Merge branch 'master' into autonb

Author: rflamary

README.md

@@ -16,7 +16,7 @@ It provides the following solvers:
 * Conditional gradient [6] and Generalized conditional gradient for regularized OT [7].
 * Joint OT matrix and mapping estimation [8].
 * Wasserstein Discriminant Analysis [11] (requires autograd + pymanopt).
-
+* Gromov-Wasserstein distances and barycenters [12]
 
 Some demonstrations (both in Python and Jupyter Notebook format) are available in the examples folder.
 
@@ -138,12 +138,12 @@ The contributors to this library are:
 * [Léo Gautheron](https://github.com/aje) (GPU implementation)
 * [Nathalie Gayraud](https://www.linkedin.com/in/nathalie-t-h-gayraud/?ppe=1)
 * [Stanislas Chambon](https://slasnista.github.io/)
+* [Antoine Rolet](https://arolet.github.io/)
 
 This toolbox benefit a lot from open source research and we would like to thank the following persons for providing some code (in various languages):
 
 * [Gabriel Peyré](http://gpeyre.github.io/) (Wasserstein Barycenters in Matlab)
 * [Nicolas Bonneel](http://liris.cnrs.fr/~nbonneel/) ( C++ code for EMD)
-* [Antoine Rolet](https://arolet.github.io/) ( Mex file for EMD )
 * [Marco Cuturi](http://marcocuturi.net/) (Sinkhorn Knopp in Matlab/Cuda)
 
 
@@ -184,3 +184,5 @@ You can also post bug reports and feature requests in Github issues. Make sure t
 [10] Chizat, L., Peyré, G., Schmitzer, B., & Vialard, F. X. (2016). [Scaling algorithms for unbalanced transport problems](https://arxiv.org/pdf/1607.05816.pdf). arXiv preprint arXiv:1607.05816.
 
 [11] Flamary, R., Cuturi, M., Courty, N., & Rakotomamonjy, A. (2016). [Wasserstein Discriminant Analysis](https://arxiv.org/pdf/1608.08063.pdf). arXiv preprint arXiv:1608.08063.
+
+[12] Gabriel Peyré, Marco Cuturi, and Justin Solomon, [Gromov-Wasserstein averaging of kernel and distance matrices](http://proceedings.mlr.press/v48/peyre16.html)  International Conference on Machine Learning (ICML). 2016.

data/cross.png

@@ -0,0 +1,147 @@
+# -*- coding: utf-8 -*-
+"""
+============================================
+OTDA unsupervised vs semi-supervised setting
+============================================
+
+This example introduces a semi supervised domain adaptation in a 2D setting.
+It explicits the problem of semi supervised domain adaptation and introduces
+some optimal transport approaches to solve it.
+
+Quantities such as optimal couplings, greater coupling coefficients and
+transported samples are represented in order to give a visual understanding
+of what the transport methods are doing.
+"""
+
+# Authors: Remi Flamary <[email protected]>
+#          Stanislas Chambon <[email protected]>
+#
+# License: MIT License
+
+import matplotlib.pylab as pl
+import ot
+
+
+##############################################################################
+# generate data
+##############################################################################
+
+n_samples_source = 150
+n_samples_target = 150
+
+Xs, ys = ot.datasets.get_data_classif('3gauss', n_samples_source)
+Xt, yt = ot.datasets.get_data_classif('3gauss2', n_samples_target)
+
+
+##############################################################################
+# Transport source samples onto target samples
+##############################################################################
+
+# unsupervised domain adaptation
+ot_sinkhorn_un = ot.da.SinkhornTransport(reg_e=1e-1)
+ot_sinkhorn_un.fit(Xs=Xs, Xt=Xt)
+transp_Xs_sinkhorn_un = ot_sinkhorn_un.transform(Xs=Xs)
+
+# semi-supervised domain adaptation
+ot_sinkhorn_semi = ot.da.SinkhornTransport(reg_e=1e-1)
+ot_sinkhorn_semi.fit(Xs=Xs, Xt=Xt, ys=ys, yt=yt)
+transp_Xs_sinkhorn_semi = ot_sinkhorn_semi.transform(Xs=Xs)
+
+# semi supervised DA uses available labaled target samples to modify the cost
+# matrix involved in the OT problem. The cost of transporting a source sample
+# of class A onto a target sample of class B != A is set to infinite, or a
+# very large value
+
+# note that in the present case we consider that all the target samples are
+# labeled. For daily applications, some target sample might not have labels,
+# in this case the element of yt corresponding to these samples should be
+# filled with -1.
+
+# Warning: we recall that -1 cannot be used as a class label
+
+
+##############################################################################
+# Fig 1 : plots source and target samples + matrix of pairwise distance
+##############################################################################
+
+pl.figure(1, figsize=(10, 10))
+pl.subplot(2, 2, 1)
+pl.scatter(Xs[:, 0], Xs[:, 1], c=ys, marker='+', label='Source samples')
+pl.xticks([])
+pl.yticks([])
+pl.legend(loc=0)
+pl.title('Source  samples')
+
+pl.subplot(2, 2, 2)
+pl.scatter(Xt[:, 0], Xt[:, 1], c=yt, marker='o', label='Target samples')
+pl.xticks([])
+pl.yticks([])
+pl.legend(loc=0)
+pl.title('Target samples')
+
+pl.subplot(2, 2, 3)
+pl.imshow(ot_sinkhorn_un.cost_, interpolation='nearest')
+pl.xticks([])
+pl.yticks([])
+pl.title('Cost matrix - unsupervised DA')
+
+pl.subplot(2, 2, 4)
+pl.imshow(ot_sinkhorn_semi.cost_, interpolation='nearest')
+pl.xticks([])
+pl.yticks([])
+pl.title('Cost matrix - semisupervised DA')
+
+pl.tight_layout()
+
+# the optimal coupling in the semi-supervised DA case will exhibit " shape
+# similar" to the cost matrix, (block diagonal matrix)
+
+
+##############################################################################
+# Fig 2 : plots optimal couplings for the different methods
+##############################################################################
+
+pl.figure(2, figsize=(8, 4))
+
+pl.subplot(1, 2, 1)
+pl.imshow(ot_sinkhorn_un.coupling_, interpolation='nearest')
+pl.xticks([])
+pl.yticks([])
+pl.title('Optimal coupling\nUnsupervised DA')
+
+pl.subplot(1, 2, 2)
+pl.imshow(ot_sinkhorn_semi.coupling_, interpolation='nearest')
+pl.xticks([])
+pl.yticks([])
+pl.title('Optimal coupling\nSemi-supervised DA')
+
+pl.tight_layout()
+
+
+##############################################################################
+# Fig 3 : plot transported samples
+##############################################################################
+
+# display transported samples
+pl.figure(4, figsize=(8, 4))
+pl.subplot(1, 2, 1)
+pl.scatter(Xt[:, 0], Xt[:, 1], c=yt, marker='o',
+           label='Target samples', alpha=0.5)
+pl.scatter(transp_Xs_sinkhorn_un[:, 0], transp_Xs_sinkhorn_un[:, 1], c=ys,
+           marker='+', label='Transp samples', s=30)
+pl.title('Transported samples\nEmdTransport')
+pl.legend(loc=0)
+pl.xticks([])
+pl.yticks([])
+
+pl.subplot(1, 2, 2)
+pl.scatter(Xt[:, 0], Xt[:, 1], c=yt, marker='o',
+           label='Target samples', alpha=0.5)
+pl.scatter(transp_Xs_sinkhorn_semi[:, 0], transp_Xs_sinkhorn_semi[:, 1], c=ys,
+           marker='+', label='Transp samples', s=30)
+pl.title('Transported samples\nSinkhornTransport')
+pl.xticks([])
+pl.yticks([])
+
+pl.tight_layout()
+pl.show()

data/square.png

@@ -0,0 +1,90 @@
+# -*- coding: utf-8 -*-
+"""
+==========================
+Gromov-Wasserstein example
+==========================
+This example is designed to show how to use the Gromov-Wassertsein distance
+computation in POT.
+"""
+
+# Author: Erwan Vautier <[email protected]>
+#         Nicolas Courty <[email protected]>
+#
+# License: MIT License
+
+import scipy as sp
+import numpy as np
+import matplotlib.pylab as pl
+
+import ot
+
+
+"""
+Sample two Gaussian distributions (2D and 3D)
+=============================================
+The Gromov-Wasserstein distance allows to compute distances with samples that
+do not belong to the same metric space. For demonstration purpose, we sample
+two Gaussian distributions in 2- and 3-dimensional spaces.
+"""
+
+n_samples = 30  # nb samples
+
+mu_s = np.array([0, 0])
+cov_s = np.array([[1, 0], [0, 1]])
+
+mu_t = np.array([4, 4, 4])
+cov_t = np.array([[1, 0, 0], [0, 1, 0], [0, 0, 1]])
+
+
+xs = ot.datasets.get_2D_samples_gauss(n_samples, mu_s, cov_s)
+P = sp.linalg.sqrtm(cov_t)
+xt = np.random.randn(n_samples, 3).dot(P) + mu_t
+
+
+"""
+Plotting the distributions
+==========================
+"""
+fig = pl.figure()
+ax1 = fig.add_subplot(121)
+ax1.plot(xs[:, 0], xs[:, 1], '+b', label='Source samples')
+ax2 = fig.add_subplot(122, projection='3d')
+ax2.scatter(xt[:, 0], xt[:, 1], xt[:, 2], color='r')
+pl.show()
+
+
+"""
+Compute distance kernels, normalize them and then display
+=========================================================
+"""
+
+C1 = sp.spatial.distance.cdist(xs, xs)
+C2 = sp.spatial.distance.cdist(xt, xt)
+
+C1 /= C1.max()
+C2 /= C2.max()
+
+pl.figure()
+pl.subplot(121)
+pl.imshow(C1)
+pl.subplot(122)
+pl.imshow(C2)
+pl.show()
+
+"""
+Compute Gromov-Wasserstein plans and distance
+=============================================
+"""
+
+p = ot.unif(n_samples)
+q = ot.unif(n_samples)
+
+gw = ot.gromov_wasserstein(C1, C2, p, q, 'square_loss', epsilon=5e-4)
+gw_dist = ot.gromov_wasserstein2(C1, C2, p, q, 'square_loss', epsilon=5e-4)
+
+print('Gromov-Wasserstein distances between the distribution: ' + str(gw_dist))
+
+pl.figure()
+pl.imshow(gw, cmap='jet')
+pl.colorbar()
+pl.show()