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.. _sphx_glr_auto_examples_plot_OTDA_2D.py:
==============================
OT for empirical distributions
==============================
.. rst-class:: sphx-glr-horizontal
*
.. image:: /auto_examples/images/sphx_glr_plot_OTDA_2D_001.png
:scale: 47
*
.. image:: /auto_examples/images/sphx_glr_plot_OTDA_2D_002.png
:scale: 47
*
.. image:: /auto_examples/images/sphx_glr_plot_OTDA_2D_003.png
:scale: 47
*
.. image:: /auto_examples/images/sphx_glr_plot_OTDA_2D_004.png
:scale: 47
.. code-block:: python
import numpy as np
import matplotlib.pylab as pl
import ot
#%% parameters
n=150 # nb bins
xs,ys=ot.datasets.get_data_classif('3gauss',n)
xt,yt=ot.datasets.get_data_classif('3gauss2',n)
a,b = ot.unif(n),ot.unif(n)
# loss matrix
M=ot.dist(xs,xt)
#M/=M.max()
#%% plot samples
pl.figure(1)
pl.subplot(2,2,1)
pl.scatter(xs[:,0],xs[:,1],c=ys,marker='+',label='Source samples')
pl.legend(loc=0)
pl.title('Source distributions')
pl.subplot(2,2,2)
pl.scatter(xt[:,0],xt[:,1],c=yt,marker='o',label='Target samples')
pl.legend(loc=0)
pl.title('target distributions')
pl.figure(2)
pl.imshow(M,interpolation='nearest')
pl.title('Cost matrix M')
#%% OT estimation
# EMD
G0=ot.emd(a,b,M)
# sinkhorn
lambd=1e-1
Gs=ot.sinkhorn(a,b,M,lambd)
# Group lasso regularization
reg=1e-1
eta=1e0
Gg=ot.da.sinkhorn_lpl1_mm(a,ys.astype(np.int),b,M,reg,eta)
#%% visu matrices
pl.figure(3)
pl.subplot(2,3,1)
pl.imshow(G0,interpolation='nearest')
pl.title('OT matrix ')
pl.subplot(2,3,2)
pl.imshow(Gs,interpolation='nearest')
pl.title('OT matrix Sinkhorn')
pl.subplot(2,3,3)
pl.imshow(Gg,interpolation='nearest')
pl.title('OT matrix Group lasso')
pl.subplot(2,3,4)
ot.plot.plot2D_samples_mat(xs,xt,G0,c=[.5,.5,1])
pl.scatter(xs[:,0],xs[:,1],c=ys,marker='+',label='Source samples')
pl.scatter(xt[:,0],xt[:,1],c=yt,marker='o',label='Target samples')
pl.subplot(2,3,5)
ot.plot.plot2D_samples_mat(xs,xt,Gs,c=[.5,.5,1])
pl.scatter(xs[:,0],xs[:,1],c=ys,marker='+',label='Source samples')
pl.scatter(xt[:,0],xt[:,1],c=yt,marker='o',label='Target samples')
pl.subplot(2,3,6)
ot.plot.plot2D_samples_mat(xs,xt,Gg,c=[.5,.5,1])
pl.scatter(xs[:,0],xs[:,1],c=ys,marker='+',label='Source samples')
pl.scatter(xt[:,0],xt[:,1],c=yt,marker='o',label='Target samples')
#%% sample interpolation
xst0=n*G0.dot(xt)
xsts=n*Gs.dot(xt)
xstg=n*Gg.dot(xt)
pl.figure(4)
pl.subplot(2,3,1)
pl.scatter(xt[:,0],xt[:,1],c=yt,marker='o',label='Target samples',alpha=0.5)
pl.scatter(xst0[:,0],xst0[:,1],c=ys,marker='+',label='Transp samples',s=30)
pl.title('Interp samples')
pl.legend(loc=0)
pl.subplot(2,3,2)
pl.scatter(xt[:,0],xt[:,1],c=yt,marker='o',label='Target samples',alpha=0.5)
pl.scatter(xsts[:,0],xsts[:,1],c=ys,marker='+',label='Transp samples',s=30)
pl.title('Interp samples Sinkhorn')
pl.subplot(2,3,3)
pl.scatter(xt[:,0],xt[:,1],c=yt,marker='o',label='Target samples',alpha=0.5)
pl.scatter(xstg[:,0],xstg[:,1],c=ys,marker='+',label='Transp samples',s=30)
pl.title('Interp samples Grouplasso')
**Total running time of the script:** ( 0 minutes 17.372 seconds)
.. container:: sphx-glr-footer
.. container:: sphx-glr-download
:download:`Download Python source code: plot_OTDA_2D.py <plot_OTDA_2D.py>`
.. container:: sphx-glr-download
:download:`Download Jupyter notebook: plot_OTDA_2D.ipynb <plot_OTDA_2D.ipynb>`
.. rst-class:: sphx-glr-signature
`Generated by Sphinx-Gallery <http://sphinx-gallery.readthedocs.io>`_
|
