presents a way of transferring colors between two image +with Optimal Transport as introduced in [6] + +[6] Ferradans, S., Papadakis, N., Peyre, G., & Aujol, J. F. (2014). +Regularized discrete optimal transport. +SIAM Journal on Imaging Sciences, 7(3), 1853-1882. + + + +.. code-block:: python + + + # Authors: Remi Flamary <remi.flamary@unice.fr> + # Stanislas Chambon <stan.chambon@gmail.com> + # + # License: MIT License + + import numpy as np + from scipy import ndimage + import matplotlib.pylab as pl + import ot + + + r = np.random.RandomState(42) + + + def im2mat(I): + """Converts and image to matrix (one pixel per line)""" + return I.reshape((I.shape[0] * I.shape[1], I.shape[2])) + + + def mat2im(X, shape): + """Converts back a matrix to an image""" + return X.reshape(shape) + + + def minmax(I): + return np.clip(I, 0, 1) + + + + + + + + +Generate data +------------- + + + +.. code-block:: python + + + # Loading images + I1 = ndimage.imread('../data/ocean_day.jpg').astype(np.float64) / 256 + I2 = ndimage.imread('../data/ocean_sunset.jpg').astype(np.float64) / 256 + + X1 = im2mat(I1) + X2 = im2mat(I2) + + # training samples + nb = 1000 + idx1 = r.randint(X1.shape[0], size=(nb,)) + idx2 = r.randint(X2.shape[0], size=(nb,)) + + Xs = X1[idx1, :] + Xt = X2[idx2, :] + + + + + + + + +Plot original image +------------------- + + + +.. code-block:: python + + + pl.figure(1, figsize=(6.4, 3)) + + pl.subplot(1, 2, 1) + pl.imshow(I1) + pl.axis('off') + pl.title('Image 1') + + pl.subplot(1, 2, 2) + pl.imshow(I2) + pl.axis('off') + pl.title('Image 2') + + + + + +.. image:: /auto_examples/images/sphx_glr_plot_otda_color_images_001.png + :align: center + + + + +Scatter plot of colors +---------------------- + + + +.. code-block:: python + + + pl.figure(2, figsize=(6.4, 3)) + + pl.subplot(1, 2, 1) + pl.scatter(Xs[:, 0], Xs[:, 2], c=Xs) + pl.axis([0, 1, 0, 1]) + pl.xlabel('Red') + pl.ylabel('Blue') + pl.title('Image 1') + + pl.subplot(1, 2, 2) + pl.scatter(Xt[:, 0], Xt[:, 2], c=Xt) + pl.axis([0, 1, 0, 1]) + pl.xlabel('Red') + pl.ylabel('Blue') + pl.title('Image 2') + pl.tight_layout() + + + + + +.. image:: /auto_examples/images/sphx_glr_plot_otda_color_images_003.png + :align: center + + + + +Instantiate the different transport algorithms and fit them +----------------------------------------------------------- + + + +.. code-block:: python + + + # EMDTransport + ot_emd = ot.da.EMDTransport() + ot_emd.fit(Xs=Xs, Xt=Xt) + + # SinkhornTransport + ot_sinkhorn = ot.da.SinkhornTransport(reg_e=1e-1) + ot_sinkhorn.fit(Xs=Xs, Xt=Xt) + + # prediction between images (using out of sample prediction as in [6]) + transp_Xs_emd = ot_emd.transform(Xs=X1) + transp_Xt_emd = ot_emd.inverse_transform(Xt=X2) + + transp_Xs_sinkhorn = ot_emd.transform(Xs=X1) + transp_Xt_sinkhorn = ot_emd.inverse_transform(Xt=X2) + + I1t = minmax(mat2im(transp_Xs_emd, I1.shape)) + I2t = minmax(mat2im(transp_Xt_emd, I2.shape)) + + I1te = minmax(mat2im(transp_Xs_sinkhorn, I1.shape)) + I2te = minmax(mat2im(transp_Xt_sinkhorn, I2.shape)) + + + + + + + + +Plot new images +--------------- + + + +.. code-block:: python + + + pl.figure(3, figsize=(8, 4)) + + pl.subplot(2, 3, 1) + pl.imshow(I1) + pl.axis('off') + pl.title('Image 1') + + pl.subplot(2, 3, 2) + pl.imshow(I1t) + pl.axis('off') + pl.title('Image 1 Adapt') + + pl.subplot(2, 3, 3) + pl.imshow(I1te) + pl.axis('off') + pl.title('Image 1 Adapt (reg)') + + pl.subplot(2, 3, 4) + pl.imshow(I2) + pl.axis('off') + pl.title('Image 2') + + pl.subplot(2, 3, 5) + pl.imshow(I2t) + pl.axis('off') + pl.title('Image 2 Adapt') + + pl.subplot(2, 3, 6) + pl.imshow(I2te) + pl.axis('off') + pl.title('Image 2 Adapt (reg)') + pl.tight_layout() + + pl.show() + + + +.. image:: /auto_examples/images/sphx_glr_plot_otda_color_images_005.png + :align: center + + + + +**Total running time of the script:** ( 2 minutes 24.561 seconds) + + + +.. container:: sphx-glr-footer + + + .. container:: sphx-glr-download + + :download:`Download Python source code: plot_otda_color_images.py <plot_otda_color_images.py>` + + + + .. container:: sphx-glr-download + + :download:`Download Jupyter notebook: plot_otda_color_images.ipynb <plot_otda_color_images.ipynb>` + +.. rst-class:: sphx-glr-signature + + `Generated by Sphinx-Gallery <https://sphinx-gallery.readthedocs.io>`_ diff --git a/docs/source/auto_examples/plot_otda_d2.ipynb b/docs/source/auto_examples/plot_otda_d2.ipynb new file mode 100644 index 0000000..7bfcc9a --- /dev/null +++ b/docs/source/auto_examples/plot_otda_d2.ipynb @@ -0,0 +1,144 @@ +{ + "nbformat_minor": 0, + "nbformat": 4, + "cells": [ + { + "execution_count": null, + "cell_type": "code", + "source": [ + "%matplotlib inline" + ], + "outputs": [], + "metadata": { + "collapsed": false + } + }, + { + "source": [ + "\n# OT for domain adaptation on empirical distributions\n\n\nThis example introduces a domain adaptation in a 2D setting. It explicits\nthe problem of domain adaptation and introduces some optimal transport\napproaches to solve it.\n\nQuantities such as optimal couplings, greater coupling coefficients and\ntransported samples are represented in order to give a visual understanding\nof what the transport methods are doing.\n\n" + ], + "cell_type": "markdown", + "metadata": {} + }, + { + "execution_count": null, + "cell_type": "code", + "source": [ + "# Authors: Remi Flamary <remi.flamary@unice.fr>\n# Stanislas Chambon <stan.chambon@gmail.com>\n#\n# License: MIT License\n\nimport matplotlib.pylab as pl\nimport ot" + ], + "outputs": [], + "metadata": { + "collapsed": false + } + }, + { + "source": [ + "generate data\n-------------\n\n" + ], + "cell_type": "markdown", + "metadata": {} + }, + { + "execution_count": null, + "cell_type": "code", + "source": [ + "n_samples_source = 150\nn_samples_target = 150\n\nXs, ys = ot.datasets.get_data_classif('3gauss', n_samples_source)\nXt, yt = ot.datasets.get_data_classif('3gauss2', n_samples_target)\n\n# Cost matrix\nM = ot.dist(Xs, Xt, metric='sqeuclidean')" + ], + "outputs": [], + "metadata": { + "collapsed": false + } + }, + { + "source": [ + "Instantiate the different transport algorithms and fit them\n-----------------------------------------------------------\n\n" + ], + "cell_type": "markdown", + "metadata": {} + }, + { + "execution_count": null, + "cell_type": "code", + "source": [ + "# EMD Transport\not_emd = ot.da.EMDTransport()\not_emd.fit(Xs=Xs, Xt=Xt)\n\n# Sinkhorn Transport\not_sinkhorn = ot.da.SinkhornTransport(reg_e=1e-1)\not_sinkhorn.fit(Xs=Xs, Xt=Xt)\n\n# Sinkhorn Transport with Group lasso regularization\not_lpl1 = ot.da.SinkhornLpl1Transport(reg_e=1e-1, reg_cl=1e0)\not_lpl1.fit(Xs=Xs, ys=ys, Xt=Xt)\n\n# transport source samples onto target samples\ntransp_Xs_emd = ot_emd.transform(Xs=Xs)\ntransp_Xs_sinkhorn = ot_sinkhorn.transform(Xs=Xs)\ntransp_Xs_lpl1 = ot_lpl1.transform(Xs=Xs)" + ], + "outputs": [], + "metadata": { + "collapsed": false + } + }, + { + "source": [ + "Fig 1 : plots source and target samples + matrix of pairwise distance\n---------------------------------------------------------------------\n\n" + ], + "cell_type": "markdown", + "metadata": {} + }, + { + "execution_count": null, + "cell_type": "code", + "source": [ + "pl.figure(1, figsize=(10, 10))\npl.subplot(2, 2, 1)\npl.scatter(Xs[:, 0], Xs[:, 1], c=ys, marker='+', label='Source samples')\npl.xticks([])\npl.yticks([])\npl.legend(loc=0)\npl.title('Source samples')\n\npl.subplot(2, 2, 2)\npl.scatter(Xt[:, 0], Xt[:, 1], c=yt, marker='o', label='Target samples')\npl.xticks([])\npl.yticks([])\npl.legend(loc=0)\npl.title('Target samples')\n\npl.subplot(2, 2, 3)\npl.imshow(M, interpolation='nearest')\npl.xticks([])\npl.yticks([])\npl.title('Matrix of pairwise distances')\npl.tight_layout()" + ], + "outputs": [], + "metadata": { + "collapsed": false + } + }, + { + "source": [ + "Fig 2 : plots optimal couplings for the different methods\n---------------------------------------------------------\n\n" + ], + "cell_type": "markdown", + "metadata": {} + }, + { + "execution_count": null, + "cell_type": "code", + "source": [ + "pl.figure(2, figsize=(10, 6))\n\npl.subplot(2, 3, 1)\npl.imshow(ot_emd.coupling_, interpolation='nearest')\npl.xticks([])\npl.yticks([])\npl.title('Optimal coupling\\nEMDTransport')\n\npl.subplot(2, 3, 2)\npl.imshow(ot_sinkhorn.coupling_, interpolation='nearest')\npl.xticks([])\npl.yticks([])\npl.title('Optimal coupling\\nSinkhornTransport')\n\npl.subplot(2, 3, 3)\npl.imshow(ot_lpl1.coupling_, interpolation='nearest')\npl.xticks([])\npl.yticks([])\npl.title('Optimal coupling\\nSinkhornLpl1Transport')\n\npl.subplot(2, 3, 4)\not.plot.plot2D_samples_mat(Xs, Xt, ot_emd.coupling_, c=[.5, .5, 1])\npl.scatter(Xs[:, 0], Xs[:, 1], c=ys, marker='+', label='Source samples')\npl.scatter(Xt[:, 0], Xt[:, 1], c=yt, marker='o', label='Target samples')\npl.xticks([])\npl.yticks([])\npl.title('Main coupling coefficients\\nEMDTransport')\n\npl.subplot(2, 3, 5)\not.plot.plot2D_samples_mat(Xs, Xt, ot_sinkhorn.coupling_, c=[.5, .5, 1])\npl.scatter(Xs[:, 0], Xs[:, 1], c=ys, marker='+', label='Source samples')\npl.scatter(Xt[:, 0], Xt[:, 1], c=yt, marker='o', label='Target samples')\npl.xticks([])\npl.yticks([])\npl.title('Main coupling coefficients\\nSinkhornTransport')\n\npl.subplot(2, 3, 6)\not.plot.plot2D_samples_mat(Xs, Xt, ot_lpl1.coupling_, c=[.5, .5, 1])\npl.scatter(Xs[:, 0], Xs[:, 1], c=ys, marker='+', label='Source samples')\npl.scatter(Xt[:, 0], Xt[:, 1], c=yt, marker='o', label='Target samples')\npl.xticks([])\npl.yticks([])\npl.title('Main coupling coefficients\\nSinkhornLpl1Transport')\npl.tight_layout()" + ], + "outputs": [], + "metadata": { + "collapsed": false + } + }, + { + "source": [ + "Fig 3 : plot transported samples\n--------------------------------\n\n" + ], + "cell_type": "markdown", + "metadata": {} + }, + { + "execution_count": null, + "cell_type": "code", + "source": [ + "# display transported samples\npl.figure(4, figsize=(10, 4))\npl.subplot(1, 3, 1)\npl.scatter(Xt[:, 0], Xt[:, 1], c=yt, marker='o',\n label='Target samples', alpha=0.5)\npl.scatter(transp_Xs_emd[:, 0], transp_Xs_emd[:, 1], c=ys,\n marker='+', label='Transp samples', s=30)\npl.title('Transported samples\\nEmdTransport')\npl.legend(loc=0)\npl.xticks([])\npl.yticks([])\n\npl.subplot(1, 3, 2)\npl.scatter(Xt[:, 0], Xt[:, 1], c=yt, marker='o',\n label='Target samples', alpha=0.5)\npl.scatter(transp_Xs_sinkhorn[:, 0], transp_Xs_sinkhorn[:, 1], c=ys,\n marker='+', label='Transp samples', s=30)\npl.title('Transported samples\\nSinkhornTransport')\npl.xticks([])\npl.yticks([])\n\npl.subplot(1, 3, 3)\npl.scatter(Xt[:, 0], Xt[:, 1], c=yt, marker='o',\n label='Target samples', alpha=0.5)\npl.scatter(transp_Xs_lpl1[:, 0], transp_Xs_lpl1[:, 1], c=ys,\n marker='+', label='Transp samples', s=30)\npl.title('Transported samples\\nSinkhornLpl1Transport')\npl.xticks([])\npl.yticks([])\n\npl.tight_layout()\npl.show()" + ], + "outputs": [], + "metadata": { + "collapsed": false + } + } + ], + "metadata": { + "kernelspec": { + "display_name": "Python 2", + "name": "python2", + "language": "python" + }, + "language_info": { + "mimetype": "text/x-python", + "nbconvert_exporter": "python", + "name": "python", + "file_extension": ".py", + "version": "2.7.12", + "pygments_lexer": "ipython2", + "codemirror_mode": { + "version": 2, + "name": "ipython" + } + } + } +}
\ No newline at end of file diff --git a/docs/source/auto_examples/plot_otda_d2.py b/docs/source/auto_examples/plot_otda_d2.py new file mode 100644 index 0000000..e53d7d6 --- /dev/null +++ b/docs/source/auto_examples/plot_otda_d2.py @@ -0,0 +1,172 @@ +# -*- coding: utf-8 -*- +""" +=================================================== +OT for domain adaptation on empirical distributions +=================================================== + +This example introduces a domain adaptation in a 2D setting. It explicits +the problem of domain adaptation and introduces some optimal transport +approaches to solve it. + +Quantities such as optimal couplings, greater coupling coefficients and +transported samples are represented in order to give a visual understanding +of what the transport methods are doing. +""" + +# Authors: Remi Flamary <remi.flamary@unice.fr> +# Stanislas Chambon <stan.chambon@gmail.com> +# +# License: MIT License + +import matplotlib.pylab as pl +import ot + + +############################################################################## +# generate data +# ------------- + +n_samples_source = 150 +n_samples_target = 150 + +Xs, ys = ot.datasets.get_data_classif('3gauss', n_samples_source) +Xt, yt = ot.datasets.get_data_classif('3gauss2', n_samples_target) + +# Cost matrix +M = ot.dist(Xs, Xt, metric='sqeuclidean') + + +############################################################################## +# Instantiate the different transport algorithms and fit them +# ----------------------------------------------------------- + +# EMD Transport +ot_emd = ot.da.EMDTransport() +ot_emd.fit(Xs=Xs, Xt=Xt) + +# Sinkhorn Transport +ot_sinkhorn = ot.da.SinkhornTransport(reg_e=1e-1) +ot_sinkhorn.fit(Xs=Xs, Xt=Xt) + +# Sinkhorn Transport with Group lasso regularization +ot_lpl1 = ot.da.SinkhornLpl1Transport(reg_e=1e-1, reg_cl=1e0) +ot_lpl1.fit(Xs=Xs, ys=ys, Xt=Xt) + +# transport source samples onto target samples +transp_Xs_emd = ot_emd.transform(Xs=Xs) +transp_Xs_sinkhorn = ot_sinkhorn.transform(Xs=Xs) +transp_Xs_lpl1 = ot_lpl1.transform(Xs=Xs) + + +############################################################################## +# Fig 1 : plots source and target samples + matrix of pairwise distance +# --------------------------------------------------------------------- + +pl.figure(1, figsize=(10, 10)) +pl.subplot(2, 2, 1) +pl.scatter(Xs[:, 0], Xs[:, 1], c=ys, marker='+', label='Source samples') +pl.xticks([]) +pl.yticks([]) +pl.legend(loc=0) +pl.title('Source samples') + +pl.subplot(2, 2, 2) +pl.scatter(Xt[:, 0], Xt[:, 1], c=yt, marker='o', label='Target samples') +pl.xticks([]) +pl.yticks([]) +pl.legend(loc=0) +pl.title('Target samples') + +pl.subplot(2, 2, 3) +pl.imshow(M, interpolation='nearest') +pl.xticks([]) +pl.yticks([]) +pl.title('Matrix of pairwise distances') +pl.tight_layout() + + +############################################################################## +# Fig 2 : plots optimal couplings for the different methods +# --------------------------------------------------------- +pl.figure(2, figsize=(10, 6)) + +pl.subplot(2, 3, 1) +pl.imshow(ot_emd.coupling_, interpolation='nearest') +pl.xticks([]) +pl.yticks([]) +pl.title('Optimal coupling\nEMDTransport') + +pl.subplot(2, 3, 2) +pl.imshow(ot_sinkhorn.coupling_, interpolation='nearest') +pl.xticks([]) +pl.yticks([]) +pl.title('Optimal coupling\nSinkhornTransport') + +pl.subplot(2, 3, 3) +pl.imshow(ot_lpl1.coupling_, interpolation='nearest') +pl.xticks([]) +pl.yticks([]) +pl.title('Optimal coupling\nSinkhornLpl1Transport') + +pl.subplot(2, 3, 4) +ot.plot.plot2D_samples_mat(Xs, Xt, ot_emd.coupling_, c=[.5, .5, 1]) +pl.scatter(Xs[:, 0], Xs[:, 1], c=ys, marker='+', label='Source samples') +pl.scatter(Xt[:, 0], Xt[:, 1], c=yt, marker='o', label='Target samples') +pl.xticks([]) +pl.yticks([]) +pl.title('Main coupling coefficients\nEMDTransport') + +pl.subplot(2, 3, 5) +ot.plot.plot2D_samples_mat(Xs, Xt, ot_sinkhorn.coupling_, c=[.5, .5, 1]) +pl.scatter(Xs[:, 0], Xs[:, 1], c=ys, marker='+', label='Source samples') +pl.scatter(Xt[:, 0], Xt[:, 1], c=yt, marker='o', label='Target samples') +pl.xticks([]) +pl.yticks([]) +pl.title('Main coupling coefficients\nSinkhornTransport') + +pl.subplot(2, 3, 6) +ot.plot.plot2D_samples_mat(Xs, Xt, ot_lpl1.coupling_, c=[.5, .5, 1]) +pl.scatter(Xs[:, 0], Xs[:, 1], c=ys, marker='+', label='Source samples') +pl.scatter(Xt[:, 0], Xt[:, 1], c=yt, marker='o', label='Target samples') +pl.xticks([]) +pl.yticks([]) +pl.title('Main coupling coefficients\nSinkhornLpl1Transport') +pl.tight_layout() + + +############################################################################## +# Fig 3 : plot transported samples +# -------------------------------- + +# display transported samples +pl.figure(4, figsize=(10, 4)) +pl.subplot(1, 3, 1) +pl.scatter(Xt[:, 0], Xt[:, 1], c=yt, marker='o', + label='Target samples', alpha=0.5) +pl.scatter(transp_Xs_emd[:, 0], transp_Xs_emd[:, 1], c=ys, + marker='+', label='Transp samples', s=30) +pl.title('Transported samples\nEmdTransport') +pl.legend(loc=0) +pl.xticks([]) +pl.yticks([]) + +pl.subplot(1, 3, 2) +pl.scatter(Xt[:, 0], Xt[:, 1], c=yt, marker='o', + label='Target samples', alpha=0.5) +pl.scatter(transp_Xs_sinkhorn[:, 0], transp_Xs_sinkhorn[:, 1], c=ys, + marker='+', label='Transp samples', s=30) +pl.title('Transported samples\nSinkhornTransport') +pl.xticks([]) +pl.yticks([]) + +pl.subplot(1, 3, 3) +pl.scatter(Xt[:, 0], Xt[:, 1], c=yt, marker='o', + label='Target samples', alpha=0.5) +pl.scatter(transp_Xs_lpl1[:, 0], transp_Xs_lpl1[:, 1], c=ys, + marker='+', label='Transp samples', s=30) +pl.title('Transported samples\nSinkhornLpl1Transport') +pl.xticks([]) +pl.yticks([]) + +pl.tight_layout() +pl.show() diff --git a/docs/source/auto_examples/plot_otda_d2.rst b/docs/source/auto_examples/plot_otda_d2.rst new file mode 100644 index 0000000..2b716e1 --- /dev/null +++ b/docs/source/auto_examples/plot_otda_d2.rst @@ -0,0 +1,264 @@ + + +.. _sphx_glr_auto_examples_plot_otda_d2.py: + + +=================================================== +OT for domain adaptation on empirical distributions +=================================================== + +This example introduces a domain adaptation in a 2D setting. It explicits +the problem of domain adaptation and introduces some optimal transport +approaches to solve it. + +Quantities such as optimal couplings, greater coupling coefficients and +transported samples are represented in order to give a visual understanding +of what the transport methods are doing. + + + +.. code-block:: python + + + # Authors: Remi Flamary <remi.flamary@unice.fr> + # Stanislas Chambon <stan.chambon@gmail.com> + # + # License: MIT License + + import matplotlib.pylab as pl + import ot + + + + + + + + +generate data +------------- + + + +.. code-block:: python + + + n_samples_source = 150 + n_samples_target = 150 + + Xs, ys = ot.datasets.get_data_classif('3gauss', n_samples_source) + Xt, yt = ot.datasets.get_data_classif('3gauss2', n_samples_target) + + # Cost matrix + M = ot.dist(Xs, Xt, metric='sqeuclidean') + + + + + + + + +Instantiate the different transport algorithms and fit them +----------------------------------------------------------- + + + +.. code-block:: python + + + # EMD Transport + ot_emd = ot.da.EMDTransport() + ot_emd.fit(Xs=Xs, Xt=Xt) + + # Sinkhorn Transport + ot_sinkhorn = ot.da.SinkhornTransport(reg_e=1e-1) + ot_sinkhorn.fit(Xs=Xs, Xt=Xt) + + # Sinkhorn Transport with Group lasso regularization + ot_lpl1 = ot.da.SinkhornLpl1Transport(reg_e=1e-1, reg_cl=1e0) + ot_lpl1.fit(Xs=Xs, ys=ys, Xt=Xt) + + # transport source samples onto target samples + transp_Xs_emd = ot_emd.transform(Xs=Xs) + transp_Xs_sinkhorn = ot_sinkhorn.transform(Xs=Xs) + transp_Xs_lpl1 = ot_lpl1.transform(Xs=Xs) + + + + + + + + +Fig 1 : plots source and target samples + matrix of pairwise distance +--------------------------------------------------------------------- + + + +.. code-block:: python + + + pl.figure(1, figsize=(10, 10)) + pl.subplot(2, 2, 1) + pl.scatter(Xs[:, 0], Xs[:, 1], c=ys, marker='+', label='Source samples') + pl.xticks([]) + pl.yticks([]) + pl.legend(loc=0) + pl.title('Source samples') + + pl.subplot(2, 2, 2) + pl.scatter(Xt[:, 0], Xt[:, 1], c=yt, marker='o', label='Target samples') + pl.xticks([]) + pl.yticks([]) + pl.legend(loc=0) + pl.title('Target samples') + + pl.subplot(2, 2, 3) + pl.imshow(M, interpolation='nearest') + pl.xticks([]) + pl.yticks([]) + pl.title('Matrix of pairwise distances') + pl.tight_layout() + + + + + +.. image:: /auto_examples/images/sphx_glr_plot_otda_d2_001.png + :align: center + + + + +Fig 2 : plots optimal couplings for the different methods +--------------------------------------------------------- + + + +.. code-block:: python + + pl.figure(2, figsize=(10, 6)) + + pl.subplot(2, 3, 1) + pl.imshow(ot_emd.coupling_, interpolation='nearest') + pl.xticks([]) + pl.yticks([]) + pl.title('Optimal coupling\nEMDTransport') + + pl.subplot(2, 3, 2) + pl.imshow(ot_sinkhorn.coupling_, interpolation='nearest') + pl.xticks([]) + pl.yticks([]) + pl.title('Optimal coupling\nSinkhornTransport') + + pl.subplot(2, 3, 3) + pl.imshow(ot_lpl1.coupling_, interpolation='nearest') + pl.xticks([]) + pl.yticks([]) + pl.title('Optimal coupling\nSinkhornLpl1Transport') + + pl.subplot(2, 3, 4) + ot.plot.plot2D_samples_mat(Xs, Xt, ot_emd.coupling_, c=[.5, .5, 1]) + pl.scatter(Xs[:, 0], Xs[:, 1], c=ys, marker='+', label='Source samples') + pl.scatter(Xt[:, 0], Xt[:, 1], c=yt, marker='o', label='Target samples') + pl.xticks([]) + pl.yticks([]) + pl.title('Main coupling coefficients\nEMDTransport') + + pl.subplot(2, 3, 5) + ot.plot.plot2D_samples_mat(Xs, Xt, ot_sinkhorn.coupling_, c=[.5, .5, 1]) + pl.scatter(Xs[:, 0], Xs[:, 1], c=ys, marker='+', label='Source samples') + pl.scatter(Xt[:, 0], Xt[:, 1], c=yt, marker='o', label='Target samples') + pl.xticks([]) + pl.yticks([]) + pl.title('Main coupling coefficients\nSinkhornTransport') + + pl.subplot(2, 3, 6) + ot.plot.plot2D_samples_mat(Xs, Xt, ot_lpl1.coupling_, c=[.5, .5, 1]) + pl.scatter(Xs[:, 0], Xs[:, 1], c=ys, marker='+', label='Source samples') + pl.scatter(Xt[:, 0], Xt[:, 1], c=yt, marker='o', label='Target samples') + pl.xticks([]) + pl.yticks([]) + pl.title('Main coupling coefficients\nSinkhornLpl1Transport') + pl.tight_layout() + + + + + +.. image:: /auto_examples/images/sphx_glr_plot_otda_d2_003.png + :align: center + + + + +Fig 3 : plot transported samples +-------------------------------- + + + +.. code-block:: python + + + # display transported samples + pl.figure(4, figsize=(10, 4)) + pl.subplot(1, 3, 1) + pl.scatter(Xt[:, 0], Xt[:, 1], c=yt, marker='o', + label='Target samples', alpha=0.5) + pl.scatter(transp_Xs_emd[:, 0], transp_Xs_emd[:, 1], c=ys, + marker='+', label='Transp samples', s=30) + pl.title('Transported samples\nEmdTransport') + pl.legend(loc=0) + pl.xticks([]) + pl.yticks([]) + + pl.subplot(1, 3, 2) + pl.scatter(Xt[:, 0], Xt[:, 1], c=yt, marker='o', + label='Target samples', alpha=0.5) + pl.scatter(transp_Xs_sinkhorn[:, 0], transp_Xs_sinkhorn[:, 1], c=ys, + marker='+', label='Transp samples', s=30) + pl.title('Transported samples\nSinkhornTransport') + pl.xticks([]) + pl.yticks([]) + + pl.subplot(1, 3, 3) + pl.scatter(Xt[:, 0], Xt[:, 1], c=yt, marker='o', + label='Target samples', alpha=0.5) + pl.scatter(transp_Xs_lpl1[:, 0], transp_Xs_lpl1[:, 1], c=ys, + marker='+', label='Transp samples', s=30) + pl.title('Transported samples\nSinkhornLpl1Transport') + pl.xticks([]) + pl.yticks([]) + + pl.tight_layout() + pl.show() + + + +.. image:: /auto_examples/images/sphx_glr_plot_otda_d2_006.png + :align: center + + + + +**Total running time of the script:** ( 0 minutes 32.084 seconds) + + + +.. container:: sphx-glr-footer + + + .. container:: sphx-glr-download + + :download:`Download Python source code: plot_otda_d2.py <plot_otda_d2.py>` + + + + .. container:: sphx-glr-download + + :download:`Download Jupyter notebook: plot_otda_d2.ipynb <plot_otda_d2.ipynb>` + +.. rst-class:: sphx-glr-signature + + `Generated by Sphinx-Gallery <https://sphinx-gallery.readthedocs.io>`_ diff --git a/docs/source/auto_examples/plot_otda_mapping.ipynb b/docs/source/auto_examples/plot_otda_mapping.ipynb new file mode 100644 index 0000000..0374146 --- /dev/null +++ b/docs/source/auto_examples/plot_otda_mapping.ipynb @@ -0,0 +1,126 @@ +{ + "nbformat_minor": 0, + "nbformat": 4, + "cells": [ + { + "execution_count": null, + "cell_type": "code", + "source": [ + "%matplotlib inline" + ], + "outputs": [], + "metadata": { + "collapsed": false + } + }, + { + "source": [ + "\n# OT mapping estimation for domain adaptation\n\n\nThis example presents how to use MappingTransport to estimate at the same\ntime both the coupling transport and approximate the transport map with either\na linear or a kernelized mapping as introduced in [8].\n\n[8] M. Perrot, N. Courty, R. Flamary, A. Habrard,\n \"Mapping estimation for discrete optimal transport\",\n Neural Information Processing Systems (NIPS), 2016.\n\n" + ], + "cell_type": "markdown", + "metadata": {} + }, + { + "execution_count": null, + "cell_type": "code", + "source": [ + "# Authors: Remi Flamary <remi.flamary@unice.fr>\n# Stanislas Chambon <stan.chambon@gmail.com>\n#\n# License: MIT License\n\nimport numpy as np\nimport matplotlib.pylab as pl\nimport ot" + ], + "outputs": [], + "metadata": { + "collapsed": false + } + }, + { + "source": [ + "Generate data\n-------------\n\n" + ], + "cell_type": "markdown", + "metadata": {} + }, + { + "execution_count": null, + "cell_type": "code", + "source": [ + "n_source_samples = 100\nn_target_samples = 100\ntheta = 2 * np.pi / 20\nnoise_level = 0.1\n\nXs, ys = ot.datasets.get_data_classif(\n 'gaussrot', n_source_samples, nz=noise_level)\nXs_new, _ = ot.datasets.get_data_classif(\n 'gaussrot', n_source_samples, nz=noise_level)\nXt, yt = ot.datasets.get_data_classif(\n 'gaussrot', n_target_samples, theta=theta, nz=noise_level)\n\n# one of the target mode changes its variance (no linear mapping)\nXt[yt == 2] *= 3\nXt = Xt + 4" + ], + "outputs": [], + "metadata": { + "collapsed": false + } + }, + { + "source": [ + "Plot data\n---------\n\n" + ], + "cell_type": "markdown", + "metadata": {} + }, + { + "execution_count": null, + "cell_type": "code", + "source": [ + "pl.figure(1, (10, 5))\npl.clf()\npl.scatter(Xs[:, 0], Xs[:, 1], c=ys, marker='+', label='Source samples')\npl.scatter(Xt[:, 0], Xt[:, 1], c=yt, marker='o', label='Target samples')\npl.legend(loc=0)\npl.title('Source and target distributions')" + ], + "outputs": [], + "metadata": { + "collapsed": false + } + }, + { + "source": [ + "Instantiate the different transport algorithms and fit them\n-----------------------------------------------------------\n\n" + ], + "cell_type": "markdown", + "metadata": {} + }, + { + "execution_count": null, + "cell_type": "code", + "source": [ + "# MappingTransport with linear kernel\not_mapping_linear = ot.da.MappingTransport(\n kernel=\"linear\", mu=1e0, eta=1e-8, bias=True,\n max_iter=20, verbose=True)\n\not_mapping_linear.fit(Xs=Xs, Xt=Xt)\n\n# for original source samples, transform applies barycentric mapping\ntransp_Xs_linear = ot_mapping_linear.transform(Xs=Xs)\n\n# for out of source samples, transform applies the linear mapping\ntransp_Xs_linear_new = ot_mapping_linear.transform(Xs=Xs_new)\n\n\n# MappingTransport with gaussian kernel\not_mapping_gaussian = ot.da.MappingTransport(\n kernel=\"gaussian\", eta=1e-5, mu=1e-1, bias=True, sigma=1,\n max_iter=10, verbose=True)\not_mapping_gaussian.fit(Xs=Xs, Xt=Xt)\n\n# for original source samples, transform applies barycentric mapping\ntransp_Xs_gaussian = ot_mapping_gaussian.transform(Xs=Xs)\n\n# for out of source samples, transform applies the gaussian mapping\ntransp_Xs_gaussian_new = ot_mapping_gaussian.transform(Xs=Xs_new)" + ], + "outputs": [], + "metadata": { + "collapsed": false + } + }, + { + "source": [ + "Plot transported samples\n------------------------\n\n" + ], + "cell_type": "markdown", + "metadata": {} + }, + { + "execution_count": null, + "cell_type": "code", + "source": [ + "pl.figure(2)\npl.clf()\npl.subplot(2, 2, 1)\npl.scatter(Xt[:, 0], Xt[:, 1], c=yt, marker='o',\n label='Target samples', alpha=.2)\npl.scatter(transp_Xs_linear[:, 0], transp_Xs_linear[:, 1], c=ys, marker='+',\n label='Mapped source samples')\npl.title(\"Bary. mapping (linear)\")\npl.legend(loc=0)\n\npl.subplot(2, 2, 2)\npl.scatter(Xt[:, 0], Xt[:, 1], c=yt, marker='o',\n label='Target samples', alpha=.2)\npl.scatter(transp_Xs_linear_new[:, 0], transp_Xs_linear_new[:, 1],\n c=ys, marker='+', label='Learned mapping')\npl.title(\"Estim. mapping (linear)\")\n\npl.subplot(2, 2, 3)\npl.scatter(Xt[:, 0], Xt[:, 1], c=yt, marker='o',\n label='Target samples', alpha=.2)\npl.scatter(transp_Xs_gaussian[:, 0], transp_Xs_gaussian[:, 1], c=ys,\n marker='+', label='barycentric mapping')\npl.title(\"Bary. mapping (kernel)\")\n\npl.subplot(2, 2, 4)\npl.scatter(Xt[:, 0], Xt[:, 1], c=yt, marker='o',\n label='Target samples', alpha=.2)\npl.scatter(transp_Xs_gaussian_new[:, 0], transp_Xs_gaussian_new[:, 1], c=ys,\n marker='+', label='Learned mapping')\npl.title(\"Estim. mapping (kernel)\")\npl.tight_layout()\n\npl.show()" + ], + "outputs": [], + "metadata": { + "collapsed": false + } + } + ], + "metadata": { + "kernelspec": { + "display_name": "Python 2", + "name": "python2", + "language": "python" + }, + "language_info": { + "mimetype": "text/x-python", + "nbconvert_exporter": "python", + "name": "python", + "file_extension": ".py", + "version": "2.7.12", + "pygments_lexer": "ipython2", + "codemirror_mode": { + "version": 2, + "name": "ipython" + } + } + } +}
\ No newline at end of file diff --git a/docs/source/auto_examples/plot_otda_mapping.py b/docs/source/auto_examples/plot_otda_mapping.py new file mode 100644 index 0000000..167c3a1 --- /dev/null +++ b/docs/source/auto_examples/plot_otda_mapping.py @@ -0,0 +1,125 @@ +# -*- coding: utf-8 -*- +""" +=========================================== +OT mapping estimation for domain adaptation +=========================================== + +This example presents how to use MappingTransport to estimate at the same +time both the coupling transport and approximate the transport map with either +a linear or a kernelized mapping as introduced in [8]. + +[8] M. Perrot, N. Courty, R. Flamary, A. Habrard, + "Mapping estimation for discrete optimal transport", + Neural Information Processing Systems (NIPS), 2016. +""" + +# Authors: Remi Flamary <remi.flamary@unice.fr> +# Stanislas Chambon <stan.chambon@gmail.com> +# +# License: MIT License + +import numpy as np +import matplotlib.pylab as pl +import ot + + +############################################################################## +# Generate data +# ------------- + +n_source_samples = 100 +n_target_samples = 100 +theta = 2 * np.pi / 20 +noise_level = 0.1 + +Xs, ys = ot.datasets.get_data_classif( + 'gaussrot', n_source_samples, nz=noise_level) +Xs_new, _ = ot.datasets.get_data_classif( + 'gaussrot', n_source_samples, nz=noise_level) +Xt, yt = ot.datasets.get_data_classif( + 'gaussrot', n_target_samples, theta=theta, nz=noise_level) + +# one of the target mode changes its variance (no linear mapping) +Xt[yt == 2] *= 3 +Xt = Xt + 4 + +############################################################################## +# Plot data +# --------- + +pl.figure(1, (10, 5)) +pl.clf() +pl.scatter(Xs[:, 0], Xs[:, 1], c=ys, marker='+', label='Source samples') +pl.scatter(Xt[:, 0], Xt[:, 1], c=yt, marker='o', label='Target samples') +pl.legend(loc=0) +pl.title('Source and target distributions') + + +############################################################################## +# Instantiate the different transport algorithms and fit them +# ----------------------------------------------------------- + +# MappingTransport with linear kernel +ot_mapping_linear = ot.da.MappingTransport( + kernel="linear", mu=1e0, eta=1e-8, bias=True, + max_iter=20, verbose=True) + +ot_mapping_linear.fit(Xs=Xs, Xt=Xt) + +# for original source samples, transform applies barycentric mapping +transp_Xs_linear = ot_mapping_linear.transform(Xs=Xs) + +# for out of source samples, transform applies the linear mapping +transp_Xs_linear_new = ot_mapping_linear.transform(Xs=Xs_new) + + +# MappingTransport with gaussian kernel +ot_mapping_gaussian = ot.da.MappingTransport( + kernel="gaussian", eta=1e-5, mu=1e-1, bias=True, sigma=1, + max_iter=10, verbose=True) +ot_mapping_gaussian.fit(Xs=Xs, Xt=Xt) + +# for original source samples, transform applies barycentric mapping +transp_Xs_gaussian = ot_mapping_gaussian.transform(Xs=Xs) + +# for out of source samples, transform applies the gaussian mapping +transp_Xs_gaussian_new = ot_mapping_gaussian.transform(Xs=Xs_new) + + +############################################################################## +# Plot transported samples +# ------------------------ + +pl.figure(2) +pl.clf() +pl.subplot(2, 2, 1) +pl.scatter(Xt[:, 0], Xt[:, 1], c=yt, marker='o', + label='Target samples', alpha=.2) +pl.scatter(transp_Xs_linear[:, 0], transp_Xs_linear[:, 1], c=ys, marker='+', + label='Mapped source samples') +pl.title("Bary. mapping (linear)") +pl.legend(loc=0) + +pl.subplot(2, 2, 2) +pl.scatter(Xt[:, 0], Xt[:, 1], c=yt, marker='o', + label='Target samples', alpha=.2) +pl.scatter(transp_Xs_linear_new[:, 0], transp_Xs_linear_new[:, 1], + c=ys, marker='+', label='Learned mapping') +pl.title("Estim. mapping (linear)") + +pl.subplot(2, 2, 3) +pl.scatter(Xt[:, 0], Xt[:, 1], c=yt, marker='o', + label='Target samples', alpha=.2) +pl.scatter(transp_Xs_gaussian[:, 0], transp_Xs_gaussian[:, 1], c=ys, + marker='+', label='barycentric mapping') +pl.title("Bary. mapping (kernel)") + +pl.subplot(2, 2, 4) +pl.scatter(Xt[:, 0], Xt[:, 1], c=yt, marker='o', + label='Target samples', alpha=.2) +pl.scatter(transp_Xs_gaussian_new[:, 0], transp_Xs_gaussian_new[:, 1], c=ys, + marker='+', label='Learned mapping') +pl.title("Estim. mapping (kernel)") +pl.tight_layout() + +pl.show() diff --git a/docs/source/auto_examples/plot_otda_mapping.rst b/docs/source/auto_examples/plot_otda_mapping.rst new file mode 100644 index 0000000..6c1c780 --- /dev/null +++ b/docs/source/auto_examples/plot_otda_mapping.rst @@ -0,0 +1,228 @@ + + +.. _sphx_glr_auto_examples_plot_otda_mapping.py: + + +=========================================== +OT mapping estimation for domain adaptation +=========================================== + +This example presents how to use MappingTransport to estimate at the same +time both the coupling transport and approximate the transport map with either +a linear or a kernelized mapping as introduced in [8]. + +[8] M. Perrot, N. Courty, R. Flamary, A. Habrard, + "Mapping estimation for discrete optimal transport", + Neural Information Processing Systems (NIPS), 2016. + + + +.. code-block:: python + + + # Authors: Remi Flamary <remi.flamary@unice.fr> + # Stanislas Chambon <stan.chambon@gmail.com> + # + # License: MIT License + + import numpy as np + import matplotlib.pylab as pl + import ot + + + + + + + + +Generate data +------------- + + + +.. code-block:: python + + + n_source_samples = 100 + n_target_samples = 100 + theta = 2 * np.pi / 20 + noise_level = 0.1 + + Xs, ys = ot.datasets.get_data_classif( + 'gaussrot', n_source_samples, nz=noise_level) + Xs_new, _ = ot.datasets.get_data_classif( + 'gaussrot', n_source_samples, nz=noise_level) + Xt, yt = ot.datasets.get_data_classif( + 'gaussrot', n_target_samples, theta=theta, nz=noise_level) + + # one of the target mode changes its variance (no linear mapping) + Xt[yt == 2] *= 3 + Xt = Xt + 4 + + + + + + + +Plot data +--------- + + + +.. code-block:: python + + + pl.figure(1, (10, 5)) + pl.clf() + pl.scatter(Xs[:, 0], Xs[:, 1], c=ys, marker='+', label='Source samples') + pl.scatter(Xt[:, 0], Xt[:, 1], c=yt, marker='o', label='Target samples') + pl.legend(loc=0) + pl.title('Source and target distributions') + + + + + +.. image:: /auto_examples/images/sphx_glr_plot_otda_mapping_001.png + :align: center + + + + +Instantiate the different transport algorithms and fit them +----------------------------------------------------------- + + + +.. code-block:: python + + + # MappingTransport with linear kernel + ot_mapping_linear = ot.da.MappingTransport( + kernel="linear", mu=1e0, eta=1e-8, bias=True, + max_iter=20, verbose=True) + + ot_mapping_linear.fit(Xs=Xs, Xt=Xt) + + # for original source samples, transform applies barycentric mapping + transp_Xs_linear = ot_mapping_linear.transform(Xs=Xs) + + # for out of source samples, transform applies the linear mapping + transp_Xs_linear_new = ot_mapping_linear.transform(Xs=Xs_new) + + + # MappingTransport with gaussian kernel + ot_mapping_gaussian = ot.da.MappingTransport( + kernel="gaussian", eta=1e-5, mu=1e-1, bias=True, sigma=1, + max_iter=10, verbose=True) + ot_mapping_gaussian.fit(Xs=Xs, Xt=Xt) + + # for original source samples, transform applies barycentric mapping + transp_Xs_gaussian = ot_mapping_gaussian.transform(Xs=Xs) + + # for out of source samples, transform applies the gaussian mapping + transp_Xs_gaussian_new = ot_mapping_gaussian.transform(Xs=Xs_new) + + + + + + +.. rst-class:: sphx-glr-script-out + + Out:: + + It. |Loss |Delta loss + -------------------------------- + 0|4.307233e+03|0.000000e+00 + 1|4.296694e+03|-2.446759e-03 + 2|4.296419e+03|-6.417421e-05 + 3|4.296328e+03|-2.110209e-05 + 4|4.296305e+03|-5.298603e-06 + It. |Loss |Delta loss + -------------------------------- + 0|4.325624e+02|0.000000e+00 + 1|4.281958e+02|-1.009489e-02 + 2|4.279370e+02|-6.042202e-04 + 3|4.278109e+02|-2.947651e-04 + 4|4.277212e+02|-2.096651e-04 + 5|4.276589e+02|-1.456221e-04 + 6|4.276141e+02|-1.048476e-04 + 7|4.275803e+02|-7.906213e-05 + 8|4.275531e+02|-6.360573e-05 + 9|4.275314e+02|-5.076642e-05 + 10|4.275129e+02|-4.325858e-05 + + +Plot transported samples +------------------------ + + + +.. code-block:: python + + + pl.figure(2) + pl.clf() + pl.subplot(2, 2, 1) + pl.scatter(Xt[:, 0], Xt[:, 1], c=yt, marker='o', + label='Target samples', alpha=.2) + pl.scatter(transp_Xs_linear[:, 0], transp_Xs_linear[:, 1], c=ys, marker='+', + label='Mapped source samples') + pl.title("Bary. mapping (linear)") + pl.legend(loc=0) + + pl.subplot(2, 2, 2) + pl.scatter(Xt[:, 0], Xt[:, 1], c=yt, marker='o', + label='Target samples', alpha=.2) + pl.scatter(transp_Xs_linear_new[:, 0], transp_Xs_linear_new[:, 1], + c=ys, marker='+', label='Learned mapping') + pl.title("Estim. mapping (linear)") + + pl.subplot(2, 2, 3) + pl.scatter(Xt[:, 0], Xt[:, 1], c=yt, marker='o', + label='Target samples', alpha=.2) + pl.scatter(transp_Xs_gaussian[:, 0], transp_Xs_gaussian[:, 1], c=ys, + marker='+', label='barycentric mapping') + pl.title("Bary. mapping (kernel)") + + pl.subplot(2, 2, 4) + pl.scatter(Xt[:, 0], Xt[:, 1], c=yt, marker='o', + label='Target samples', alpha=.2) + pl.scatter(transp_Xs_gaussian_new[:, 0], transp_Xs_gaussian_new[:, 1], c=ys, + marker='+', label='Learned mapping') + pl.title("Estim. mapping (kernel)") + pl.tight_layout() + + pl.show() + + + +.. image:: /auto_examples/images/sphx_glr_plot_otda_mapping_003.png + :align: center + + + + +**Total running time of the script:** ( 0 minutes 0.747 seconds) + + + +.. container:: sphx-glr-footer + + + .. container:: sphx-glr-download + + :download:`Download Python source code: plot_otda_mapping.py <plot_otda_mapping.py>` + + + + .. container:: sphx-glr-download + + :download:`Download Jupyter notebook: plot_otda_mapping.ipynb <plot_otda_mapping.ipynb>` + +.. rst-class:: sphx-glr-signature + + `Generated by Sphinx-Gallery <https://sphinx-gallery.readthedocs.io>`_ diff --git a/docs/source/auto_examples/plot_otda_mapping_colors_images.ipynb b/docs/source/auto_examples/plot_otda_mapping_colors_images.ipynb new file mode 100644 index 0000000..56caa8a --- /dev/null +++ b/docs/source/auto_examples/plot_otda_mapping_colors_images.ipynb @@ -0,0 +1,144 @@ +{ + "nbformat_minor": 0, + "nbformat": 4, + "cells": [ + { + "execution_count": null, + "cell_type": "code", + "source": [ + "%matplotlib inline" + ], + "outputs": [], + "metadata": { + "collapsed": false + } + }, + { + "source": [ + "\n# OT for image color adaptation with mapping estimation\n\n\nOT for domain adaptation with image color adaptation [6] with mapping\nestimation [8].\n\n[6] Ferradans, S., Papadakis, N., Peyre, G., & Aujol, J. F. (2014). Regularized\n discrete optimal transport. SIAM Journal on Imaging Sciences, 7(3),\n 1853-1882.\n[8] M. Perrot, N. Courty, R. Flamary, A. Habrard, \"Mapping estimation for\n discrete optimal transport\", Neural Information Processing Systems (NIPS),\n 2016.\n\n\n" + ], + "cell_type": "markdown", + "metadata": {} + }, + { + "execution_count": null, + "cell_type": "code", + "source": [ + "# Authors: Remi Flamary <remi.flamary@unice.fr>\n# Stanislas Chambon <stan.chambon@gmail.com>\n#\n# License: MIT License\n\nimport numpy as np\nfrom scipy import ndimage\nimport matplotlib.pylab as pl\nimport ot\n\nr = np.random.RandomState(42)\n\n\ndef im2mat(I):\n \"\"\"Converts and image to matrix (one pixel per line)\"\"\"\n return I.reshape((I.shape[0] * I.shape[1], I.shape[2]))\n\n\ndef mat2im(X, shape):\n \"\"\"Converts back a matrix to an image\"\"\"\n return X.reshape(shape)\n\n\ndef minmax(I):\n return np.clip(I, 0, 1)" + ], + "outputs": [], + "metadata": { + "collapsed": false + } + }, + { + "source": [ + "Generate data\n-------------\n\n" + ], + "cell_type": "markdown", + "metadata": {} + }, + { + "execution_count": null, + "cell_type": "code", + "source": [ + "# Loading images\nI1 = ndimage.imread('../data/ocean_day.jpg').astype(np.float64) / 256\nI2 = ndimage.imread('../data/ocean_sunset.jpg').astype(np.float64) / 256\n\n\nX1 = im2mat(I1)\nX2 = im2mat(I2)\n\n# training samples\nnb = 1000\nidx1 = r.randint(X1.shape[0], size=(nb,))\nidx2 = r.randint(X2.shape[0], size=(nb,))\n\nXs = X1[idx1, :]\nXt = X2[idx2, :]" + ], + "outputs": [], + "metadata": { + "collapsed": false + } + }, + { + "source": [ + "Domain adaptation for pixel distribution transfer\n-------------------------------------------------\n\n" + ], + "cell_type": "markdown", + "metadata": {} + }, + { + "execution_count": null, + "cell_type": "code", + "source": [ + "# EMDTransport\not_emd = ot.da.EMDTransport()\not_emd.fit(Xs=Xs, Xt=Xt)\ntransp_Xs_emd = ot_emd.transform(Xs=X1)\nImage_emd = minmax(mat2im(transp_Xs_emd, I1.shape))\n\n# SinkhornTransport\not_sinkhorn = ot.da.SinkhornTransport(reg_e=1e-1)\not_sinkhorn.fit(Xs=Xs, Xt=Xt)\ntransp_Xs_sinkhorn = ot_emd.transform(Xs=X1)\nImage_sinkhorn = minmax(mat2im(transp_Xs_sinkhorn, I1.shape))\n\not_mapping_linear = ot.da.MappingTransport(\n mu=1e0, eta=1e-8, bias=True, max_iter=20, verbose=True)\not_mapping_linear.fit(Xs=Xs, Xt=Xt)\n\nX1tl = ot_mapping_linear.transform(Xs=X1)\nImage_mapping_linear = minmax(mat2im(X1tl, I1.shape))\n\not_mapping_gaussian = ot.da.MappingTransport(\n mu=1e0, eta=1e-2, sigma=1, bias=False, max_iter=10, verbose=True)\not_mapping_gaussian.fit(Xs=Xs, Xt=Xt)\n\nX1tn = ot_mapping_gaussian.transform(Xs=X1) # use the estimated mapping\nImage_mapping_gaussian = minmax(mat2im(X1tn, I1.shape))" + ], + "outputs": [], + "metadata": { + "collapsed": false + } + }, + { + "source": [ + "Plot original images\n--------------------\n\n" + ], + "cell_type": "markdown", + "metadata": {} + }, + { + "execution_count": null, + "cell_type": "code", + "source": [ + "pl.figure(1, figsize=(6.4, 3))\npl.subplot(1, 2, 1)\npl.imshow(I1)\npl.axis('off')\npl.title('Image 1')\n\npl.subplot(1, 2, 2)\npl.imshow(I2)\npl.axis('off')\npl.title('Image 2')\npl.tight_layout()" + ], + "outputs": [], + "metadata": { + "collapsed": false + } + }, + { + "source": [ + "Plot pixel values distribution\n------------------------------\n\n" + ], + "cell_type": "markdown", + "metadata": {} + }, + { + "execution_count": null, + "cell_type": "code", + "source": [ + "pl.figure(2, figsize=(6.4, 5))\n\npl.subplot(1, 2, 1)\npl.scatter(Xs[:, 0], Xs[:, 2], c=Xs)\npl.axis([0, 1, 0, 1])\npl.xlabel('Red')\npl.ylabel('Blue')\npl.title('Image 1')\n\npl.subplot(1, 2, 2)\npl.scatter(Xt[:, 0], Xt[:, 2], c=Xt)\npl.axis([0, 1, 0, 1])\npl.xlabel('Red')\npl.ylabel('Blue')\npl.title('Image 2')\npl.tight_layout()" + ], + "outputs": [], + "metadata": { + "collapsed": false + } + }, + { + "source": [ + "Plot transformed images\n-----------------------\n\n" + ], + "cell_type": "markdown", + "metadata": {} + }, + { + "execution_count": null, + "cell_type": "code", + "source": [ + "pl.figure(2, figsize=(10, 5))\n\npl.subplot(2, 3, 1)\npl.imshow(I1)\npl.axis('off')\npl.title('Im. 1')\n\npl.subplot(2, 3, 4)\npl.imshow(I2)\npl.axis('off')\npl.title('Im. 2')\n\npl.subplot(2, 3, 2)\npl.imshow(Image_emd)\npl.axis('off')\npl.title('EmdTransport')\n\npl.subplot(2, 3, 5)\npl.imshow(Image_sinkhorn)\npl.axis('off')\npl.title('SinkhornTransport')\n\npl.subplot(2, 3, 3)\npl.imshow(Image_mapping_linear)\npl.axis('off')\npl.title('MappingTransport (linear)')\n\npl.subplot(2, 3, 6)\npl.imshow(Image_mapping_gaussian)\npl.axis('off')\npl.title('MappingTransport (gaussian)')\npl.tight_layout()\n\npl.show()" + ], + "outputs": [], + "metadata": { + "collapsed": false + } + } + ], + "metadata": { + "kernelspec": { + "display_name": "Python 2", + "name": "python2", + "language": "python" + }, + "language_info": { + "mimetype": "text/x-python", + "nbconvert_exporter": "python", + "name": "python", + "file_extension": ".py", + "version": "2.7.12", + "pygments_lexer": "ipython2", + "codemirror_mode": { + "version": 2, + "name": "ipython" + } + } + } +}
\ No newline at end of file diff --git a/docs/source/auto_examples/plot_otda_mapping_colors_images.py b/docs/source/auto_examples/plot_otda_mapping_colors_images.py new file mode 100644 index 0000000..5f1e844 --- /dev/null +++ b/docs/source/auto_examples/plot_otda_mapping_colors_images.py @@ -0,0 +1,174 @@ +# -*- coding: utf-8 -*- +""" +===================================================== +OT for image color adaptation with mapping estimation +===================================================== + +OT for domain adaptation with image color adaptation [6] with mapping +estimation [8]. + +[6] Ferradans, S., Papadakis, N., Peyre, G., & Aujol, J. F. (2014). Regularized + discrete optimal transport. SIAM Journal on Imaging Sciences, 7(3), + 1853-1882. +[8] M. Perrot, N. Courty, R. Flamary, A. Habrard, "Mapping estimation for + discrete optimal transport", Neural Information Processing Systems (NIPS), + 2016. + +""" + +# Authors: Remi Flamary <remi.flamary@unice.fr> +# Stanislas Chambon <stan.chambon@gmail.com> +# +# License: MIT License + +import numpy as np +from scipy import ndimage +import matplotlib.pylab as pl +import ot + +r = np.random.RandomState(42) + + +def im2mat(I): + """Converts and image to matrix (one pixel per line)""" + return I.reshape((I.shape[0] * I.shape[1], I.shape[2])) + + +def mat2im(X, shape): + """Converts back a matrix to an image""" + return X.reshape(shape) + + +def minmax(I): + return np.clip(I, 0, 1) + + +############################################################################## +# Generate data +# ------------- + +# Loading images +I1 = ndimage.imread('../data/ocean_day.jpg').astype(np.float64) / 256 +I2 = ndimage.imread('../data/ocean_sunset.jpg').astype(np.float64) / 256 + + +X1 = im2mat(I1) +X2 = im2mat(I2) + +# training samples +nb = 1000 +idx1 = r.randint(X1.shape[0], size=(nb,)) +idx2 = r.randint(X2.shape[0], size=(nb,)) + +Xs = X1[idx1, :] +Xt = X2[idx2, :] + + +############################################################################## +# Domain adaptation for pixel distribution transfer +# ------------------------------------------------- + +# EMDTransport +ot_emd = ot.da.EMDTransport() +ot_emd.fit(Xs=Xs, Xt=Xt) +transp_Xs_emd = ot_emd.transform(Xs=X1) +Image_emd = minmax(mat2im(transp_Xs_emd, I1.shape)) + +# SinkhornTransport +ot_sinkhorn = ot.da.SinkhornTransport(reg_e=1e-1) +ot_sinkhorn.fit(Xs=Xs, Xt=Xt) +transp_Xs_sinkhorn = ot_emd.transform(Xs=X1) +Image_sinkhorn = minmax(mat2im(transp_Xs_sinkhorn, I1.shape)) + +ot_mapping_linear = ot.da.MappingTransport( + mu=1e0, eta=1e-8, bias=True, max_iter=20, verbose=True) +ot_mapping_linear.fit(Xs=Xs, Xt=Xt) + +X1tl = ot_mapping_linear.transform(Xs=X1) +Image_mapping_linear = minmax(mat2im(X1tl, I1.shape)) + +ot_mapping_gaussian = ot.da.MappingTransport( + mu=1e0, eta=1e-2, sigma=1, bias=False, max_iter=10, verbose=True) +ot_mapping_gaussian.fit(Xs=Xs, Xt=Xt) + +X1tn = ot_mapping_gaussian.transform(Xs=X1) # use the estimated mapping +Image_mapping_gaussian = minmax(mat2im(X1tn, I1.shape)) + + +############################################################################## +# Plot original images +# -------------------- + +pl.figure(1, figsize=(6.4, 3)) +pl.subplot(1, 2, 1) +pl.imshow(I1) +pl.axis('off') +pl.title('Image 1') + +pl.subplot(1, 2, 2) +pl.imshow(I2) +pl.axis('off') +pl.title('Image 2') +pl.tight_layout() + + +############################################################################## +# Plot pixel values distribution +# ------------------------------ + +pl.figure(2, figsize=(6.4, 5)) + +pl.subplot(1, 2, 1) +pl.scatter(Xs[:, 0], Xs[:, 2], c=Xs) +pl.axis([0, 1, 0, 1]) +pl.xlabel('Red') +pl.ylabel('Blue') +pl.title('Image 1') + +pl.subplot(1, 2, 2) +pl.scatter(Xt[:, 0], Xt[:, 2], c=Xt) +pl.axis([0, 1, 0, 1]) +pl.xlabel('Red') +pl.ylabel('Blue') +pl.title('Image 2') +pl.tight_layout() + + +############################################################################## +# Plot transformed images +# ----------------------- + +pl.figure(2, figsize=(10, 5)) + +pl.subplot(2, 3, 1) +pl.imshow(I1) +pl.axis('off') +pl.title('Im. 1') + +pl.subplot(2, 3, 4) +pl.imshow(I2) +pl.axis('off') +pl.title('Im. 2') + +pl.subplot(2, 3, 2) +pl.imshow(Image_emd) +pl.axis('off') +pl.title('EmdTransport') + +pl.subplot(2, 3, 5) +pl.imshow(Image_sinkhorn) +pl.axis('off') +pl.title('SinkhornTransport') + +pl.subplot(2, 3, 3) +pl.imshow(Image_mapping_linear) +pl.axis('off') +pl.title('MappingTransport (linear)') + +pl.subplot(2, 3, 6) +pl.imshow(Image_mapping_gaussian) +pl.axis('off') +pl.title('MappingTransport (gaussian)') +pl.tight_layout() + +pl.show() diff --git a/docs/source/auto_examples/plot_otda_mapping_colors_images.rst b/docs/source/auto_examples/plot_otda_mapping_colors_images.rst new file mode 100644 index 0000000..86b1312 --- /dev/null +++ b/docs/source/auto_examples/plot_otda_mapping_colors_images.rst @@ -0,0 +1,305 @@ + + +.. _sphx_glr_auto_examples_plot_otda_mapping_colors_images.py: + + +===================================================== +OT for image color adaptation with mapping estimation +===================================================== + +OT for domain adaptation with image color adaptation [6] with mapping +estimation [8]. + +[6] Ferradans, S., Papadakis, N., Peyre, G., & Aujol, J. F. (2014). Regularized + discrete optimal transport. SIAM Journal on Imaging Sciences, 7(3), + 1853-1882. +[8] M. Perrot, N. Courty, R. Flamary, A. Habrard, "Mapping estimation for + discrete optimal transport", Neural Information Processing Systems (NIPS), + 2016. + + + + +.. code-block:: python + + + # Authors: Remi Flamary <remi.flamary@unice.fr> + # Stanislas Chambon <stan.chambon@gmail.com> + # + # License: MIT License + + import numpy as np + from scipy import ndimage + import matplotlib.pylab as pl + import ot + + r = np.random.RandomState(42) + + + def im2mat(I): + """Converts and image to matrix (one pixel per line)""" + return I.reshape((I.shape[0] * I.shape[1], I.shape[2])) + + + def mat2im(X, shape): + """Converts back a matrix to an image""" + return X.reshape(shape) + + + def minmax(I): + return np.clip(I, 0, 1) + + + + + + + + +Generate data +------------- + + + +.. code-block:: python + + + # Loading images + I1 = ndimage.imread('../data/ocean_day.jpg').astype(np.float64) / 256 + I2 = ndimage.imread('../data/ocean_sunset.jpg').astype(np.float64) / 256 + + + X1 = im2mat(I1) + X2 = im2mat(I2) + + # training samples + nb = 1000 + idx1 = r.randint(X1.shape[0], size=(nb,)) + idx2 = r.randint(X2.shape[0], size=(nb,)) + + Xs = X1[idx1, :] + Xt = X2[idx2, :] + + + + + + + + +Domain adaptation for pixel distribution transfer +------------------------------------------------- + + + +.. code-block:: python + + + # EMDTransport + ot_emd = ot.da.EMDTransport() + ot_emd.fit(Xs=Xs, Xt=Xt) + transp_Xs_emd = ot_emd.transform(Xs=X1) + Image_emd = minmax(mat2im(transp_Xs_emd, I1.shape)) + + # SinkhornTransport + ot_sinkhorn = ot.da.SinkhornTransport(reg_e=1e-1) + ot_sinkhorn.fit(Xs=Xs, Xt=Xt) + transp_Xs_sinkhorn = ot_emd.transform(Xs=X1) + Image_sinkhorn = minmax(mat2im(transp_Xs_sinkhorn, I1.shape)) + + ot_mapping_linear = ot.da.MappingTransport( + mu=1e0, eta=1e-8, bias=True, max_iter=20, verbose=True) + ot_mapping_linear.fit(Xs=Xs, Xt=Xt) + + X1tl = ot_mapping_linear.transform(Xs=X1) + Image_mapping_linear = minmax(mat2im(X1tl, I1.shape)) + + ot_mapping_gaussian = ot.da.MappingTransport( + mu=1e0, eta=1e-2, sigma=1, bias=False, max_iter=10, verbose=True) + ot_mapping_gaussian.fit(Xs=Xs, Xt=Xt) + + X1tn = ot_mapping_gaussian.transform(Xs=X1) # use the estimated mapping + Image_mapping_gaussian = minmax(mat2im(X1tn, I1.shape)) + + + + + + +.. rst-class:: sphx-glr-script-out + + Out:: + + It. |Loss |Delta loss + -------------------------------- + 0|3.680512e+02|0.000000e+00 + 1|3.592454e+02|-2.392562e-02 + 2|3.590671e+02|-4.960473e-04 + 3|3.589736e+02|-2.604894e-04 + 4|3.589161e+02|-1.602816e-04 + 5|3.588766e+02|-1.099971e-04 + 6|3.588476e+02|-8.084400e-05 + 7|3.588256e+02|-6.131161e-05 + 8|3.588083e+02|-4.807549e-05 + 9|3.587943e+02|-3.899414e-05 + 10|3.587827e+02|-3.245280e-05 + 11|3.587729e+02|-2.721256e-05 + 12|3.587646e+02|-2.316249e-05 + 13|3.587574e+02|-2.000192e-05 + 14|3.587512e+02|-1.748898e-05 + 15|3.587457e+02|-1.535131e-05 + 16|3.587408e+02|-1.366515e-05 + 17|3.587364e+02|-1.210563e-05 + 18|3.587325e+02|-1.097138e-05 + 19|3.587310e+02|-4.099596e-06 + It. |Loss |Delta loss + -------------------------------- + 0|3.784805e+02|0.000000e+00 + 1|3.646476e+02|-3.654847e-02 + 2|3.642970e+02|-9.615381e-04 + 3|3.641622e+02|-3.699897e-04 + 4|3.640886e+02|-2.021154e-04 + 5|3.640419e+02|-1.280913e-04 + 6|3.640096e+02|-8.898145e-05 + 7|3.639858e+02|-6.514301e-05 + 8|3.639677e+02|-4.977195e-05 + 9|3.639534e+02|-3.936050e-05 + 10|3.639417e+02|-3.205223e-05 + + +Plot original images +-------------------- + + + +.. code-block:: python + + + pl.figure(1, figsize=(6.4, 3)) + pl.subplot(1, 2, 1) + pl.imshow(I1) + pl.axis('off') + pl.title('Image 1') + + pl.subplot(1, 2, 2) + pl.imshow(I2) + pl.axis('off') + pl.title('Image 2') + pl.tight_layout() + + + + + +.. image:: /auto_examples/images/sphx_glr_plot_otda_mapping_colors_images_001.png + :align: center + + + + +Plot pixel values distribution +------------------------------ + + + +.. code-block:: python + + + pl.figure(2, figsize=(6.4, 5)) + + pl.subplot(1, 2, 1) + pl.scatter(Xs[:, 0], Xs[:, 2], c=Xs) + pl.axis([0, 1, 0, 1]) + pl.xlabel('Red') + pl.ylabel('Blue') + pl.title('Image 1') + + pl.subplot(1, 2, 2) + pl.scatter(Xt[:, 0], Xt[:, 2], c=Xt) + pl.axis([0, 1, 0, 1]) + pl.xlabel('Red') + pl.ylabel('Blue') + pl.title('Image 2') + pl.tight_layout() + + + + + +.. image:: /auto_examples/images/sphx_glr_plot_otda_mapping_colors_images_003.png + :align: center + + + + +Plot transformed images +----------------------- + + + +.. code-block:: python + + + pl.figure(2, figsize=(10, 5)) + + pl.subplot(2, 3, 1) + pl.imshow(I1) + pl.axis('off') + pl.title('Im. 1') + + pl.subplot(2, 3, 4) + pl.imshow(I2) + pl.axis('off') + pl.title('Im. 2') + + pl.subplot(2, 3, 2) + pl.imshow(Image_emd) + pl.axis('off') + pl.title('EmdTransport') + + pl.subplot(2, 3, 5) + pl.imshow(Image_sinkhorn) + pl.axis('off') + pl.title('SinkhornTransport') + + pl.subplot(2, 3, 3) + pl.imshow(Image_mapping_linear) + pl.axis('off') + pl.title('MappingTransport (linear)') + + pl.subplot(2, 3, 6) + pl.imshow(Image_mapping_gaussian) + pl.axis('off') + pl.title('MappingTransport (gaussian)') + pl.tight_layout() + + pl.show() + + + +.. image:: /auto_examples/images/sphx_glr_plot_otda_mapping_colors_images_004.png + :align: center + + + + +**Total running time of the script:** ( 2 minutes 5.213 seconds) + + + +.. container:: sphx-glr-footer + + + .. container:: sphx-glr-download + + :download:`Download Python source code: plot_otda_mapping_colors_images.py <plot_otda_mapping_colors_images.py>` + + + + .. container:: sphx-glr-download + + :download:`Download Jupyter notebook: plot_otda_mapping_colors_images.ipynb <plot_otda_mapping_colors_images.ipynb>` + +.. rst-class:: sphx-glr-signature + + `Generated by Sphinx-Gallery <https://sphinx-gallery.readthedocs.io>`_ diff --git a/docs/source/auto_examples/searchindex b/docs/source/auto_examples/searchindex Binary files differnew file mode 100644 index 0000000..2cad500 --- /dev/null +++ b/docs/source/auto_examples/searchindex diff --git a/docs/source/conf.py b/docs/source/conf.py index ff08899..4105d87 100644 --- a/docs/source/conf.py +++ b/docs/source/conf.py @@ -50,7 +50,7 @@ sys.path.insert(0, os.path.abspath("../..")) #needs_sphinx = '1.0' # Add any Sphinx extension module names here, as strings. They can be -# extensions coming with Sphinx (named 'sphinx.ext.*') or your custom +# extensions coming with Sphinx (named #'sphinx.ext.*') or your custom # ones. extensions = [ 'sphinx.ext.autodoc', @@ -62,7 +62,7 @@ extensions = [ 'sphinx.ext.ifconfig', 'sphinx.ext.viewcode', 'sphinx.ext.napoleon', -# 'sphinx_gallery.gen_gallery', + #'sphinx_gallery.gen_gallery', ] # Add any paths that contain templates here, relative to this directory. @@ -261,7 +261,7 @@ latex_elements = { # author, documentclass [howto, manual, or own class]). latex_documents = [ (master_doc, 'POT.tex', u'POT Python Optimal Transport library', - u'Rémi Flamary, Nicolas Courty', 'manual'), + author, 'manual'), ] # The name of an image file (relative to this directory) to place at the top of @@ -305,7 +305,7 @@ man_pages = [ # dir menu entry, description, category) texinfo_documents = [ (master_doc, 'POT', u'POT Python Optimal Transport library Documentation', - author, 'POT', 'One line description of project.', + author, 'POT', 'Python Optimal Transport librar.', 'Miscellaneous'), ] @@ -326,9 +326,9 @@ texinfo_documents = [ intersphinx_mapping = {'https://docs.python.org/': None} sphinx_gallery_conf = { - 'examples_dirs': '../../examples', + 'examples_dirs': ['../../examples','../../examples/da'], 'gallery_dirs': 'auto_examples', - 'mod_example_dir': '../modules/generated/', + 'backreferences_dir': '../modules/generated/', 'reference_url': { 'numpy': 'http://docs.scipy.org/doc/numpy-1.9.1', 'scipy': 'http://docs.scipy.org/doc/scipy-0.17.0/reference'} diff --git a/docs/source/examples.rst b/docs/source/examples.rst deleted file mode 100644 index f209543..0000000 --- a/docs/source/examples.rst +++ /dev/null @@ -1,39 +0,0 @@ - - -Examples -============ - -1D Optimal transport ---------------------- - -.. literalinclude:: ../../examples/demo_OT_1D.py - -2D Optimal transport on empirical distributions ------------------------------------------------ - -.. literalinclude:: ../../examples/demo_OT_2D_samples.py - -1D Wasserstein barycenter -------------------------- - -.. literalinclude:: ../../examples/demo_barycenter_1D.py - -OT with user provided regularization ------------------------------------- - -.. literalinclude:: ../../examples/demo_optim_OTreg.py - -Domain adaptation with optimal transport ----------------------------------------- - -.. literalinclude:: ../../examples/demo_OTDA_classes.py - -Color transfer in images ------------------------- - -.. literalinclude:: ../../examples/demo_OTDA_color_images.py - -OT mapping estimation for domain adaptation -------------------------------------------- - -.. literalinclude:: ../../examples/demo_OTDA_mapping.py diff --git a/docs/source/readme.rst b/docs/source/readme.rst index c1e0017..1482838 100644 --- a/docs/source/readme.rst +++ b/docs/source/readme.rst @@ -150,27 +150,27 @@ Here is a list of the Python notebooks available want a quick look: - `1D optimal - transport <https://github.com/rflamary/POT/blob/master/notebooks/Demo_1D_OT.ipynb>`__ + transport <https://github.com/rflamary/POT/blob/master/notebooks/plot_OT_1D.ipynb>`__ - `OT Ground - Loss <https://github.com/rflamary/POT/blob/master/notebooks/Demo_Ground_Loss.ipynb>`__ + Loss <https://github.com/rflamary/POT/blob/master/notebooks/plot_OT_L1_vs_L2.ipynb>`__ - `Multiple EMD - computation <https://github.com/rflamary/POT/blob/master/notebooks/Demo_Compute_EMD.ipynb>`__ + computation <https://github.com/rflamary/POT/blob/master/notebooks/plot_compute_emd.ipynb>`__ - `2D optimal transport on empirical - distributions <https://github.com/rflamary/POT/blob/master/notebooks/Demo_2D_OT_samples.ipynb>`__ + distributions <https://github.com/rflamary/POT/blob/master/notebooks/plot_OT_2D_samples.ipynb>`__ - `1D Wasserstein - barycenter <https://github.com/rflamary/POT/blob/master/notebooks/Demo_1D_barycenter.ipynb>`__ + barycenter <https://github.com/rflamary/POT/blob/master/notebooks/plot_barycenter_1D.ipynb>`__ - `OT with user provided - regularization <https://github.com/rflamary/POT/blob/master/notebooks/Demo_Optim_OTreg.ipynb>`__ + regularization <https://github.com/rflamary/POT/blob/master/notebooks/plot_optim_OTreg.ipynb>`__ - `Domain adaptation with optimal - transport <https://github.com/rflamary/POT/blob/master/notebooks/Demo_2D_OT_DomainAdaptation.ipynb>`__ + transport <https://github.com/rflamary/POT/blob/master/notebooks/plot_otda_d2.ipynb>`__ - `Color transfer in - images <https://github.com/rflamary/POT/blob/master/notebooks/Demo_Image_ColorAdaptation.ipynb>`__ + images <https://github.com/rflamary/POT/blob/master/notebooks/plot_otda_color_images.ipynb>`__ - `OT mapping estimation for domain - adaptation <https://github.com/rflamary/POT/blob/master/notebooks/Demo_2D_OTmapping_DomainAdaptation.ipynb>`__ + adaptation <https://github.com/rflamary/POT/blob/master/notebooks/plot_otda_mapping.ipynb>`__ - `OT mapping estimation for color transfer in - images <https://github.com/rflamary/POT/blob/master/notebooks/Demo_Image_ColorAdaptation_mapping.ipynb>`__ + images <https://github.com/rflamary/POT/blob/master/notebooks/plot_otda_mapping_colors_images.ipynb>`__ - `Wasserstein Discriminant - Analysis <https://github.com/rflamary/POT/blob/master/notebooks/Demo_Wasserstein_Discriminant_Analysis.ipynb>`__ + Analysis <https://github.com/rflamary/POT/blob/master/notebooks/plot_WDA.ipynb>`__ You can also see the notebooks with `Jupyter nbviewer <https://nbviewer.jupyter.org/github/rflamary/POT/tree/master/notebooks/>`__. @@ -187,6 +187,9 @@ The contributors to this library are: - `Michael Perrot <http://perso.univ-st-etienne.fr/pem82055/>`__ (Mapping estimation) - `Léo Gautheron <https://github.com/aje>`__ (GPU implementation) +- `Nathalie + Gayraud <https://www.linkedin.com/in/nathalie-t-h-gayraud/?ppe=1>`__ +- `Stanislas Chambon <https://slasnista.github.io/>`__ This toolbox benefit a lot from open source research and we would like to thank the following persons for providing some code (in various |
