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| author | Nicolas Courty <ncourty@irisa.fr> | 2020-02-28 11:46:51 +0100 |
|---|---|---|
| committer | GitHub <noreply@github.com> | 2020-02-28 11:46:51 +0100 |
| commit | 00535f30ba5374f95df0a9f0781a12bea37abf63 (patch) | |
| tree | ff4d363ce36677928d9d828c26148c3eac07a5da /docs/source/auto_examples | |
| parent | e23f4d0646a3e8d28cc146c28574359585295249 (diff) | |
| parent | 81e9d425b905b1b7fc0ee888556e60c692d9bb18 (diff) | |
Merge branch 'master' into osx-issue
Diffstat (limited to 'docs/source/auto_examples')
62 files changed, 2616 insertions, 374 deletions
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a/docs/source/auto_examples/images/thumb/sphx_glr_plot_otda_color_images_thumb.png +++ b/docs/source/auto_examples/images/thumb/sphx_glr_plot_otda_color_images_thumb.png diff --git a/docs/source/auto_examples/images/thumb/sphx_glr_plot_otda_mapping_colors_images_thumb.png b/docs/source/auto_examples/images/thumb/sphx_glr_plot_otda_mapping_colors_images_thumb.png Binary files differindex f7fd217..61a5137 100644 --- a/docs/source/auto_examples/images/thumb/sphx_glr_plot_otda_mapping_colors_images_thumb.png +++ b/docs/source/auto_examples/images/thumb/sphx_glr_plot_otda_mapping_colors_images_thumb.png diff --git a/docs/source/auto_examples/index.rst b/docs/source/auto_examples/index.rst index 259fca1..fe6702d 100644 --- a/docs/source/auto_examples/index.rst +++ b/docs/source/auto_examples/index.rst @@ -29,13 +29,13 @@ This is a gallery of all the POT example files. .. raw:: html - <div class="sphx-glr-thumbcontainer" tooltip="Illustrates the use of the generic solver for regularized OT with user-designed regularization ..."> + <div class="sphx-glr-thumbcontainer" tooltip="This example illustrates the computation of Unbalanced Optimal transport using a Kullback-Leibl..."> .. only:: html - .. figure:: /auto_examples/images/thumb/sphx_glr_plot_optim_OTreg_thumb.png + .. figure:: /auto_examples/images/thumb/sphx_glr_plot_UOT_1D_thumb.png - :ref:`sphx_glr_auto_examples_plot_optim_OTreg.py` + :ref:`sphx_glr_auto_examples_plot_UOT_1D.py` .. raw:: html @@ -45,17 +45,17 @@ This is a gallery of all the POT example files. .. toctree:: :hidden: - /auto_examples/plot_optim_OTreg + /auto_examples/plot_UOT_1D .. raw:: html - <div class="sphx-glr-thumbcontainer" tooltip="Illustration of 2D Wasserstein barycenters if discributions that are weighted sum of diracs."> + <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_free_support_barycenter_thumb.png + .. figure:: /auto_examples/images/thumb/sphx_glr_plot_optim_OTreg_thumb.png - :ref:`sphx_glr_auto_examples_plot_free_support_barycenter.py` + :ref:`sphx_glr_auto_examples_plot_optim_OTreg.py` .. raw:: html @@ -65,17 +65,17 @@ This is a gallery of all the POT example files. .. toctree:: :hidden: - /auto_examples/plot_free_support_barycenter + /auto_examples/plot_optim_OTreg .. raw:: html - <div class="sphx-glr-thumbcontainer" tooltip="This example illustrates the computation of EMD, Sinkhorn and smooth OT plans and their visuali..."> + <div class="sphx-glr-thumbcontainer" tooltip="Illustration of 2D Wasserstein barycenters if discributions that are weighted sum of diracs."> .. only:: html - .. figure:: /auto_examples/images/thumb/sphx_glr_plot_OT_1D_smooth_thumb.png + .. figure:: /auto_examples/images/thumb/sphx_glr_plot_free_support_barycenter_thumb.png - :ref:`sphx_glr_auto_examples_plot_OT_1D_smooth.py` + :ref:`sphx_glr_auto_examples_plot_free_support_barycenter.py` .. raw:: html @@ -85,17 +85,17 @@ This is a gallery of all the POT example files. .. toctree:: :hidden: - /auto_examples/plot_OT_1D_smooth + /auto_examples/plot_free_support_barycenter .. raw:: html - <div class="sphx-glr-thumbcontainer" tooltip="This example is designed to show how to use the Gromov-Wassertsein distance computation in POT...."> + <div class="sphx-glr-thumbcontainer" tooltip="This example illustrates the computation of EMD, Sinkhorn and smooth OT plans and their visuali..."> .. only:: html - .. figure:: /auto_examples/images/thumb/sphx_glr_plot_gromov_thumb.png + .. figure:: /auto_examples/images/thumb/sphx_glr_plot_OT_1D_smooth_thumb.png - :ref:`sphx_glr_auto_examples_plot_gromov.py` + :ref:`sphx_glr_auto_examples_plot_OT_1D_smooth.py` .. raw:: html @@ -105,17 +105,17 @@ This is a gallery of all the POT example files. .. toctree:: :hidden: - /auto_examples/plot_gromov + /auto_examples/plot_OT_1D_smooth .. raw:: html - <div class="sphx-glr-thumbcontainer" tooltip="Illustration of 2D optimal transport between discributions that are weighted sum of diracs. The..."> + <div class="sphx-glr-thumbcontainer" tooltip="This example is designed to show how to use the Gromov-Wassertsein distance computation in POT...."> .. only:: html - .. figure:: /auto_examples/images/thumb/sphx_glr_plot_OT_2D_samples_thumb.png + .. figure:: /auto_examples/images/thumb/sphx_glr_plot_gromov_thumb.png - :ref:`sphx_glr_auto_examples_plot_OT_2D_samples.py` + :ref:`sphx_glr_auto_examples_plot_gromov.py` .. raw:: html @@ -125,7 +125,7 @@ This is a gallery of all the POT example files. .. toctree:: :hidden: - /auto_examples/plot_OT_2D_samples + /auto_examples/plot_gromov .. raw:: html @@ -209,6 +209,26 @@ This is a gallery of all the POT example files. .. raw:: html + <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_OT_2D_samples_thumb.png + + :ref:`sphx_glr_auto_examples_plot_OT_2D_samples.py` + +.. raw:: html + + </div> + + +.. toctree:: + :hidden: + + /auto_examples/plot_OT_2D_samples + +.. raw:: html + <div class="sphx-glr-thumbcontainer" tooltip="This example is designed to show how to use the stochatic optimization algorithms for descrete ..."> .. only:: html @@ -229,7 +249,7 @@ This is a gallery of all the POT example files. .. raw:: html - <div class="sphx-glr-thumbcontainer" tooltip="This example presents a way of transferring colors between two image with Optimal Transport as ..."> + <div class="sphx-glr-thumbcontainer" tooltip="This example presents a way of transferring colors between two images with Optimal Transport as..."> .. only:: html @@ -289,6 +309,26 @@ This is a gallery of all the POT example files. .. raw:: html + <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_UOT_barycenter_1D_thumb.png + + :ref:`sphx_glr_auto_examples_plot_UOT_barycenter_1D.py` + +.. raw:: html + + </div> + + +.. toctree:: + :hidden: + + /auto_examples/plot_UOT_barycenter_1D + +.. raw:: html + <div class="sphx-glr-thumbcontainer" tooltip="This example presents how to use MappingTransport to estimate at the same time both the couplin..."> .. only:: html @@ -329,6 +369,26 @@ This is a gallery of all the POT example files. .. raw:: html + <div class="sphx-glr-thumbcontainer" tooltip="This example illustrates the computation of FGW for 1D measures[18]."> + +.. only:: html + + .. figure:: /auto_examples/images/thumb/sphx_glr_plot_fgw_thumb.png + + :ref:`sphx_glr_auto_examples_plot_fgw.py` + +.. raw:: html + + </div> + + +.. toctree:: + :hidden: + + /auto_examples/plot_fgw + +.. raw:: html + <div class="sphx-glr-thumbcontainer" tooltip="This example introduces a domain adaptation in a 2D setting and the 4 OTDA approaches currently..."> .. only:: html @@ -409,6 +469,26 @@ This is a gallery of all the POT example files. .. raw:: html + <div class="sphx-glr-thumbcontainer" tooltip="This example illustrates the computation barycenter of labeled graphs using FGW"> + +.. only:: html + + .. figure:: /auto_examples/images/thumb/sphx_glr_plot_barycenter_fgw_thumb.png + + :ref:`sphx_glr_auto_examples_plot_barycenter_fgw.py` + +.. raw:: html + + </div> + + +.. toctree:: + :hidden: + + /auto_examples/plot_barycenter_fgw + +.. raw:: html + <div class="sphx-glr-thumbcontainer" tooltip="This example is designed to show how to use the Gromov-Wasserstein distance computation in POT...."> .. only:: html diff --git a/docs/source/auto_examples/plot_OT_2D_samples.ipynb b/docs/source/auto_examples/plot_OT_2D_samples.ipynb index 26831f9..dad138b 100644 --- a/docs/source/auto_examples/plot_OT_2D_samples.ipynb +++ b/docs/source/auto_examples/plot_OT_2D_samples.ipynb @@ -26,7 +26,7 @@ }, "outputs": [], "source": [ - "# Author: Remi Flamary <remi.flamary@unice.fr>\n#\n# License: MIT License\n\nimport numpy as np\nimport matplotlib.pylab as pl\nimport ot\nimport ot.plot" + "# Author: Remi Flamary <remi.flamary@unice.fr>\n# Kilian Fatras <kilian.fatras@irisa.fr>\n#\n# License: MIT License\n\nimport numpy as np\nimport matplotlib.pylab as pl\nimport ot\nimport ot.plot" ] }, { @@ -100,6 +100,24 @@ "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()" ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "Emprirical Sinkhorn\n----------------\n\n" + ] + }, + { + "cell_type": "code", + "execution_count": null, + "metadata": { + "collapsed": false + }, + "outputs": [], + "source": [ + "#%% sinkhorn\n\n# reg term\nlambd = 1e-3\n\nGes = ot.bregman.empirical_sinkhorn(xs, xt, lambd)\n\npl.figure(7)\npl.imshow(Ges, interpolation='nearest')\npl.title('OT matrix empirical sinkhorn')\n\npl.figure(8)\not.plot.plot2D_samples_mat(xs, xt, Ges, 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 from samples')\n\npl.show()" + ] } ], "metadata": { @@ -118,7 +136,7 @@ "name": "python", "nbconvert_exporter": "python", "pygments_lexer": "ipython3", - "version": "3.6.5" + "version": "3.6.8" } }, "nbformat": 4, diff --git a/docs/source/auto_examples/plot_OT_2D_samples.py b/docs/source/auto_examples/plot_OT_2D_samples.py index bb952a0..63126ba 100644 --- a/docs/source/auto_examples/plot_OT_2D_samples.py +++ b/docs/source/auto_examples/plot_OT_2D_samples.py @@ -10,6 +10,7 @@ sum of diracs. The OT matrix is plotted with the samples. """ # Author: Remi Flamary <remi.flamary@unice.fr> +# Kilian Fatras <kilian.fatras@irisa.fr> # # License: MIT License @@ -100,3 +101,28 @@ pl.legend(loc=0) pl.title('OT matrix Sinkhorn with samples') pl.show() + + +############################################################################## +# Emprirical Sinkhorn +# ---------------- + +#%% sinkhorn + +# reg term +lambd = 1e-3 + +Ges = ot.bregman.empirical_sinkhorn(xs, xt, lambd) + +pl.figure(7) +pl.imshow(Ges, interpolation='nearest') +pl.title('OT matrix empirical sinkhorn') + +pl.figure(8) +ot.plot.plot2D_samples_mat(xs, xt, Ges, 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 from 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 624ae3e..1f1d713 100644 --- a/docs/source/auto_examples/plot_OT_2D_samples.rst +++ b/docs/source/auto_examples/plot_OT_2D_samples.rst @@ -17,6 +17,7 @@ sum of diracs. The OT matrix is plotted with the samples. # Author: Remi Flamary <remi.flamary@unice.fr> + # Kilian Fatras <kilian.fatras@irisa.fr> # # License: MIT License @@ -176,6 +177,8 @@ Compute Sinkhorn + + .. rst-class:: sphx-glr-horizontal @@ -192,7 +195,58 @@ Compute Sinkhorn -**Total running time of the script:** ( 0 minutes 3.027 seconds) +Emprirical Sinkhorn +---------------- + + + +.. code-block:: python + + + #%% sinkhorn + + # reg term + lambd = 1e-3 + + Ges = ot.bregman.empirical_sinkhorn(xs, xt, lambd) + + pl.figure(7) + pl.imshow(Ges, interpolation='nearest') + pl.title('OT matrix empirical sinkhorn') + + pl.figure(8) + ot.plot.plot2D_samples_mat(xs, xt, Ges, 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 from samples') + + pl.show() + + + +.. rst-class:: sphx-glr-horizontal + + + * + + .. image:: /auto_examples/images/sphx_glr_plot_OT_2D_samples_013.png + :scale: 47 + + * + + .. image:: /auto_examples/images/sphx_glr_plot_OT_2D_samples_014.png + :scale: 47 + + +.. rst-class:: sphx-glr-script-out + + Out:: + + Warning: numerical errors at iteration 0 + + +**Total running time of the script:** ( 0 minutes 2.616 seconds) diff --git a/docs/source/auto_examples/plot_UOT_1D.ipynb b/docs/source/auto_examples/plot_UOT_1D.ipynb new file mode 100644 index 0000000..c695306 --- /dev/null +++ b/docs/source/auto_examples/plot_UOT_1D.ipynb @@ -0,0 +1,108 @@ +{ + "cells": [ + { + "cell_type": "code", + "execution_count": null, + "metadata": { + "collapsed": false + }, + "outputs": [], + "source": [ + "%matplotlib inline" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "\n# 1D Unbalanced optimal transport\n\n\nThis example illustrates the computation of Unbalanced Optimal transport\nusing a Kullback-Leibler relaxation.\n\n" + ] + }, + { + "cell_type": "code", + "execution_count": null, + "metadata": { + "collapsed": false + }, + "outputs": [], + "source": [ + "# Author: Hicham Janati <hicham.janati@inria.fr>\n#\n# License: MIT License\n\nimport numpy as np\nimport matplotlib.pylab as pl\nimport ot\nimport ot.plot\nfrom ot.datasets import make_1D_gauss as gauss" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "Generate data\n-------------\n\n" + ] + }, + { + "cell_type": "code", + "execution_count": null, + "metadata": { + "collapsed": false + }, + "outputs": [], + "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# make distributions unbalanced\nb *= 5.\n\n# loss matrix\nM = ot.dist(x.reshape((n, 1)), x.reshape((n, 1)))\nM /= M.max()" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "Plot distributions and loss matrix\n----------------------------------\n\n" + ] + }, + { + "cell_type": "code", + "execution_count": null, + "metadata": { + "collapsed": false + }, + "outputs": [], + "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')" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "Solve Unbalanced Sinkhorn\n--------------\n\n" + ] + }, + { + "cell_type": "code", + "execution_count": null, + "metadata": { + "collapsed": false + }, + "outputs": [], + "source": [ + "# Sinkhorn\n\nepsilon = 0.1 # entropy parameter\nalpha = 1. # Unbalanced KL relaxation parameter\nGs = ot.unbalanced.sinkhorn_unbalanced(a, b, M, epsilon, alpha, verbose=True)\n\npl.figure(4, figsize=(5, 5))\not.plot.plot1D_mat(a, b, Gs, 'UOT matrix Sinkhorn')\n\npl.show()" + ] + } + ], + "metadata": { + "kernelspec": { + "display_name": "Python 3", + "language": "python", + "name": "python3" + }, + "language_info": { + "codemirror_mode": { + "name": "ipython", + "version": 3 + }, + "file_extension": ".py", + "mimetype": "text/x-python", + "name": "python", + "nbconvert_exporter": "python", + "pygments_lexer": "ipython3", + "version": "3.6.8" + } + }, + "nbformat": 4, + "nbformat_minor": 0 +}
\ No newline at end of file diff --git a/docs/source/auto_examples/plot_UOT_1D.py b/docs/source/auto_examples/plot_UOT_1D.py new file mode 100644 index 0000000..2ea8b05 --- /dev/null +++ b/docs/source/auto_examples/plot_UOT_1D.py @@ -0,0 +1,76 @@ +# -*- coding: utf-8 -*- +""" +=============================== +1D Unbalanced optimal transport +=============================== + +This example illustrates the computation of Unbalanced Optimal transport +using a Kullback-Leibler relaxation. +""" + +# Author: Hicham Janati <hicham.janati@inria.fr> +# +# License: MIT License + +import numpy as np +import matplotlib.pylab as pl +import ot +import ot.plot +from ot.datasets import make_1D_gauss as gauss + +############################################################################## +# Generate data +# ------------- + + +#%% 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) + +# make distributions unbalanced +b *= 5. + +# loss matrix +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, 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') + + +############################################################################## +# Solve Unbalanced Sinkhorn +# -------------- + + +# Sinkhorn + +epsilon = 0.1 # entropy parameter +alpha = 1. # Unbalanced KL relaxation parameter +Gs = ot.unbalanced.sinkhorn_unbalanced(a, b, M, epsilon, alpha, verbose=True) + +pl.figure(4, figsize=(5, 5)) +ot.plot.plot1D_mat(a, b, Gs, 'UOT matrix Sinkhorn') + +pl.show() diff --git a/docs/source/auto_examples/plot_UOT_1D.rst b/docs/source/auto_examples/plot_UOT_1D.rst new file mode 100644 index 0000000..8e618b4 --- /dev/null +++ b/docs/source/auto_examples/plot_UOT_1D.rst @@ -0,0 +1,173 @@ + + +.. _sphx_glr_auto_examples_plot_UOT_1D.py: + + +=============================== +1D Unbalanced optimal transport +=============================== + +This example illustrates the computation of Unbalanced Optimal transport +using a Kullback-Leibler relaxation. + + + +.. code-block:: python + + + # Author: Hicham Janati <hicham.janati@inria.fr> + # + # License: MIT License + + import numpy as np + import matplotlib.pylab as pl + import ot + import ot.plot + from ot.datasets import make_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) + + # make distributions unbalanced + b *= 5. + + # 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') + + + + + +.. rst-class:: sphx-glr-horizontal + + + * + + .. image:: /auto_examples/images/sphx_glr_plot_UOT_1D_001.png + :scale: 47 + + * + + .. image:: /auto_examples/images/sphx_glr_plot_UOT_1D_002.png + :scale: 47 + + + + +Solve Unbalanced Sinkhorn +-------------- + + + +.. code-block:: python + + + + # Sinkhorn + + epsilon = 0.1 # entropy parameter + alpha = 1. # Unbalanced KL relaxation parameter + Gs = ot.unbalanced.sinkhorn_unbalanced(a, b, M, epsilon, alpha, verbose=True) + + pl.figure(4, figsize=(5, 5)) + ot.plot.plot1D_mat(a, b, Gs, 'UOT matrix Sinkhorn') + + pl.show() + + + +.. image:: /auto_examples/images/sphx_glr_plot_UOT_1D_006.png + :align: center + + +.. rst-class:: sphx-glr-script-out + + Out:: + + It. |Err + ------------------- + 0|1.838786e+00| + 10|1.242379e-01| + 20|2.581314e-03| + 30|5.674552e-05| + 40|1.252959e-06| + 50|2.768136e-08| + 60|6.116090e-10| + + +**Total running time of the script:** ( 0 minutes 0.259 seconds) + + + +.. only :: html + + .. container:: sphx-glr-footer + + + .. container:: sphx-glr-download + + :download:`Download Python source code: plot_UOT_1D.py <plot_UOT_1D.py>` + + + + .. container:: sphx-glr-download + + :download:`Download Jupyter notebook: plot_UOT_1D.ipynb <plot_UOT_1D.ipynb>` + + +.. only:: html + + .. rst-class:: sphx-glr-signature + + `Gallery generated by Sphinx-Gallery <https://sphinx-gallery.readthedocs.io>`_ diff --git a/docs/source/auto_examples/plot_UOT_barycenter_1D.ipynb b/docs/source/auto_examples/plot_UOT_barycenter_1D.ipynb new file mode 100644 index 0000000..e59cdc2 --- /dev/null +++ b/docs/source/auto_examples/plot_UOT_barycenter_1D.ipynb @@ -0,0 +1,126 @@ +{ + "cells": [ + { + "cell_type": "code", + "execution_count": null, + "metadata": { + "collapsed": false + }, + "outputs": [], + "source": [ + "%matplotlib inline" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "\n# 1D Wasserstein barycenter demo for Unbalanced distributions\n\n\nThis example illustrates the computation of regularized Wassersyein Barycenter\nas proposed in [10] for Unbalanced inputs.\n\n\n[10] Chizat, L., Peyr\u00e9, G., Schmitzer, B., & Vialard, F. X. (2016). Scaling algorithms for unbalanced transport problems. arXiv preprint arXiv:1607.05816.\n\n\n" + ] + }, + { + "cell_type": "code", + "execution_count": null, + "metadata": { + "collapsed": false + }, + "outputs": [], + "source": [ + "# Author: Hicham Janati <hicham.janati@inria.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" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "Generate data\n-------------\n\n" + ] + }, + { + "cell_type": "code", + "execution_count": null, + "metadata": { + "collapsed": false + }, + "outputs": [], + "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.make_1D_gauss(n, m=20, s=5) # m= mean, s= std\na2 = ot.datasets.make_1D_gauss(n, m=60, s=8)\n\n# make unbalanced dists\na2 *= 3.\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()" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "Plot data\n---------\n\n" + ] + }, + { + "cell_type": "code", + "execution_count": null, + "metadata": { + "collapsed": false + }, + "outputs": [], + "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()" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "Barycenter computation\n----------------------\n\n" + ] + }, + { + "cell_type": "code", + "execution_count": null, + "metadata": { + "collapsed": false + }, + "outputs": [], + "source": [ + "# non weighted barycenter computation\n\nweight = 0.5 # 0<=weight<=1\nweights = np.array([1 - weight, weight])\n\n# l2bary\nbary_l2 = A.dot(weights)\n\n# wasserstein\nreg = 1e-3\nalpha = 1.\n\nbary_wass = ot.unbalanced.barycenter_unbalanced(A, M, reg, alpha, 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()" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "Barycentric interpolation\n-------------------------\n\n" + ] + }, + { + "cell_type": "code", + "execution_count": null, + "metadata": { + "collapsed": false + }, + "outputs": [], + "source": [ + "# barycenter interpolation\n\nn_weight = 11\nweight_list = np.linspace(0, 1, n_weight)\n\n\nB_l2 = np.zeros((n, n_weight))\n\nB_wass = np.copy(B_l2)\n\nfor i in range(0, n_weight):\n weight = weight_list[i]\n weights = np.array([1 - weight, weight])\n B_l2[:, i] = A.dot(weights)\n B_wass[:, i] = ot.unbalanced.barycenter_unbalanced(A, M, reg, alpha, weights)\n\n\n# plot interpolation\n\npl.figure(3)\n\ncmap = pl.cm.get_cmap('viridis')\nverts = []\nzs = weight_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 weight_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(r'$\\alpha$')\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 = weight_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 weight_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(r'$\\alpha$')\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()" + ] + } + ], + "metadata": { + "kernelspec": { + "display_name": "Python 3", + "language": "python", + "name": "python3" + }, + "language_info": { + "codemirror_mode": { + "name": "ipython", + "version": 3 + }, + "file_extension": ".py", + "mimetype": "text/x-python", + "name": "python", + "nbconvert_exporter": "python", + "pygments_lexer": "ipython3", + "version": "3.6.8" + } + }, + "nbformat": 4, + "nbformat_minor": 0 +}
\ No newline at end of file diff --git a/docs/source/auto_examples/plot_UOT_barycenter_1D.py b/docs/source/auto_examples/plot_UOT_barycenter_1D.py new file mode 100644 index 0000000..c8d9d3b --- /dev/null +++ b/docs/source/auto_examples/plot_UOT_barycenter_1D.py @@ -0,0 +1,164 @@ +# -*- coding: utf-8 -*- +""" +=========================================================== +1D Wasserstein barycenter demo for Unbalanced distributions +=========================================================== + +This example illustrates the computation of regularized Wassersyein Barycenter +as proposed in [10] for Unbalanced inputs. + + +[10] Chizat, L., Peyré, G., Schmitzer, B., & Vialard, F. X. (2016). Scaling algorithms for unbalanced transport problems. arXiv preprint arXiv:1607.05816. + +""" + +# Author: Hicham Janati <hicham.janati@inria.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 + +############################################################################## +# Generate data +# ------------- + +# parameters + +n = 100 # nb bins + +# bin positions +x = np.arange(n, dtype=np.float64) + +# Gaussian distributions +a1 = ot.datasets.make_1D_gauss(n, m=20, s=5) # m= mean, s= std +a2 = ot.datasets.make_1D_gauss(n, m=60, s=8) + +# make unbalanced dists +a2 *= 3. + +# creating matrix A containing all distributions +A = np.vstack((a1, a2)).T +n_distributions = A.shape[1] + +# loss matrix + normalization +M = ot.utils.dist0(n) +M /= M.max() + +############################################################################## +# Plot data +# --------- + +# plot the distributions + +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 +# ---------------------- + +# non weighted barycenter computation + +weight = 0.5 # 0<=weight<=1 +weights = np.array([1 - weight, weight]) + +# l2bary +bary_l2 = A.dot(weights) + +# wasserstein +reg = 1e-3 +alpha = 1. + +bary_wass = ot.unbalanced.barycenter_unbalanced(A, M, reg, alpha, weights) + +pl.figure(2) +pl.clf() +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.legend() +pl.title('Barycenters') +pl.tight_layout() + +############################################################################## +# Barycentric interpolation +# ------------------------- + +# barycenter interpolation + +n_weight = 11 +weight_list = np.linspace(0, 1, n_weight) + + +B_l2 = np.zeros((n, n_weight)) + +B_wass = np.copy(B_l2) + +for i in range(0, n_weight): + weight = weight_list[i] + weights = np.array([1 - weight, weight]) + B_l2[:, i] = A.dot(weights) + B_wass[:, i] = ot.unbalanced.barycenter_unbalanced(A, M, reg, alpha, weights) + + +# plot interpolation + +pl.figure(3) + +cmap = pl.cm.get_cmap('viridis') +verts = [] +zs = weight_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 weight_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(r'$\alpha$') +ax.set_ylim3d(0, 1) +ax.set_zlabel('') +ax.set_zlim3d(0, B_l2.max() * 1.01) +pl.title('Barycenter interpolation with l2') +pl.tight_layout() + +pl.figure(4) +cmap = pl.cm.get_cmap('viridis') +verts = [] +zs = weight_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 weight_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(r'$\alpha$') +ax.set_ylim3d(0, 1) +ax.set_zlabel('') +ax.set_zlim3d(0, B_l2.max() * 1.01) +pl.title('Barycenter interpolation with Wasserstein') +pl.tight_layout() + +pl.show() diff --git a/docs/source/auto_examples/plot_UOT_barycenter_1D.rst b/docs/source/auto_examples/plot_UOT_barycenter_1D.rst new file mode 100644 index 0000000..ac17587 --- /dev/null +++ b/docs/source/auto_examples/plot_UOT_barycenter_1D.rst @@ -0,0 +1,261 @@ + + +.. _sphx_glr_auto_examples_plot_UOT_barycenter_1D.py: + + +=========================================================== +1D Wasserstein barycenter demo for Unbalanced distributions +=========================================================== + +This example illustrates the computation of regularized Wassersyein Barycenter +as proposed in [10] for Unbalanced inputs. + + +[10] Chizat, L., Peyré, G., Schmitzer, B., & Vialard, F. X. (2016). Scaling algorithms for unbalanced transport problems. arXiv preprint arXiv:1607.05816. + + + + +.. code-block:: python + + + # Author: Hicham Janati <hicham.janati@inria.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 + + + + + + + +Generate data +------------- + + + +.. code-block:: python + + + # parameters + + n = 100 # nb bins + + # bin positions + x = np.arange(n, dtype=np.float64) + + # Gaussian distributions + a1 = ot.datasets.make_1D_gauss(n, m=20, s=5) # m= mean, s= std + a2 = ot.datasets.make_1D_gauss(n, m=60, s=8) + + # make unbalanced dists + a2 *= 3. + + # creating matrix A containing all distributions + A = np.vstack((a1, a2)).T + n_distributions = A.shape[1] + + # loss matrix + normalization + M = ot.utils.dist0(n) + M /= M.max() + + + + + + + +Plot data +--------- + + + +.. code-block:: python + + + # plot the distributions + + 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_UOT_barycenter_1D_001.png + :align: center + + + + +Barycenter computation +---------------------- + + + +.. code-block:: python + + + # non weighted barycenter computation + + weight = 0.5 # 0<=weight<=1 + weights = np.array([1 - weight, weight]) + + # l2bary + bary_l2 = A.dot(weights) + + # wasserstein + reg = 1e-3 + alpha = 1. + + bary_wass = ot.unbalanced.barycenter_unbalanced(A, M, reg, alpha, weights) + + pl.figure(2) + pl.clf() + 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.legend() + pl.title('Barycenters') + pl.tight_layout() + + + + +.. image:: /auto_examples/images/sphx_glr_plot_UOT_barycenter_1D_003.png + :align: center + + + + +Barycentric interpolation +------------------------- + + + +.. code-block:: python + + + # barycenter interpolation + + n_weight = 11 + weight_list = np.linspace(0, 1, n_weight) + + + B_l2 = np.zeros((n, n_weight)) + + B_wass = np.copy(B_l2) + + for i in range(0, n_weight): + weight = weight_list[i] + weights = np.array([1 - weight, weight]) + B_l2[:, i] = A.dot(weights) + B_wass[:, i] = ot.unbalanced.barycenter_unbalanced(A, M, reg, alpha, weights) + + + # plot interpolation + + pl.figure(3) + + cmap = pl.cm.get_cmap('viridis') + verts = [] + zs = weight_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 weight_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(r'$\alpha$') + ax.set_ylim3d(0, 1) + ax.set_zlabel('') + ax.set_zlim3d(0, B_l2.max() * 1.01) + pl.title('Barycenter interpolation with l2') + pl.tight_layout() + + pl.figure(4) + cmap = pl.cm.get_cmap('viridis') + verts = [] + zs = weight_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 weight_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(r'$\alpha$') + ax.set_ylim3d(0, 1) + ax.set_zlabel('') + ax.set_zlim3d(0, B_l2.max() * 1.01) + pl.title('Barycenter interpolation with Wasserstein') + pl.tight_layout() + + pl.show() + + + +.. rst-class:: sphx-glr-horizontal + + + * + + .. image:: /auto_examples/images/sphx_glr_plot_UOT_barycenter_1D_005.png + :scale: 47 + + * + + .. image:: /auto_examples/images/sphx_glr_plot_UOT_barycenter_1D_006.png + :scale: 47 + + + + +**Total running time of the script:** ( 0 minutes 0.344 seconds) + + + +.. only :: html + + .. container:: sphx-glr-footer + + + .. container:: sphx-glr-download + + :download:`Download Python source code: plot_UOT_barycenter_1D.py <plot_UOT_barycenter_1D.py>` + + + + .. container:: sphx-glr-download + + :download:`Download Jupyter notebook: plot_UOT_barycenter_1D.ipynb <plot_UOT_barycenter_1D.ipynb>` + + +.. only:: html + + .. rst-class:: sphx-glr-signature + + `Gallery generated by Sphinx-Gallery <https://sphinx-gallery.readthedocs.io>`_ diff --git a/docs/source/auto_examples/plot_barycenter_fgw.ipynb b/docs/source/auto_examples/plot_barycenter_fgw.ipynb new file mode 100644 index 0000000..28229b2 --- /dev/null +++ b/docs/source/auto_examples/plot_barycenter_fgw.ipynb @@ -0,0 +1,126 @@ +{ + "cells": [ + { + "cell_type": "code", + "execution_count": null, + "metadata": { + "collapsed": false + }, + "outputs": [], + "source": [ + "%matplotlib inline" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "\n=================================\nPlot graphs' barycenter using FGW\n=================================\n\nThis example illustrates the computation barycenter of labeled graphs using FGW\n\nRequires networkx >=2\n\n.. [18] Vayer Titouan, Chapel Laetitia, Flamary R{'e}mi, Tavenard Romain\n and Courty Nicolas\n \"Optimal Transport for structured data with application on graphs\"\n International Conference on Machine Learning (ICML). 2019.\n\n\n" + ] + }, + { + "cell_type": "code", + "execution_count": null, + "metadata": { + "collapsed": false + }, + "outputs": [], + "source": [ + "# Author: Titouan Vayer <titouan.vayer@irisa.fr>\n#\n# License: MIT License\n\n#%% load libraries\nimport numpy as np\nimport matplotlib.pyplot as plt\nimport networkx as nx\nimport math\nfrom scipy.sparse.csgraph import shortest_path\nimport matplotlib.colors as mcol\nfrom matplotlib import cm\nfrom ot.gromov import fgw_barycenters\n#%% Graph functions\n\n\ndef find_thresh(C, inf=0.5, sup=3, step=10):\n \"\"\" Trick to find the adequate thresholds from where value of the C matrix are considered close enough to say that nodes are connected\n Tthe threshold is found by a linesearch between values \"inf\" and \"sup\" with \"step\" thresholds tested.\n The optimal threshold is the one which minimizes the reconstruction error between the shortest_path matrix coming from the thresholded adjency matrix\n and the original matrix.\n Parameters\n ----------\n C : ndarray, shape (n_nodes,n_nodes)\n The structure matrix to threshold\n inf : float\n The beginning of the linesearch\n sup : float\n The end of the linesearch\n step : integer\n Number of thresholds tested\n \"\"\"\n dist = []\n search = np.linspace(inf, sup, step)\n for thresh in search:\n Cprime = sp_to_adjency(C, 0, thresh)\n SC = shortest_path(Cprime, method='D')\n SC[SC == float('inf')] = 100\n dist.append(np.linalg.norm(SC - C))\n return search[np.argmin(dist)], dist\n\n\ndef sp_to_adjency(C, threshinf=0.2, threshsup=1.8):\n \"\"\" Thresholds the structure matrix in order to compute an adjency matrix.\n All values between threshinf and threshsup are considered representing connected nodes and set to 1. Else are set to 0\n Parameters\n ----------\n C : ndarray, shape (n_nodes,n_nodes)\n The structure matrix to threshold\n threshinf : float\n The minimum value of distance from which the new value is set to 1\n threshsup : float\n The maximum value of distance from which the new value is set to 1\n Returns\n -------\n C : ndarray, shape (n_nodes,n_nodes)\n The threshold matrix. Each element is in {0,1}\n \"\"\"\n H = np.zeros_like(C)\n np.fill_diagonal(H, np.diagonal(C))\n C = C - H\n C = np.minimum(np.maximum(C, threshinf), threshsup)\n C[C == threshsup] = 0\n C[C != 0] = 1\n\n return C\n\n\ndef build_noisy_circular_graph(N=20, mu=0, sigma=0.3, with_noise=False, structure_noise=False, p=None):\n \"\"\" Create a noisy circular graph\n \"\"\"\n g = nx.Graph()\n g.add_nodes_from(list(range(N)))\n for i in range(N):\n noise = float(np.random.normal(mu, sigma, 1))\n if with_noise:\n g.add_node(i, attr_name=math.sin((2 * i * math.pi / N)) + noise)\n else:\n g.add_node(i, attr_name=math.sin(2 * i * math.pi / N))\n g.add_edge(i, i + 1)\n if structure_noise:\n randomint = np.random.randint(0, p)\n if randomint == 0:\n if i <= N - 3:\n g.add_edge(i, i + 2)\n if i == N - 2:\n g.add_edge(i, 0)\n if i == N - 1:\n g.add_edge(i, 1)\n g.add_edge(N, 0)\n noise = float(np.random.normal(mu, sigma, 1))\n if with_noise:\n g.add_node(N, attr_name=math.sin((2 * N * math.pi / N)) + noise)\n else:\n g.add_node(N, attr_name=math.sin(2 * N * math.pi / N))\n return g\n\n\ndef graph_colors(nx_graph, vmin=0, vmax=7):\n cnorm = mcol.Normalize(vmin=vmin, vmax=vmax)\n cpick = cm.ScalarMappable(norm=cnorm, cmap='viridis')\n cpick.set_array([])\n val_map = {}\n for k, v in nx.get_node_attributes(nx_graph, 'attr_name').items():\n val_map[k] = cpick.to_rgba(v)\n colors = []\n for node in nx_graph.nodes():\n colors.append(val_map[node])\n return colors" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "Generate data\n-------------\n\n" + ] + }, + { + "cell_type": "code", + "execution_count": null, + "metadata": { + "collapsed": false + }, + "outputs": [], + "source": [ + "#%% circular dataset\n# We build a dataset of noisy circular graphs.\n# Noise is added on the structures by random connections and on the features by gaussian noise.\n\n\nnp.random.seed(30)\nX0 = []\nfor k in range(9):\n X0.append(build_noisy_circular_graph(np.random.randint(15, 25), with_noise=True, structure_noise=True, p=3))" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "Plot data\n---------\n\n" + ] + }, + { + "cell_type": "code", + "execution_count": null, + "metadata": { + "collapsed": false + }, + "outputs": [], + "source": [ + "#%% Plot graphs\n\nplt.figure(figsize=(8, 10))\nfor i in range(len(X0)):\n plt.subplot(3, 3, i + 1)\n g = X0[i]\n pos = nx.kamada_kawai_layout(g)\n nx.draw(g, pos=pos, node_color=graph_colors(g, vmin=-1, vmax=1), with_labels=False, node_size=100)\nplt.suptitle('Dataset of noisy graphs. Color indicates the label', fontsize=20)\nplt.show()" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "Barycenter computation\n----------------------\n\n" + ] + }, + { + "cell_type": "code", + "execution_count": null, + "metadata": { + "collapsed": false + }, + "outputs": [], + "source": [ + "#%% We compute the barycenter using FGW. Structure matrices are computed using the shortest_path distance in the graph\n# Features distances are the euclidean distances\nCs = [shortest_path(nx.adjacency_matrix(x)) for x in X0]\nps = [np.ones(len(x.nodes())) / len(x.nodes()) for x in X0]\nYs = [np.array([v for (k, v) in nx.get_node_attributes(x, 'attr_name').items()]).reshape(-1, 1) for x in X0]\nlambdas = np.array([np.ones(len(Ys)) / len(Ys)]).ravel()\nsizebary = 15 # we choose a barycenter with 15 nodes\n\nA, C, log = fgw_barycenters(sizebary, Ys, Cs, ps, lambdas, alpha=0.95, log=True)" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "Plot Barycenter\n-------------------------\n\n" + ] + }, + { + "cell_type": "code", + "execution_count": null, + "metadata": { + "collapsed": false + }, + "outputs": [], + "source": [ + "#%% Create the barycenter\nbary = nx.from_numpy_matrix(sp_to_adjency(C, threshinf=0, threshsup=find_thresh(C, sup=100, step=100)[0]))\nfor i, v in enumerate(A.ravel()):\n bary.add_node(i, attr_name=v)\n\n#%%\npos = nx.kamada_kawai_layout(bary)\nnx.draw(bary, pos=pos, node_color=graph_colors(bary, vmin=-1, vmax=1), with_labels=False)\nplt.suptitle('Barycenter', fontsize=20)\nplt.show()" + ] + } + ], + "metadata": { + "kernelspec": { + "display_name": "Python 3", + "language": "python", + "name": "python3" + }, + "language_info": { + "codemirror_mode": { + "name": "ipython", + "version": 3 + }, + "file_extension": ".py", + "mimetype": "text/x-python", + "name": "python", + "nbconvert_exporter": "python", + "pygments_lexer": "ipython3", + "version": "3.6.8" + } + }, + "nbformat": 4, + "nbformat_minor": 0 +}
\ No newline at end of file diff --git a/docs/source/auto_examples/plot_barycenter_fgw.py b/docs/source/auto_examples/plot_barycenter_fgw.py new file mode 100644 index 0000000..77b0370 --- /dev/null +++ b/docs/source/auto_examples/plot_barycenter_fgw.py @@ -0,0 +1,184 @@ +# -*- coding: utf-8 -*- +""" +================================= +Plot graphs' barycenter using FGW +================================= + +This example illustrates the computation barycenter of labeled graphs using FGW + +Requires networkx >=2 + +.. [18] Vayer Titouan, Chapel Laetitia, Flamary R{\'e}mi, Tavenard Romain + and Courty Nicolas + "Optimal Transport for structured data with application on graphs" + International Conference on Machine Learning (ICML). 2019. + +""" + +# Author: Titouan Vayer <titouan.vayer@irisa.fr> +# +# License: MIT License + +#%% load libraries +import numpy as np +import matplotlib.pyplot as plt +import networkx as nx +import math +from scipy.sparse.csgraph import shortest_path +import matplotlib.colors as mcol +from matplotlib import cm +from ot.gromov import fgw_barycenters +#%% Graph functions + + +def find_thresh(C, inf=0.5, sup=3, step=10): + """ Trick to find the adequate thresholds from where value of the C matrix are considered close enough to say that nodes are connected + Tthe threshold is found by a linesearch between values "inf" and "sup" with "step" thresholds tested. + The optimal threshold is the one which minimizes the reconstruction error between the shortest_path matrix coming from the thresholded adjency matrix + and the original matrix. + Parameters + ---------- + C : ndarray, shape (n_nodes,n_nodes) + The structure matrix to threshold + inf : float + The beginning of the linesearch + sup : float + The end of the linesearch + step : integer + Number of thresholds tested + """ + dist = [] + search = np.linspace(inf, sup, step) + for thresh in search: + Cprime = sp_to_adjency(C, 0, thresh) + SC = shortest_path(Cprime, method='D') + SC[SC == float('inf')] = 100 + dist.append(np.linalg.norm(SC - C)) + return search[np.argmin(dist)], dist + + +def sp_to_adjency(C, threshinf=0.2, threshsup=1.8): + """ Thresholds the structure matrix in order to compute an adjency matrix. + All values between threshinf and threshsup are considered representing connected nodes and set to 1. Else are set to 0 + Parameters + ---------- + C : ndarray, shape (n_nodes,n_nodes) + The structure matrix to threshold + threshinf : float + The minimum value of distance from which the new value is set to 1 + threshsup : float + The maximum value of distance from which the new value is set to 1 + Returns + ------- + C : ndarray, shape (n_nodes,n_nodes) + The threshold matrix. Each element is in {0,1} + """ + H = np.zeros_like(C) + np.fill_diagonal(H, np.diagonal(C)) + C = C - H + C = np.minimum(np.maximum(C, threshinf), threshsup) + C[C == threshsup] = 0 + C[C != 0] = 1 + + return C + + +def build_noisy_circular_graph(N=20, mu=0, sigma=0.3, with_noise=False, structure_noise=False, p=None): + """ Create a noisy circular graph + """ + g = nx.Graph() + g.add_nodes_from(list(range(N))) + for i in range(N): + noise = float(np.random.normal(mu, sigma, 1)) + if with_noise: + g.add_node(i, attr_name=math.sin((2 * i * math.pi / N)) + noise) + else: + g.add_node(i, attr_name=math.sin(2 * i * math.pi / N)) + g.add_edge(i, i + 1) + if structure_noise: + randomint = np.random.randint(0, p) + if randomint == 0: + if i <= N - 3: + g.add_edge(i, i + 2) + if i == N - 2: + g.add_edge(i, 0) + if i == N - 1: + g.add_edge(i, 1) + g.add_edge(N, 0) + noise = float(np.random.normal(mu, sigma, 1)) + if with_noise: + g.add_node(N, attr_name=math.sin((2 * N * math.pi / N)) + noise) + else: + g.add_node(N, attr_name=math.sin(2 * N * math.pi / N)) + return g + + +def graph_colors(nx_graph, vmin=0, vmax=7): + cnorm = mcol.Normalize(vmin=vmin, vmax=vmax) + cpick = cm.ScalarMappable(norm=cnorm, cmap='viridis') + cpick.set_array([]) + val_map = {} + for k, v in nx.get_node_attributes(nx_graph, 'attr_name').items(): + val_map[k] = cpick.to_rgba(v) + colors = [] + for node in nx_graph.nodes(): + colors.append(val_map[node]) + return colors + +############################################################################## +# Generate data +# ------------- + +#%% circular dataset +# We build a dataset of noisy circular graphs. +# Noise is added on the structures by random connections and on the features by gaussian noise. + + +np.random.seed(30) +X0 = [] +for k in range(9): + X0.append(build_noisy_circular_graph(np.random.randint(15, 25), with_noise=True, structure_noise=True, p=3)) + +############################################################################## +# Plot data +# --------- + +#%% Plot graphs + +plt.figure(figsize=(8, 10)) +for i in range(len(X0)): + plt.subplot(3, 3, i + 1) + g = X0[i] + pos = nx.kamada_kawai_layout(g) + nx.draw(g, pos=pos, node_color=graph_colors(g, vmin=-1, vmax=1), with_labels=False, node_size=100) +plt.suptitle('Dataset of noisy graphs. Color indicates the label', fontsize=20) +plt.show() + +############################################################################## +# Barycenter computation +# ---------------------- + +#%% We compute the barycenter using FGW. Structure matrices are computed using the shortest_path distance in the graph +# Features distances are the euclidean distances +Cs = [shortest_path(nx.adjacency_matrix(x)) for x in X0] +ps = [np.ones(len(x.nodes())) / len(x.nodes()) for x in X0] +Ys = [np.array([v for (k, v) in nx.get_node_attributes(x, 'attr_name').items()]).reshape(-1, 1) for x in X0] +lambdas = np.array([np.ones(len(Ys)) / len(Ys)]).ravel() +sizebary = 15 # we choose a barycenter with 15 nodes + +A, C, log = fgw_barycenters(sizebary, Ys, Cs, ps, lambdas, alpha=0.95, log=True) + +############################################################################## +# Plot Barycenter +# ------------------------- + +#%% Create the barycenter +bary = nx.from_numpy_matrix(sp_to_adjency(C, threshinf=0, threshsup=find_thresh(C, sup=100, step=100)[0])) +for i, v in enumerate(A.ravel()): + bary.add_node(i, attr_name=v) + +#%% +pos = nx.kamada_kawai_layout(bary) +nx.draw(bary, pos=pos, node_color=graph_colors(bary, vmin=-1, vmax=1), with_labels=False) +plt.suptitle('Barycenter', fontsize=20) +plt.show() diff --git a/docs/source/auto_examples/plot_barycenter_fgw.rst b/docs/source/auto_examples/plot_barycenter_fgw.rst new file mode 100644 index 0000000..2c44a65 --- /dev/null +++ b/docs/source/auto_examples/plot_barycenter_fgw.rst @@ -0,0 +1,268 @@ + + +.. _sphx_glr_auto_examples_plot_barycenter_fgw.py: + + +================================= +Plot graphs' barycenter using FGW +================================= + +This example illustrates the computation barycenter of labeled graphs using FGW + +Requires networkx >=2 + +.. [18] Vayer Titouan, Chapel Laetitia, Flamary R{'e}mi, Tavenard Romain + and Courty Nicolas + "Optimal Transport for structured data with application on graphs" + International Conference on Machine Learning (ICML). 2019. + + + + +.. code-block:: python + + + # Author: Titouan Vayer <titouan.vayer@irisa.fr> + # + # License: MIT License + + #%% load libraries + import numpy as np + import matplotlib.pyplot as plt + import networkx as nx + import math + from scipy.sparse.csgraph import shortest_path + import matplotlib.colors as mcol + from matplotlib import cm + from ot.gromov import fgw_barycenters + #%% Graph functions + + + def find_thresh(C, inf=0.5, sup=3, step=10): + """ Trick to find the adequate thresholds from where value of the C matrix are considered close enough to say that nodes are connected + Tthe threshold is found by a linesearch between values "inf" and "sup" with "step" thresholds tested. + The optimal threshold is the one which minimizes the reconstruction error between the shortest_path matrix coming from the thresholded adjency matrix + and the original matrix. + Parameters + ---------- + C : ndarray, shape (n_nodes,n_nodes) + The structure matrix to threshold + inf : float + The beginning of the linesearch + sup : float + The end of the linesearch + step : integer + Number of thresholds tested + """ + dist = [] + search = np.linspace(inf, sup, step) + for thresh in search: + Cprime = sp_to_adjency(C, 0, thresh) + SC = shortest_path(Cprime, method='D') + SC[SC == float('inf')] = 100 + dist.append(np.linalg.norm(SC - C)) + return search[np.argmin(dist)], dist + + + def sp_to_adjency(C, threshinf=0.2, threshsup=1.8): + """ Thresholds the structure matrix in order to compute an adjency matrix. + All values between threshinf and threshsup are considered representing connected nodes and set to 1. Else are set to 0 + Parameters + ---------- + C : ndarray, shape (n_nodes,n_nodes) + The structure matrix to threshold + threshinf : float + The minimum value of distance from which the new value is set to 1 + threshsup : float + The maximum value of distance from which the new value is set to 1 + Returns + ------- + C : ndarray, shape (n_nodes,n_nodes) + The threshold matrix. Each element is in {0,1} + """ + H = np.zeros_like(C) + np.fill_diagonal(H, np.diagonal(C)) + C = C - H + C = np.minimum(np.maximum(C, threshinf), threshsup) + C[C == threshsup] = 0 + C[C != 0] = 1 + + return C + + + def build_noisy_circular_graph(N=20, mu=0, sigma=0.3, with_noise=False, structure_noise=False, p=None): + """ Create a noisy circular graph + """ + g = nx.Graph() + g.add_nodes_from(list(range(N))) + for i in range(N): + noise = float(np.random.normal(mu, sigma, 1)) + if with_noise: + g.add_node(i, attr_name=math.sin((2 * i * math.pi / N)) + noise) + else: + g.add_node(i, attr_name=math.sin(2 * i * math.pi / N)) + g.add_edge(i, i + 1) + if structure_noise: + randomint = np.random.randint(0, p) + if randomint == 0: + if i <= N - 3: + g.add_edge(i, i + 2) + if i == N - 2: + g.add_edge(i, 0) + if i == N - 1: + g.add_edge(i, 1) + g.add_edge(N, 0) + noise = float(np.random.normal(mu, sigma, 1)) + if with_noise: + g.add_node(N, attr_name=math.sin((2 * N * math.pi / N)) + noise) + else: + g.add_node(N, attr_name=math.sin(2 * N * math.pi / N)) + return g + + + def graph_colors(nx_graph, vmin=0, vmax=7): + cnorm = mcol.Normalize(vmin=vmin, vmax=vmax) + cpick = cm.ScalarMappable(norm=cnorm, cmap='viridis') + cpick.set_array([]) + val_map = {} + for k, v in nx.get_node_attributes(nx_graph, 'attr_name').items(): + val_map[k] = cpick.to_rgba(v) + colors = [] + for node in nx_graph.nodes(): + colors.append(val_map[node]) + return colors + + + + + + + +Generate data +------------- + + + +.. code-block:: python + + + #%% circular dataset + # We build a dataset of noisy circular graphs. + # Noise is added on the structures by random connections and on the features by gaussian noise. + + + np.random.seed(30) + X0 = [] + for k in range(9): + X0.append(build_noisy_circular_graph(np.random.randint(15, 25), with_noise=True, structure_noise=True, p=3)) + + + + + + + +Plot data +--------- + + + +.. code-block:: python + + + #%% Plot graphs + + plt.figure(figsize=(8, 10)) + for i in range(len(X0)): + plt.subplot(3, 3, i + 1) + g = X0[i] + pos = nx.kamada_kawai_layout(g) + nx.draw(g, pos=pos, node_color=graph_colors(g, vmin=-1, vmax=1), with_labels=False, node_size=100) + plt.suptitle('Dataset of noisy graphs. Color indicates the label', fontsize=20) + plt.show() + + + + +.. image:: /auto_examples/images/sphx_glr_plot_barycenter_fgw_001.png + :align: center + + + + +Barycenter computation +---------------------- + + + +.. code-block:: python + + + #%% We compute the barycenter using FGW. Structure matrices are computed using the shortest_path distance in the graph + # Features distances are the euclidean distances + Cs = [shortest_path(nx.adjacency_matrix(x)) for x in X0] + ps = [np.ones(len(x.nodes())) / len(x.nodes()) for x in X0] + Ys = [np.array([v for (k, v) in nx.get_node_attributes(x, 'attr_name').items()]).reshape(-1, 1) for x in X0] + lambdas = np.array([np.ones(len(Ys)) / len(Ys)]).ravel() + sizebary = 15 # we choose a barycenter with 15 nodes + + A, C, log = fgw_barycenters(sizebary, Ys, Cs, ps, lambdas, alpha=0.95, log=True) + + + + + + + +Plot Barycenter +------------------------- + + + +.. code-block:: python + + + #%% Create the barycenter + bary = nx.from_numpy_matrix(sp_to_adjency(C, threshinf=0, threshsup=find_thresh(C, sup=100, step=100)[0])) + for i, v in enumerate(A.ravel()): + bary.add_node(i, attr_name=v) + + #%% + pos = nx.kamada_kawai_layout(bary) + nx.draw(bary, pos=pos, node_color=graph_colors(bary, vmin=-1, vmax=1), with_labels=False) + plt.suptitle('Barycenter', fontsize=20) + plt.show() + + + +.. image:: /auto_examples/images/sphx_glr_plot_barycenter_fgw_002.png + :align: center + + + + +**Total running time of the script:** ( 0 minutes 2.065 seconds) + + + +.. only :: html + + .. container:: sphx-glr-footer + + + .. container:: sphx-glr-download + + :download:`Download Python source code: plot_barycenter_fgw.py <plot_barycenter_fgw.py>` + + + + .. container:: sphx-glr-download + + :download:`Download Jupyter notebook: plot_barycenter_fgw.ipynb <plot_barycenter_fgw.ipynb>` + + +.. only:: html + + .. rst-class:: sphx-glr-signature + + `Gallery generated by Sphinx-Gallery <https://sphinx-gallery.readthedocs.io>`_ diff --git a/docs/source/auto_examples/plot_fgw.ipynb b/docs/source/auto_examples/plot_fgw.ipynb new file mode 100644 index 0000000..1b150bd --- /dev/null +++ b/docs/source/auto_examples/plot_fgw.ipynb @@ -0,0 +1,162 @@ +{ + "cells": [ + { + "cell_type": "code", + "execution_count": null, + "metadata": { + "collapsed": false + }, + "outputs": [], + "source": [ + "%matplotlib inline" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "\n# Plot Fused-gromov-Wasserstein\n\n\nThis example illustrates the computation of FGW for 1D measures[18].\n\n.. [18] Vayer Titouan, Chapel Laetitia, Flamary R{'e}mi, Tavenard Romain\n and Courty Nicolas\n \"Optimal Transport for structured data with application on graphs\"\n International Conference on Machine Learning (ICML). 2019.\n\n\n" + ] + }, + { + "cell_type": "code", + "execution_count": null, + "metadata": { + "collapsed": false + }, + "outputs": [], + "source": [ + "# Author: Titouan Vayer <titouan.vayer@irisa.fr>\n#\n# License: MIT License\n\nimport matplotlib.pyplot as pl\nimport numpy as np\nimport ot\nfrom ot.gromov import gromov_wasserstein, fused_gromov_wasserstein" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "Generate data\n---------\n\n" + ] + }, + { + "cell_type": "code", + "execution_count": null, + "metadata": { + "collapsed": false + }, + "outputs": [], + "source": [ + "#%% parameters\n# We create two 1D random measures\nn = 20 # number of points in the first distribution\nn2 = 30 # number of points in the second distribution\nsig = 1 # std of first distribution\nsig2 = 0.1 # std of second distribution\n\nnp.random.seed(0)\n\nphi = np.arange(n)[:, None]\nxs = phi + sig * np.random.randn(n, 1)\nys = np.vstack((np.ones((n // 2, 1)), 0 * np.ones((n // 2, 1)))) + sig2 * np.random.randn(n, 1)\n\nphi2 = np.arange(n2)[:, None]\nxt = phi2 + sig * np.random.randn(n2, 1)\nyt = np.vstack((np.ones((n2 // 2, 1)), 0 * np.ones((n2 // 2, 1)))) + sig2 * np.random.randn(n2, 1)\nyt = yt[::-1, :]\n\np = ot.unif(n)\nq = ot.unif(n2)" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "Plot data\n---------\n\n" + ] + }, + { + "cell_type": "code", + "execution_count": null, + "metadata": { + "collapsed": false + }, + "outputs": [], + "source": [ + "#%% plot the distributions\n\npl.close(10)\npl.figure(10, (7, 7))\n\npl.subplot(2, 1, 1)\n\npl.scatter(ys, xs, c=phi, s=70)\npl.ylabel('Feature value a', fontsize=20)\npl.title('$\\mu=\\sum_i \\delta_{x_i,a_i}$', fontsize=25, usetex=True, y=1)\npl.xticks(())\npl.yticks(())\npl.subplot(2, 1, 2)\npl.scatter(yt, xt, c=phi2, s=70)\npl.xlabel('coordinates x/y', fontsize=25)\npl.ylabel('Feature value b', fontsize=20)\npl.title('$\\\\nu=\\sum_j \\delta_{y_j,b_j}$', fontsize=25, usetex=True, y=1)\npl.yticks(())\npl.tight_layout()\npl.show()" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "Create structure matrices and across-feature distance matrix\n---------\n\n" + ] + }, + { + "cell_type": "code", + "execution_count": null, + "metadata": { + "collapsed": false + }, + "outputs": [], + "source": [ + "#%% Structure matrices and across-features distance matrix\nC1 = ot.dist(xs)\nC2 = ot.dist(xt)\nM = ot.dist(ys, yt)\nw1 = ot.unif(C1.shape[0])\nw2 = ot.unif(C2.shape[0])\nGot = ot.emd([], [], M)" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "Plot matrices\n---------\n\n" + ] + }, + { + "cell_type": "code", + "execution_count": null, + "metadata": { + "collapsed": false + }, + "outputs": [], + "source": [ + "#%%\ncmap = 'Reds'\npl.close(10)\npl.figure(10, (5, 5))\nfs = 15\nl_x = [0, 5, 10, 15]\nl_y = [0, 5, 10, 15, 20, 25]\ngs = pl.GridSpec(5, 5)\n\nax1 = pl.subplot(gs[3:, :2])\n\npl.imshow(C1, cmap=cmap, interpolation='nearest')\npl.title(\"$C_1$\", fontsize=fs)\npl.xlabel(\"$k$\", fontsize=fs)\npl.ylabel(\"$i$\", fontsize=fs)\npl.xticks(l_x)\npl.yticks(l_x)\n\nax2 = pl.subplot(gs[:3, 2:])\n\npl.imshow(C2, cmap=cmap, interpolation='nearest')\npl.title(\"$C_2$\", fontsize=fs)\npl.ylabel(\"$l$\", fontsize=fs)\n#pl.ylabel(\"$l$\",fontsize=fs)\npl.xticks(())\npl.yticks(l_y)\nax2.set_aspect('auto')\n\nax3 = pl.subplot(gs[3:, 2:], sharex=ax2, sharey=ax1)\npl.imshow(M, cmap=cmap, interpolation='nearest')\npl.yticks(l_x)\npl.xticks(l_y)\npl.ylabel(\"$i$\", fontsize=fs)\npl.title(\"$M_{AB}$\", fontsize=fs)\npl.xlabel(\"$j$\", fontsize=fs)\npl.tight_layout()\nax3.set_aspect('auto')\npl.show()" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "Compute FGW/GW\n---------\n\n" + ] + }, + { + "cell_type": "code", + "execution_count": null, + "metadata": { + "collapsed": false + }, + "outputs": [], + "source": [ + "#%% Computing FGW and GW\nalpha = 1e-3\n\not.tic()\nGwg, logw = fused_gromov_wasserstein(M, C1, C2, p, q, loss_fun='square_loss', alpha=alpha, verbose=True, log=True)\not.toc()\n\n#%reload_ext WGW\nGg, log = gromov_wasserstein(C1, C2, p, q, loss_fun='square_loss', verbose=True, log=True)" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "Visualize transport matrices\n---------\n\n" + ] + }, + { + "cell_type": "code", + "execution_count": null, + "metadata": { + "collapsed": false + }, + "outputs": [], + "source": [ + "#%% visu OT matrix\ncmap = 'Blues'\nfs = 15\npl.figure(2, (13, 5))\npl.clf()\npl.subplot(1, 3, 1)\npl.imshow(Got, cmap=cmap, interpolation='nearest')\n#pl.xlabel(\"$y$\",fontsize=fs)\npl.ylabel(\"$i$\", fontsize=fs)\npl.xticks(())\n\npl.title('Wasserstein ($M$ only)')\n\npl.subplot(1, 3, 2)\npl.imshow(Gg, cmap=cmap, interpolation='nearest')\npl.title('Gromov ($C_1,C_2$ only)')\npl.xticks(())\npl.subplot(1, 3, 3)\npl.imshow(Gwg, cmap=cmap, interpolation='nearest')\npl.title('FGW ($M+C_1,C_2$)')\n\npl.xlabel(\"$j$\", fontsize=fs)\npl.ylabel(\"$i$\", fontsize=fs)\n\npl.tight_layout()\npl.show()" + ] + } + ], + "metadata": { + "kernelspec": { + "display_name": "Python 3", + "language": "python", + "name": "python3" + }, + "language_info": { + "codemirror_mode": { + "name": "ipython", + "version": 3 + }, + "file_extension": ".py", + "mimetype": "text/x-python", + "name": "python", + "nbconvert_exporter": "python", + "pygments_lexer": "ipython3", + "version": "3.6.8" + } + }, + "nbformat": 4, + "nbformat_minor": 0 +}
\ No newline at end of file diff --git a/docs/source/auto_examples/plot_fgw.py b/docs/source/auto_examples/plot_fgw.py new file mode 100644 index 0000000..43efc94 --- /dev/null +++ b/docs/source/auto_examples/plot_fgw.py @@ -0,0 +1,173 @@ +# -*- coding: utf-8 -*- +""" +============================== +Plot Fused-gromov-Wasserstein +============================== + +This example illustrates the computation of FGW for 1D measures[18]. + +.. [18] Vayer Titouan, Chapel Laetitia, Flamary R{\'e}mi, Tavenard Romain + and Courty Nicolas + "Optimal Transport for structured data with application on graphs" + International Conference on Machine Learning (ICML). 2019. + +""" + +# Author: Titouan Vayer <titouan.vayer@irisa.fr> +# +# License: MIT License + +import matplotlib.pyplot as pl +import numpy as np +import ot +from ot.gromov import gromov_wasserstein, fused_gromov_wasserstein + +############################################################################## +# Generate data +# --------- + +#%% parameters +# We create two 1D random measures +n = 20 # number of points in the first distribution +n2 = 30 # number of points in the second distribution +sig = 1 # std of first distribution +sig2 = 0.1 # std of second distribution + +np.random.seed(0) + +phi = np.arange(n)[:, None] +xs = phi + sig * np.random.randn(n, 1) +ys = np.vstack((np.ones((n // 2, 1)), 0 * np.ones((n // 2, 1)))) + sig2 * np.random.randn(n, 1) + +phi2 = np.arange(n2)[:, None] +xt = phi2 + sig * np.random.randn(n2, 1) +yt = np.vstack((np.ones((n2 // 2, 1)), 0 * np.ones((n2 // 2, 1)))) + sig2 * np.random.randn(n2, 1) +yt = yt[::-1, :] + +p = ot.unif(n) +q = ot.unif(n2) + +############################################################################## +# Plot data +# --------- + +#%% plot the distributions + +pl.close(10) +pl.figure(10, (7, 7)) + +pl.subplot(2, 1, 1) + +pl.scatter(ys, xs, c=phi, s=70) +pl.ylabel('Feature value a', fontsize=20) +pl.title('$\mu=\sum_i \delta_{x_i,a_i}$', fontsize=25, usetex=True, y=1) +pl.xticks(()) +pl.yticks(()) +pl.subplot(2, 1, 2) +pl.scatter(yt, xt, c=phi2, s=70) +pl.xlabel('coordinates x/y', fontsize=25) +pl.ylabel('Feature value b', fontsize=20) +pl.title('$\\nu=\sum_j \delta_{y_j,b_j}$', fontsize=25, usetex=True, y=1) +pl.yticks(()) +pl.tight_layout() +pl.show() + +############################################################################## +# Create structure matrices and across-feature distance matrix +# --------- + +#%% Structure matrices and across-features distance matrix +C1 = ot.dist(xs) +C2 = ot.dist(xt) +M = ot.dist(ys, yt) +w1 = ot.unif(C1.shape[0]) +w2 = ot.unif(C2.shape[0]) +Got = ot.emd([], [], M) + +############################################################################## +# Plot matrices +# --------- + +#%% +cmap = 'Reds' +pl.close(10) +pl.figure(10, (5, 5)) +fs = 15 +l_x = [0, 5, 10, 15] +l_y = [0, 5, 10, 15, 20, 25] +gs = pl.GridSpec(5, 5) + +ax1 = pl.subplot(gs[3:, :2]) + +pl.imshow(C1, cmap=cmap, interpolation='nearest') +pl.title("$C_1$", fontsize=fs) +pl.xlabel("$k$", fontsize=fs) +pl.ylabel("$i$", fontsize=fs) +pl.xticks(l_x) +pl.yticks(l_x) + +ax2 = pl.subplot(gs[:3, 2:]) + +pl.imshow(C2, cmap=cmap, interpolation='nearest') +pl.title("$C_2$", fontsize=fs) +pl.ylabel("$l$", fontsize=fs) +#pl.ylabel("$l$",fontsize=fs) +pl.xticks(()) +pl.yticks(l_y) +ax2.set_aspect('auto') + +ax3 = pl.subplot(gs[3:, 2:], sharex=ax2, sharey=ax1) +pl.imshow(M, cmap=cmap, interpolation='nearest') +pl.yticks(l_x) +pl.xticks(l_y) +pl.ylabel("$i$", fontsize=fs) +pl.title("$M_{AB}$", fontsize=fs) +pl.xlabel("$j$", fontsize=fs) +pl.tight_layout() +ax3.set_aspect('auto') +pl.show() + +############################################################################## +# Compute FGW/GW +# --------- + +#%% Computing FGW and GW +alpha = 1e-3 + +ot.tic() +Gwg, logw = fused_gromov_wasserstein(M, C1, C2, p, q, loss_fun='square_loss', alpha=alpha, verbose=True, log=True) +ot.toc() + +#%reload_ext WGW +Gg, log = gromov_wasserstein(C1, C2, p, q, loss_fun='square_loss', verbose=True, log=True) + +############################################################################## +# Visualize transport matrices +# --------- + +#%% visu OT matrix +cmap = 'Blues' +fs = 15 +pl.figure(2, (13, 5)) +pl.clf() +pl.subplot(1, 3, 1) +pl.imshow(Got, cmap=cmap, interpolation='nearest') +#pl.xlabel("$y$",fontsize=fs) +pl.ylabel("$i$", fontsize=fs) +pl.xticks(()) + +pl.title('Wasserstein ($M$ only)') + +pl.subplot(1, 3, 2) +pl.imshow(Gg, cmap=cmap, interpolation='nearest') +pl.title('Gromov ($C_1,C_2$ only)') +pl.xticks(()) +pl.subplot(1, 3, 3) +pl.imshow(Gwg, cmap=cmap, interpolation='nearest') +pl.title('FGW ($M+C_1,C_2$)') + +pl.xlabel("$j$", fontsize=fs) +pl.ylabel("$i$", fontsize=fs) + +pl.tight_layout() +pl.show() diff --git a/docs/source/auto_examples/plot_fgw.rst b/docs/source/auto_examples/plot_fgw.rst new file mode 100644 index 0000000..aec725d --- /dev/null +++ b/docs/source/auto_examples/plot_fgw.rst @@ -0,0 +1,297 @@ + + +.. _sphx_glr_auto_examples_plot_fgw.py: + + +============================== +Plot Fused-gromov-Wasserstein +============================== + +This example illustrates the computation of FGW for 1D measures[18]. + +.. [18] Vayer Titouan, Chapel Laetitia, Flamary R{'e}mi, Tavenard Romain + and Courty Nicolas + "Optimal Transport for structured data with application on graphs" + International Conference on Machine Learning (ICML). 2019. + + + + +.. code-block:: python + + + # Author: Titouan Vayer <titouan.vayer@irisa.fr> + # + # License: MIT License + + import matplotlib.pyplot as pl + import numpy as np + import ot + from ot.gromov import gromov_wasserstein, fused_gromov_wasserstein + + + + + + + +Generate data +--------- + + + +.. code-block:: python + + + #%% parameters + # We create two 1D random measures + n = 20 # number of points in the first distribution + n2 = 30 # number of points in the second distribution + sig = 1 # std of first distribution + sig2 = 0.1 # std of second distribution + + np.random.seed(0) + + phi = np.arange(n)[:, None] + xs = phi + sig * np.random.randn(n, 1) + ys = np.vstack((np.ones((n // 2, 1)), 0 * np.ones((n // 2, 1)))) + sig2 * np.random.randn(n, 1) + + phi2 = np.arange(n2)[:, None] + xt = phi2 + sig * np.random.randn(n2, 1) + yt = np.vstack((np.ones((n2 // 2, 1)), 0 * np.ones((n2 // 2, 1)))) + sig2 * np.random.randn(n2, 1) + yt = yt[::-1, :] + + p = ot.unif(n) + q = ot.unif(n2) + + + + + + + +Plot data +--------- + + + +.. code-block:: python + + + #%% plot the distributions + + pl.close(10) + pl.figure(10, (7, 7)) + + pl.subplot(2, 1, 1) + + pl.scatter(ys, xs, c=phi, s=70) + pl.ylabel('Feature value a', fontsize=20) + pl.title('$\mu=\sum_i \delta_{x_i,a_i}$', fontsize=25, usetex=True, y=1) + pl.xticks(()) + pl.yticks(()) + pl.subplot(2, 1, 2) + pl.scatter(yt, xt, c=phi2, s=70) + pl.xlabel('coordinates x/y', fontsize=25) + pl.ylabel('Feature value b', fontsize=20) + pl.title('$\\nu=\sum_j \delta_{y_j,b_j}$', fontsize=25, usetex=True, y=1) + pl.yticks(()) + pl.tight_layout() + pl.show() + + + + +.. image:: /auto_examples/images/sphx_glr_plot_fgw_010.png + :align: center + + + + +Create structure matrices and across-feature distance matrix +--------- + + + +.. code-block:: python + + + #%% Structure matrices and across-features distance matrix + C1 = ot.dist(xs) + C2 = ot.dist(xt) + M = ot.dist(ys, yt) + w1 = ot.unif(C1.shape[0]) + w2 = ot.unif(C2.shape[0]) + Got = ot.emd([], [], M) + + + + + + + +Plot matrices +--------- + + + +.. code-block:: python + + + #%% + cmap = 'Reds' + pl.close(10) + pl.figure(10, (5, 5)) + fs = 15 + l_x = [0, 5, 10, 15] + l_y = [0, 5, 10, 15, 20, 25] + gs = pl.GridSpec(5, 5) + + ax1 = pl.subplot(gs[3:, :2]) + + pl.imshow(C1, cmap=cmap, interpolation='nearest') + pl.title("$C_1$", fontsize=fs) + pl.xlabel("$k$", fontsize=fs) + pl.ylabel("$i$", fontsize=fs) + pl.xticks(l_x) + pl.yticks(l_x) + + ax2 = pl.subplot(gs[:3, 2:]) + + pl.imshow(C2, cmap=cmap, interpolation='nearest') + pl.title("$C_2$", fontsize=fs) + pl.ylabel("$l$", fontsize=fs) + #pl.ylabel("$l$",fontsize=fs) + pl.xticks(()) + pl.yticks(l_y) + ax2.set_aspect('auto') + + ax3 = pl.subplot(gs[3:, 2:], sharex=ax2, sharey=ax1) + pl.imshow(M, cmap=cmap, interpolation='nearest') + pl.yticks(l_x) + pl.xticks(l_y) + pl.ylabel("$i$", fontsize=fs) + pl.title("$M_{AB}$", fontsize=fs) + pl.xlabel("$j$", fontsize=fs) + pl.tight_layout() + ax3.set_aspect('auto') + pl.show() + + + + +.. image:: /auto_examples/images/sphx_glr_plot_fgw_011.png + :align: center + + + + +Compute FGW/GW +--------- + + + +.. code-block:: python + + + #%% Computing FGW and GW + alpha = 1e-3 + + ot.tic() + Gwg, logw = fused_gromov_wasserstein(M, C1, C2, p, q, loss_fun='square_loss', alpha=alpha, verbose=True, log=True) + ot.toc() + + #%reload_ext WGW + Gg, log = gromov_wasserstein(C1, C2, p, q, loss_fun='square_loss', verbose=True, log=True) + + + + + +.. rst-class:: sphx-glr-script-out + + Out:: + + It. |Loss |Relative loss|Absolute loss + ------------------------------------------------ + 0|4.734462e+01|0.000000e+00|0.000000e+00 + 1|2.508258e+01|8.875498e-01|2.226204e+01 + 2|2.189329e+01|1.456747e-01|3.189297e+00 + 3|2.189329e+01|0.000000e+00|0.000000e+00 + Elapsed time : 0.0016989707946777344 s + It. |Loss |Relative loss|Absolute loss + ------------------------------------------------ + 0|4.683978e+04|0.000000e+00|0.000000e+00 + 1|3.860061e+04|2.134468e-01|8.239175e+03 + 2|2.182948e+04|7.682787e-01|1.677113e+04 + 3|2.182948e+04|0.000000e+00|0.000000e+00 + + +Visualize transport matrices +--------- + + + +.. code-block:: python + + + #%% visu OT matrix + cmap = 'Blues' + fs = 15 + pl.figure(2, (13, 5)) + pl.clf() + pl.subplot(1, 3, 1) + pl.imshow(Got, cmap=cmap, interpolation='nearest') + #pl.xlabel("$y$",fontsize=fs) + pl.ylabel("$i$", fontsize=fs) + pl.xticks(()) + + pl.title('Wasserstein ($M$ only)') + + pl.subplot(1, 3, 2) + pl.imshow(Gg, cmap=cmap, interpolation='nearest') + pl.title('Gromov ($C_1,C_2$ only)') + pl.xticks(()) + pl.subplot(1, 3, 3) + pl.imshow(Gwg, cmap=cmap, interpolation='nearest') + pl.title('FGW ($M+C_1,C_2$)') + + pl.xlabel("$j$", fontsize=fs) + pl.ylabel("$i$", fontsize=fs) + + pl.tight_layout() + pl.show() + + + +.. image:: /auto_examples/images/sphx_glr_plot_fgw_004.png + :align: center + + + + +**Total running time of the script:** ( 0 minutes 1.468 seconds) + + + +.. only :: html + + .. container:: sphx-glr-footer + + + .. container:: sphx-glr-download + + :download:`Download Python source code: plot_fgw.py <plot_fgw.py>` + + + + .. container:: sphx-glr-download + + :download:`Download Jupyter notebook: plot_fgw.ipynb <plot_fgw.ipynb>` + + +.. only:: html + + .. rst-class:: sphx-glr-signature + + `Gallery 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 index 2daf406..103bdec 100644 --- a/docs/source/auto_examples/plot_otda_color_images.ipynb +++ b/docs/source/auto_examples/plot_otda_color_images.ipynb @@ -1,144 +1,144 @@ { - "nbformat_minor": 0, - "nbformat": 4, "cells": [ { - "execution_count": null, - "cell_type": "code", - "source": [ - "%matplotlib inline" - ], - "outputs": [], + "cell_type": "code", + "execution_count": null, "metadata": { "collapsed": false - } - }, - { + }, + "outputs": [], "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": {} - }, + "%matplotlib inline" + ] + }, { - "execution_count": null, - "cell_type": "code", + "cell_type": "markdown", + "metadata": {}, "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": [], + "\n# OT for image color adaptation\n\n\nThis example presents a way of transferring colors between two images\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": "code", + "execution_count": null, "metadata": { "collapsed": false - } - }, + }, + "outputs": [], + "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 an 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)" + ] + }, { + "cell_type": "markdown", + "metadata": {}, "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": [], + "cell_type": "code", + "execution_count": null, "metadata": { "collapsed": false - } - }, + }, + "outputs": [], + "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, :]" + ] + }, { + "cell_type": "markdown", + "metadata": {}, "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": [], + "cell_type": "code", + "execution_count": null, "metadata": { "collapsed": false - } - }, + }, + "outputs": [], + "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')" + ] + }, { + "cell_type": "markdown", + "metadata": {}, "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": [], + "cell_type": "code", + "execution_count": null, "metadata": { "collapsed": false - } - }, + }, + "outputs": [], + "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()" + ] + }, { + "cell_type": "markdown", + "metadata": {}, "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": [], + "cell_type": "code", + "execution_count": null, "metadata": { "collapsed": false - } - }, + }, + "outputs": [], + "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_sinkhorn.transform(Xs=X1)\ntransp_Xt_sinkhorn = ot_sinkhorn.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))" + ] + }, { + "cell_type": "markdown", + "metadata": {}, "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": [], + "cell_type": "code", + "execution_count": null, "metadata": { "collapsed": false - } + }, + "outputs": [], + "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()" + ] } - ], + ], "metadata": { "kernelspec": { - "display_name": "Python 2", - "name": "python2", - "language": "python" - }, + "display_name": "Python 3", + "language": "python", + "name": "python3" + }, "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" - } + "name": "ipython", + "version": 3 + }, + "file_extension": ".py", + "mimetype": "text/x-python", + "name": "python", + "nbconvert_exporter": "python", + "pygments_lexer": "ipython3", + "version": "3.6.7" } - } + }, + "nbformat": 4, + "nbformat_minor": 0 }
\ 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 index e77aec0..62383a2 100644 --- a/docs/source/auto_examples/plot_otda_color_images.py +++ b/docs/source/auto_examples/plot_otda_color_images.py @@ -4,7 +4,7 @@ OT for image color adaptation ============================= -This example presents a way of transferring colors between two image +This example presents a way of transferring colors between two images with Optimal Transport as introduced in [6] [6] Ferradans, S., Papadakis, N., Peyre, G., & Aujol, J. F. (2014). @@ -27,7 +27,7 @@ r = np.random.RandomState(42) def im2mat(I): - """Converts and image to matrix (one pixel per line)""" + """Converts an image to matrix (one pixel per line)""" return I.reshape((I.shape[0] * I.shape[1], I.shape[2])) @@ -115,8 +115,8 @@ ot_sinkhorn.fit(Xs=Xs, Xt=Xt) 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) +transp_Xs_sinkhorn = ot_sinkhorn.transform(Xs=X1) +transp_Xt_sinkhorn = ot_sinkhorn.inverse_transform(Xt=X2) I1t = minmax(mat2im(transp_Xs_emd, I1.shape)) I2t = minmax(mat2im(transp_Xt_emd, I2.shape)) diff --git a/docs/source/auto_examples/plot_otda_color_images.rst b/docs/source/auto_examples/plot_otda_color_images.rst index 9c31ba7..ab0406e 100644 --- a/docs/source/auto_examples/plot_otda_color_images.rst +++ b/docs/source/auto_examples/plot_otda_color_images.rst @@ -7,7 +7,7 @@ OT for image color adaptation ============================= -This example presents a way of transferring colors between two image +This example presents a way of transferring colors between two images with Optimal Transport as introduced in [6] [6] Ferradans, S., Papadakis, N., Peyre, G., & Aujol, J. F. (2014). @@ -34,7 +34,7 @@ SIAM Journal on Imaging Sciences, 7(3), 1853-1882. def im2mat(I): - """Converts and image to matrix (one pixel per line)""" + """Converts an image to matrix (one pixel per line)""" return I.reshape((I.shape[0] * I.shape[1], I.shape[2])) @@ -168,8 +168,8 @@ Instantiate the different transport algorithms and fit them 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) + transp_Xs_sinkhorn = ot_sinkhorn.transform(Xs=X1) + transp_Xt_sinkhorn = ot_sinkhorn.inverse_transform(Xt=X2) I1t = minmax(mat2im(transp_Xs_emd, I1.shape)) I2t = minmax(mat2im(transp_Xt_emd, I2.shape)) @@ -235,11 +235,13 @@ Plot new images -**Total running time of the script:** ( 3 minutes 16.469 seconds) +**Total running time of the script:** ( 3 minutes 55.541 seconds) -.. container:: sphx-glr-footer +.. only :: html + + .. container:: sphx-glr-footer .. container:: sphx-glr-download @@ -252,6 +254,9 @@ Plot new images :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>`_ +.. only:: html + + .. rst-class:: sphx-glr-signature + + `Gallery 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 index 56caa8a..baffef4 100644 --- a/docs/source/auto_examples/plot_otda_mapping_colors_images.ipynb +++ b/docs/source/auto_examples/plot_otda_mapping_colors_images.ipynb @@ -1,144 +1,144 @@ { - "nbformat_minor": 0, - "nbformat": 4, "cells": [ { - "execution_count": null, - "cell_type": "code", - "source": [ - "%matplotlib inline" - ], - "outputs": [], + "cell_type": "code", + "execution_count": null, "metadata": { "collapsed": false - } - }, + }, + "outputs": [], + "source": [ + "%matplotlib inline" + ] + }, { + "cell_type": "markdown", + "metadata": {}, "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": [], + "cell_type": "code", + "execution_count": null, "metadata": { "collapsed": false - } - }, + }, + "outputs": [], + "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)" + ] + }, { + "cell_type": "markdown", + "metadata": {}, "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": [], + "cell_type": "code", + "execution_count": null, "metadata": { "collapsed": false - } - }, + }, + "outputs": [], + "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, :]" + ] + }, { + "cell_type": "markdown", + "metadata": {}, "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": [], + "cell_type": "code", + "execution_count": null, "metadata": { "collapsed": false - } - }, + }, + "outputs": [], + "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_sinkhorn.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))" + ] + }, { + "cell_type": "markdown", + "metadata": {}, "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": [], + "cell_type": "code", + "execution_count": null, "metadata": { "collapsed": false - } - }, + }, + "outputs": [], + "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()" + ] + }, { + "cell_type": "markdown", + "metadata": {}, "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": [], + "cell_type": "code", + "execution_count": null, "metadata": { "collapsed": false - } - }, + }, + "outputs": [], + "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()" + ] + }, { + "cell_type": "markdown", + "metadata": {}, "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": [], + "cell_type": "code", + "execution_count": null, "metadata": { "collapsed": false - } + }, + "outputs": [], + "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()" + ] } - ], + ], "metadata": { "kernelspec": { - "display_name": "Python 2", - "name": "python2", - "language": "python" - }, + "display_name": "Python 3", + "language": "python", + "name": "python3" + }, "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" - } + "name": "ipython", + "version": 3 + }, + "file_extension": ".py", + "mimetype": "text/x-python", + "name": "python", + "nbconvert_exporter": "python", + "pygments_lexer": "ipython3", + "version": "3.6.7" } - } + }, + "nbformat": 4, + "nbformat_minor": 0 }
\ 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 index 5f1e844..a20eca8 100644 --- a/docs/source/auto_examples/plot_otda_mapping_colors_images.py +++ b/docs/source/auto_examples/plot_otda_mapping_colors_images.py @@ -77,7 +77,7 @@ 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) +transp_Xs_sinkhorn = ot_sinkhorn.transform(Xs=X1) Image_sinkhorn = minmax(mat2im(transp_Xs_sinkhorn, I1.shape)) ot_mapping_linear = ot.da.MappingTransport( diff --git a/docs/source/auto_examples/plot_otda_mapping_colors_images.rst b/docs/source/auto_examples/plot_otda_mapping_colors_images.rst index 8394fb0..2afdc8a 100644 --- a/docs/source/auto_examples/plot_otda_mapping_colors_images.rst +++ b/docs/source/auto_examples/plot_otda_mapping_colors_images.rst @@ -104,7 +104,7 @@ Domain adaptation for pixel distribution transfer # 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) + transp_Xs_sinkhorn = ot_sinkhorn.transform(Xs=X1) Image_sinkhorn = minmax(mat2im(transp_Xs_sinkhorn, I1.shape)) ot_mapping_linear = ot.da.MappingTransport( @@ -132,39 +132,39 @@ Domain adaptation for pixel distribution transfer It. |Loss |Delta loss -------------------------------- - 0|3.680518e+02|0.000000e+00 - 1|3.592439e+02|-2.393116e-02 - 2|3.590632e+02|-5.030248e-04 - 3|3.589698e+02|-2.601358e-04 - 4|3.589118e+02|-1.614977e-04 - 5|3.588724e+02|-1.097608e-04 - 6|3.588436e+02|-8.035205e-05 - 7|3.588215e+02|-6.141923e-05 - 8|3.588042e+02|-4.832627e-05 - 9|3.587902e+02|-3.909574e-05 - 10|3.587786e+02|-3.225418e-05 - 11|3.587688e+02|-2.712592e-05 - 12|3.587605e+02|-2.314041e-05 - 13|3.587534e+02|-1.991287e-05 - 14|3.587471e+02|-1.744348e-05 - 15|3.587416e+02|-1.544523e-05 - 16|3.587367e+02|-1.364654e-05 - 17|3.587323e+02|-1.230435e-05 - 18|3.587284e+02|-1.093370e-05 - 19|3.587276e+02|-2.052728e-06 + 0|3.680534e+02|0.000000e+00 + 1|3.592501e+02|-2.391854e-02 + 2|3.590682e+02|-5.061555e-04 + 3|3.589745e+02|-2.610227e-04 + 4|3.589167e+02|-1.611644e-04 + 5|3.588768e+02|-1.109242e-04 + 6|3.588482e+02|-7.972733e-05 + 7|3.588261e+02|-6.166174e-05 + 8|3.588086e+02|-4.871697e-05 + 9|3.587946e+02|-3.919056e-05 + 10|3.587830e+02|-3.228124e-05 + 11|3.587731e+02|-2.744744e-05 + 12|3.587648e+02|-2.334451e-05 + 13|3.587576e+02|-1.995629e-05 + 14|3.587513e+02|-1.761058e-05 + 15|3.587457e+02|-1.542568e-05 + 16|3.587408e+02|-1.366315e-05 + 17|3.587365e+02|-1.221732e-05 + 18|3.587325e+02|-1.102488e-05 + 19|3.587303e+02|-6.062107e-06 It. |Loss |Delta loss -------------------------------- - 0|3.784758e+02|0.000000e+00 - 1|3.646352e+02|-3.656911e-02 - 2|3.642861e+02|-9.574714e-04 - 3|3.641523e+02|-3.672061e-04 - 4|3.640788e+02|-2.020990e-04 - 5|3.640321e+02|-1.282701e-04 - 6|3.640002e+02|-8.751240e-05 - 7|3.639765e+02|-6.521203e-05 - 8|3.639582e+02|-5.007767e-05 - 9|3.639439e+02|-3.938917e-05 - 10|3.639323e+02|-3.187865e-05 + 0|3.784871e+02|0.000000e+00 + 1|3.646491e+02|-3.656142e-02 + 2|3.642975e+02|-9.642655e-04 + 3|3.641626e+02|-3.702413e-04 + 4|3.640888e+02|-2.026301e-04 + 5|3.640419e+02|-1.289607e-04 + 6|3.640097e+02|-8.831646e-05 + 7|3.639861e+02|-6.487612e-05 + 8|3.639679e+02|-4.994063e-05 + 9|3.639536e+02|-3.941436e-05 + 10|3.639419e+02|-3.209753e-05 Plot original images @@ -283,11 +283,13 @@ Plot transformed images -**Total running time of the script:** ( 2 minutes 52.212 seconds) +**Total running time of the script:** ( 3 minutes 14.206 seconds) -.. container:: sphx-glr-footer +.. only :: html + + .. container:: sphx-glr-footer .. container:: sphx-glr-download @@ -300,6 +302,9 @@ Plot transformed images :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 <http://sphinx-gallery.readthedocs.io>`_ +.. only:: html + + .. rst-class:: sphx-glr-signature + + `Gallery generated by Sphinx-Gallery <https://sphinx-gallery.readthedocs.io>`_ diff --git a/docs/source/auto_examples/plot_stochastic.ipynb b/docs/source/auto_examples/plot_stochastic.ipynb index c6f0013..7f6ff3d 100644 --- a/docs/source/auto_examples/plot_stochastic.ipynb +++ b/docs/source/auto_examples/plot_stochastic.ipynb @@ -33,25 +33,7 @@ "cell_type": "markdown", "metadata": {}, "source": [ - "COMPUTE TRANSPORTATION MATRIX FOR SEMI-DUAL PROBLEM\n############################################################################\n\n" - ] - }, - { - "cell_type": "code", - "execution_count": null, - "metadata": { - "collapsed": false - }, - "outputs": [], - "source": [ - "print(\"------------SEMI-DUAL PROBLEM------------\")" - ] - }, - { - "cell_type": "markdown", - "metadata": {}, - "source": [ - "DISCRETE CASE\nSample two discrete measures for the discrete case\n---------------------------------------------\n\nDefine 2 discrete measures a and b, the points where are defined the source\nand the target measures and finally the cost matrix c.\n\n" + "COMPUTE TRANSPORTATION MATRIX FOR SEMI-DUAL PROBLEM\n############################################################################\n############################################################################\n DISCRETE CASE:\n\n Sample two discrete measures for the discrete case\n ---------------------------------------------\n\n Define 2 discrete measures a and b, the points where are defined the source\n and the target measures and finally the cost matrix c.\n\n" ] }, { @@ -87,7 +69,7 @@ "cell_type": "markdown", "metadata": {}, "source": [ - "SEMICONTINOUS CASE\nSample one general measure a, one discrete measures b for the semicontinous\ncase\n---------------------------------------------\n\nDefine one general measure a, one discrete measures b, the points where\nare defined the source and the target measures and finally the cost matrix c.\n\n" + "SEMICONTINOUS CASE:\n\nSample one general measure a, one discrete measures b for the semicontinous\ncase\n---------------------------------------------\n\nDefine one general measure a, one discrete measures b, the points where\nare defined the source and the target measures and finally the cost matrix c.\n\n" ] }, { @@ -202,25 +184,7 @@ "cell_type": "markdown", "metadata": {}, "source": [ - "COMPUTE TRANSPORTATION MATRIX FOR DUAL PROBLEM\n############################################################################\n\n" - ] - }, - { - "cell_type": "code", - "execution_count": null, - "metadata": { - "collapsed": false - }, - "outputs": [], - "source": [ - "print(\"------------DUAL PROBLEM------------\")" - ] - }, - { - "cell_type": "markdown", - "metadata": {}, - "source": [ - "SEMICONTINOUS CASE\nSample one general measure a, one discrete measures b for the semicontinous\ncase\n---------------------------------------------\n\nDefine one general measure a, one discrete measures b, the points where\nare defined the source and the target measures and finally the cost matrix c.\n\n" + "COMPUTE TRANSPORTATION MATRIX FOR DUAL PROBLEM\n############################################################################\n############################################################################\n SEMICONTINOUS CASE:\n\n Sample one general measure a, one discrete measures b for the semicontinous\n case\n ---------------------------------------------\n\n Define one general measure a, one discrete measures b, the points where\n are defined the source and the target measures and finally the cost matrix c.\n\n" ] }, { @@ -323,7 +287,7 @@ "name": "python", "nbconvert_exporter": "python", "pygments_lexer": "ipython3", - "version": "3.6.5" + "version": "3.6.7" } }, "nbformat": 4, diff --git a/docs/source/auto_examples/plot_stochastic.py b/docs/source/auto_examples/plot_stochastic.py index b9375d4..742f8d9 100644 --- a/docs/source/auto_examples/plot_stochastic.py +++ b/docs/source/auto_examples/plot_stochastic.py @@ -21,9 +21,9 @@ import ot.plot ############################################################################# # COMPUTE TRANSPORTATION MATRIX FOR SEMI-DUAL PROBLEM ############################################################################# -print("------------SEMI-DUAL PROBLEM------------") ############################################################################# -# DISCRETE CASE +# DISCRETE CASE: +# # Sample two discrete measures for the discrete case # --------------------------------------------- # @@ -57,7 +57,8 @@ sag_pi = ot.stochastic.solve_semi_dual_entropic(a, b, M, reg, method, print(sag_pi) ############################################################################# -# SEMICONTINOUS CASE +# SEMICONTINOUS CASE: +# # Sample one general measure a, one discrete measures b for the semicontinous # case # --------------------------------------------- @@ -139,9 +140,9 @@ pl.show() ############################################################################# # COMPUTE TRANSPORTATION MATRIX FOR DUAL PROBLEM ############################################################################# -print("------------DUAL PROBLEM------------") ############################################################################# -# SEMICONTINOUS CASE +# SEMICONTINOUS CASE: +# # Sample one general measure a, one discrete measures b for the semicontinous # case # --------------------------------------------- diff --git a/docs/source/auto_examples/plot_stochastic.rst b/docs/source/auto_examples/plot_stochastic.rst index a49bc05..d531045 100644 --- a/docs/source/auto_examples/plot_stochastic.rst +++ b/docs/source/auto_examples/plot_stochastic.rst @@ -34,29 +34,14 @@ algorithms for descrete and semicontinous measures from the POT library. COMPUTE TRANSPORTATION MATRIX FOR SEMI-DUAL PROBLEM ############################################################################ +############################################################################ + DISCRETE CASE: + Sample two discrete measures for the discrete case + --------------------------------------------- - -.. code-block:: python - - print("------------SEMI-DUAL PROBLEM------------") - - - - -.. rst-class:: sphx-glr-script-out - - Out:: - - ------------SEMI-DUAL PROBLEM------------ - - -DISCRETE CASE -Sample two discrete measures for the discrete case ---------------------------------------------- - -Define 2 discrete measures a and b, the points where are defined the source -and the target measures and finally the cost matrix c. + Define 2 discrete measures a and b, the points where are defined the source + and the target measures and finally the cost matrix c. @@ -115,7 +100,8 @@ results. [4.15462212e-02 2.65987989e-02 7.23177216e-02 2.39440107e-03]] -SEMICONTINOUS CASE +SEMICONTINOUS CASE: + Sample one general measure a, one discrete measures b for the semicontinous case --------------------------------------------- @@ -174,15 +160,15 @@ results. Out:: - [3.9018759 7.63059124 3.93260224 2.67274989 1.43888443 3.26904884 - 2.78748299] [-2.48511647 -2.43621119 -0.93585194 5.8571796 ] - [[2.56614773e-02 9.96758169e-02 1.75151781e-02 4.67049862e-06] - [1.21201047e-01 1.24433535e-02 1.28173754e-03 7.93100436e-03] - [3.58778167e-03 7.64232233e-02 6.28459924e-02 1.45441936e-07] - [2.63551754e-02 3.35577920e-02 8.25011211e-02 4.43054320e-04] - [9.24518246e-03 7.03074064e-04 1.00325744e-02 1.22876312e-01] - [2.03656325e-02 8.45420425e-04 1.73604569e-03 1.19910044e-01] - [4.17781688e-02 2.66463708e-02 7.18353075e-02 2.59729583e-03]] + [3.98220325 7.76235856 3.97645524 2.72051681 1.23219313 3.07696856 + 2.84476972] [-2.65544161 -2.50838395 -0.9397765 6.10360206] + [[2.34528761e-02 1.00491956e-01 1.89058354e-02 6.47543413e-06] + [1.16616747e-01 1.32074516e-02 1.45653361e-03 1.15764107e-02] + [3.16154850e-03 7.42892944e-02 6.54061055e-02 1.94426150e-07] + [2.33152216e-02 3.27486992e-02 8.61986263e-02 5.94595747e-04] + [6.34131496e-03 5.31975896e-04 8.12724003e-03 1.27856612e-01] + [1.41744829e-02 6.49096245e-04 1.42704389e-03 1.26606520e-01] + [3.73127657e-02 2.62526499e-02 7.57727161e-02 3.51901117e-03]] Compare the results with the Sinkhorn algorithm @@ -288,30 +274,15 @@ Plot Sinkhorn results COMPUTE TRANSPORTATION MATRIX FOR DUAL PROBLEM ############################################################################ +############################################################################ + SEMICONTINOUS CASE: + Sample one general measure a, one discrete measures b for the semicontinous + case + --------------------------------------------- - -.. code-block:: python - - print("------------DUAL PROBLEM------------") - - - - -.. rst-class:: sphx-glr-script-out - - Out:: - - ------------DUAL PROBLEM------------ - - -SEMICONTINOUS CASE -Sample one general measure a, one discrete measures b for the semicontinous -case ---------------------------------------------- - -Define one general measure a, one discrete measures b, the points where -are defined the source and the target measures and finally the cost matrix c. + Define one general measure a, one discrete measures b, the points where + are defined the source and the target measures and finally the cost matrix c. @@ -365,15 +336,15 @@ Call ot.solve_dual_entropic and plot the results. Out:: - [ 1.29325617 5.0435082 1.30996326 0.05538236 -1.08113283 0.73711558 - 0.18086364] [0.08840343 0.17710082 1.68604226 8.37377551] - [[2.47763879e-02 1.00144623e-01 1.77492330e-02 4.25988443e-06] - [1.19568278e-01 1.27740478e-02 1.32714202e-03 7.39121816e-03] - [3.41581121e-03 7.57137404e-02 6.27992039e-02 1.30808430e-07] - [2.52245323e-02 3.34219732e-02 8.28754229e-02 4.00582912e-04] - [9.75329554e-03 7.71824343e-04 1.11085400e-02 1.22456628e-01] - [2.12304276e-02 9.17096580e-04 1.89946234e-03 1.18084973e-01] - [4.04179693e-02 2.68253041e-02 7.29410047e-02 2.37369404e-03]] + [0.92449986 2.75486107 1.07923806 0.02741145 0.61355413 1.81961594 + 0.12072562] [0.33831611 0.46806842 1.5640451 4.96947652] + [[2.20001105e-02 9.26497883e-02 1.08654588e-02 9.78995555e-08] + [1.55669974e-02 1.73279561e-03 1.19120878e-04 2.49058251e-05] + [3.48198483e-03 8.04151063e-02 4.41335396e-02 3.45115752e-09] + [3.14927954e-02 4.34760520e-02 7.13338154e-02 1.29442395e-05] + [6.81836550e-02 5.62182457e-03 5.35386584e-02 2.21568095e-02] + [8.04671052e-02 3.62163462e-03 4.96331605e-03 1.15837801e-02] + [4.88644009e-02 3.37903481e-02 6.07955004e-02 7.42743505e-05]] Compare the results with the Sinkhorn algorithm @@ -448,7 +419,7 @@ Plot Sinkhorn results -**Total running time of the script:** ( 0 minutes 22.857 seconds) +**Total running time of the script:** ( 0 minutes 20.889 seconds) |
