add da exmaples

5 files changed, 785 insertions, 0 deletions

diff --git a/examples/plot_otda_classes.py b/examples/plot_otda_classes.py
new file mode 100644
index 0000000..ec57a37
--- /dev/null
+++ b/examples/plot_otda_classes.py
@@ -0,0 +1,150 @@
+# -*- coding: utf-8 -*-
+"""
+========================
+OT for domain adaptation
+========================
+
+This example introduces a domain adaptation in a 2D setting and the 4 OTDA
+approaches currently supported in POT.
+
+"""
+
+# Authors: Remi Flamary <remi.flamary@unice.fr>
+#          Stanislas Chambon <stan.chambon@gmail.com>
+#
+# License: MIT License
+
+import matplotlib.pylab as pl
+import ot
+
+
+##############################################################################
+# generate data
+##############################################################################
+
+n_source_samples = 150
+n_target_samples = 150
+
+Xs, ys = ot.datasets.get_data_classif('3gauss', n_source_samples)
+Xt, yt = ot.datasets.get_data_classif('3gauss2', n_target_samples)
+
+
+##############################################################################
+# Instantiate the different transport algorithms and fit them
+##############################################################################
+
+# EMD Transport
+ot_emd = ot.da.EMDTransport()
+ot_emd.fit(Xs=Xs, Xt=Xt)
+
+# Sinkhorn Transport
+ot_sinkhorn = ot.da.SinkhornTransport(reg_e=1e-1)
+ot_sinkhorn.fit(Xs=Xs, Xt=Xt)
+
+# Sinkhorn Transport with Group lasso regularization
+ot_lpl1 = ot.da.SinkhornLpl1Transport(reg_e=1e-1, reg_cl=1e0)
+ot_lpl1.fit(Xs=Xs, ys=ys, Xt=Xt)
+
+# Sinkhorn Transport with Group lasso regularization l1l2
+ot_l1l2 = ot.da.SinkhornL1l2Transport(reg_e=1e-1, reg_cl=2e0, max_iter=20,
+                                      verbose=True)
+ot_l1l2.fit(Xs=Xs, ys=ys, Xt=Xt)
+
+# transport source samples onto target samples
+transp_Xs_emd = ot_emd.transform(Xs=Xs)
+transp_Xs_sinkhorn = ot_sinkhorn.transform(Xs=Xs)
+transp_Xs_lpl1 = ot_lpl1.transform(Xs=Xs)
+transp_Xs_l1l2 = ot_l1l2.transform(Xs=Xs)
+
+
+##############################################################################
+# Fig 1 : plots source and target samples
+##############################################################################
+
+pl.figure(1, figsize=(10, 5))
+pl.subplot(1, 2, 1)
+pl.scatter(Xs[:, 0], Xs[:, 1], c=ys, marker='+', label='Source samples')
+pl.xticks([])
+pl.yticks([])
+pl.legend(loc=0)
+pl.title('Source  samples')
+
+pl.subplot(1, 2, 2)
+pl.scatter(Xt[:, 0], Xt[:, 1], c=yt, marker='o', label='Target samples')
+pl.xticks([])
+pl.yticks([])
+pl.legend(loc=0)
+pl.title('Target samples')
+pl.tight_layout()
+
+
+##############################################################################
+# Fig 2 : plot optimal couplings and transported samples
+##############################################################################
+
+param_img = {'interpolation': 'nearest', 'cmap': 'spectral'}
+
+pl.figure(2, figsize=(15, 8))
+pl.subplot(2, 4, 1)
+pl.imshow(ot_emd.coupling_, **param_img)
+pl.xticks([])
+pl.yticks([])
+pl.title('Optimal coupling\nEMDTransport')
+
+pl.subplot(2, 4, 2)
+pl.imshow(ot_sinkhorn.coupling_, **param_img)
+pl.xticks([])
+pl.yticks([])
+pl.title('Optimal coupling\nSinkhornTransport')
+
+pl.subplot(2, 4, 3)
+pl.imshow(ot_lpl1.coupling_, **param_img)
+pl.xticks([])
+pl.yticks([])
+pl.title('Optimal coupling\nSinkhornLpl1Transport')
+
+pl.subplot(2, 4, 4)
+pl.imshow(ot_l1l2.coupling_, **param_img)
+pl.xticks([])
+pl.yticks([])
+pl.title('Optimal coupling\nSinkhornL1l2Transport')
+
+pl.subplot(2, 4, 5)
+pl.scatter(Xt[:, 0], Xt[:, 1], c=yt, marker='o',
+           label='Target samples', alpha=0.3)
+pl.scatter(transp_Xs_emd[:, 0], transp_Xs_emd[:, 1], c=ys,
+           marker='+', label='Transp samples', s=30)
+pl.xticks([])
+pl.yticks([])
+pl.title('Transported samples\nEmdTransport')
+pl.legend(loc="lower left")
+
+pl.subplot(2, 4, 6)
+pl.scatter(Xt[:, 0], Xt[:, 1], c=yt, marker='o',
+           label='Target samples', alpha=0.3)
+pl.scatter(transp_Xs_sinkhorn[:, 0], transp_Xs_sinkhorn[:, 1], c=ys,
+           marker='+', label='Transp samples', s=30)
+pl.xticks([])
+pl.yticks([])
+pl.title('Transported samples\nSinkhornTransport')
+
+pl.subplot(2, 4, 7)
+pl.scatter(Xt[:, 0], Xt[:, 1], c=yt, marker='o',
+           label='Target samples', alpha=0.3)
+pl.scatter(transp_Xs_lpl1[:, 0], transp_Xs_lpl1[:, 1], c=ys,
+           marker='+', label='Transp samples', s=30)
+pl.xticks([])
+pl.yticks([])
+pl.title('Transported samples\nSinkhornLpl1Transport')
+
+pl.subplot(2, 4, 8)
+pl.scatter(Xt[:, 0], Xt[:, 1], c=yt, marker='o',
+           label='Target samples', alpha=0.3)
+pl.scatter(transp_Xs_l1l2[:, 0], transp_Xs_l1l2[:, 1], c=ys,
+           marker='+', label='Transp samples', s=30)
+pl.xticks([])
+pl.yticks([])
+pl.title('Transported samples\nSinkhornL1l2Transport')
+pl.tight_layout()
+
+pl.show()
diff --git a/examples/plot_otda_color_images.py b/examples/plot_otda_color_images.py
new file mode 100644
index 0000000..46ad44b
--- /dev/null
+++ b/examples/plot_otda_color_images.py
@@ -0,0 +1,165 @@
+# -*- coding: utf-8 -*-
+"""
+========================================================
+OT for domain adaptation with image color adaptation [6]
+========================================================
+
+This example presents a way of transferring colors between two image
+with Optimal Transport as introduced in [6]
+
+[6] Ferradans, S., Papadakis, N., Peyre, G., & Aujol, J. F. (2014).
+Regularized discrete optimal transport.
+SIAM Journal on Imaging Sciences, 7(3), 1853-1882.
+"""
+
+# Authors: Remi Flamary <remi.flamary@unice.fr>
+#          Stanislas Chambon <stan.chambon@gmail.com>
+#
+# License: MIT License
+
+import numpy as np
+from scipy import ndimage
+import matplotlib.pylab as pl
+import ot
+
+
+r = np.random.RandomState(42)
+
+
+def im2mat(I):
+    """Converts and image to matrix (one pixel per line)"""
+    return I.reshape((I.shape[0] * I.shape[1], I.shape[2]))
+
+
+def mat2im(X, shape):
+    """Converts back a matrix to an image"""
+    return X.reshape(shape)
+
+
+def minmax(I):
+    return np.clip(I, 0, 1)
+
+
+##############################################################################
+# generate data
+##############################################################################
+
+# Loading images
+I1 = ndimage.imread('../data/ocean_day.jpg').astype(np.float64) / 256
+I2 = ndimage.imread('../data/ocean_sunset.jpg').astype(np.float64) / 256
+
+X1 = im2mat(I1)
+X2 = im2mat(I2)
+
+# training samples
+nb = 1000
+idx1 = r.randint(X1.shape[0], size=(nb,))
+idx2 = r.randint(X2.shape[0], size=(nb,))
+
+Xs = X1[idx1, :]
+Xt = X2[idx2, :]
+
+
+##############################################################################
+# Instantiate the different transport algorithms and fit them
+##############################################################################
+
+# EMDTransport
+ot_emd = ot.da.EMDTransport()
+ot_emd.fit(Xs=Xs, Xt=Xt)
+
+# SinkhornTransport
+ot_sinkhorn = ot.da.SinkhornTransport(reg_e=1e-1)
+ot_sinkhorn.fit(Xs=Xs, Xt=Xt)
+
+# prediction between images (using out of sample prediction as in [6])
+transp_Xs_emd = ot_emd.transform(Xs=X1)
+transp_Xt_emd = ot_emd.inverse_transform(Xt=X2)
+
+transp_Xs_sinkhorn = ot_emd.transform(Xs=X1)
+transp_Xt_sinkhorn = ot_emd.inverse_transform(Xt=X2)
+
+I1t = minmax(mat2im(transp_Xs_emd, I1.shape))
+I2t = minmax(mat2im(transp_Xt_emd, I2.shape))
+
+I1te = minmax(mat2im(transp_Xs_sinkhorn, I1.shape))
+I2te = minmax(mat2im(transp_Xt_sinkhorn, I2.shape))
+
+
+##############################################################################
+# plot original image
+##############################################################################
+
+pl.figure(1, figsize=(6.4, 3))
+
+pl.subplot(1, 2, 1)
+pl.imshow(I1)
+pl.axis('off')
+pl.title('Image 1')
+
+pl.subplot(1, 2, 2)
+pl.imshow(I2)
+pl.axis('off')
+pl.title('Image 2')
+
+
+##############################################################################
+# scatter plot of colors
+##############################################################################
+
+pl.figure(2, figsize=(6.4, 3))
+
+pl.subplot(1, 2, 1)
+pl.scatter(Xs[:, 0], Xs[:, 2], c=Xs)
+pl.axis([0, 1, 0, 1])
+pl.xlabel('Red')
+pl.ylabel('Blue')
+pl.title('Image 1')
+
+pl.subplot(1, 2, 2)
+pl.scatter(Xt[:, 0], Xt[:, 2], c=Xt)
+pl.axis([0, 1, 0, 1])
+pl.xlabel('Red')
+pl.ylabel('Blue')
+pl.title('Image 2')
+pl.tight_layout()
+
+
+##############################################################################
+# plot new images
+##############################################################################
+
+pl.figure(3, figsize=(8, 4))
+
+pl.subplot(2, 3, 1)
+pl.imshow(I1)
+pl.axis('off')
+pl.title('Image 1')
+
+pl.subplot(2, 3, 2)
+pl.imshow(I1t)
+pl.axis('off')
+pl.title('Image 1 Adapt')
+
+pl.subplot(2, 3, 3)
+pl.imshow(I1te)
+pl.axis('off')
+pl.title('Image 1 Adapt (reg)')
+
+pl.subplot(2, 3, 4)
+pl.imshow(I2)
+pl.axis('off')
+pl.title('Image 2')
+
+pl.subplot(2, 3, 5)
+pl.imshow(I2t)
+pl.axis('off')
+pl.title('Image 2 Adapt')
+
+pl.subplot(2, 3, 6)
+pl.imshow(I2te)
+pl.axis('off')
+pl.title('Image 2 Adapt (reg)')
+pl.tight_layout()
+
+pl.show()
diff --git a/examples/plot_otda_d2.py b/examples/plot_otda_d2.py
new file mode 100644
index 0000000..3daa0a6
--- /dev/null
+++ b/examples/plot_otda_d2.py
@@ -0,0 +1,173 @@
+# -*- coding: utf-8 -*-
+"""
+==============================
+OT for empirical distributions
+==============================
+
+This example introduces a domain adaptation in a 2D setting. It explicits
+the problem of domain adaptation and introduces some optimal transport
+approaches to solve it.
+
+Quantities such as optimal couplings, greater coupling coefficients and
+transported samples are represented in order to give a visual understanding
+of what the transport methods are doing.
+"""
+
+# Authors: Remi Flamary <remi.flamary@unice.fr>
+#          Stanislas Chambon <stan.chambon@gmail.com>
+#
+# License: MIT License
+
+import matplotlib.pylab as pl
+import ot
+
+
+##############################################################################
+# generate data
+##############################################################################
+
+n_samples_source = 150
+n_samples_target = 150
+
+Xs, ys = ot.datasets.get_data_classif('3gauss', n_samples_source)
+Xt, yt = ot.datasets.get_data_classif('3gauss2', n_samples_target)
+
+# Cost matrix
+M = ot.dist(Xs, Xt, metric='sqeuclidean')
+
+
+##############################################################################
+# Instantiate the different transport algorithms and fit them
+##############################################################################
+
+# EMD Transport
+ot_emd = ot.da.EMDTransport()
+ot_emd.fit(Xs=Xs, Xt=Xt)
+
+# Sinkhorn Transport
+ot_sinkhorn = ot.da.SinkhornTransport(reg_e=1e-1)
+ot_sinkhorn.fit(Xs=Xs, Xt=Xt)
+
+# Sinkhorn Transport with Group lasso regularization
+ot_lpl1 = ot.da.SinkhornLpl1Transport(reg_e=1e-1, reg_cl=1e0)
+ot_lpl1.fit(Xs=Xs, ys=ys, Xt=Xt)
+
+# transport source samples onto target samples
+transp_Xs_emd = ot_emd.transform(Xs=Xs)
+transp_Xs_sinkhorn = ot_sinkhorn.transform(Xs=Xs)
+transp_Xs_lpl1 = ot_lpl1.transform(Xs=Xs)
+
+
+##############################################################################
+# Fig 1 : plots source and target samples + matrix of pairwise distance
+##############################################################################
+
+pl.figure(1, figsize=(10, 10))
+pl.subplot(2, 2, 1)
+pl.scatter(Xs[:, 0], Xs[:, 1], c=ys, marker='+', label='Source samples')
+pl.xticks([])
+pl.yticks([])
+pl.legend(loc=0)
+pl.title('Source  samples')
+
+pl.subplot(2, 2, 2)
+pl.scatter(Xt[:, 0], Xt[:, 1], c=yt, marker='o', label='Target samples')
+pl.xticks([])
+pl.yticks([])
+pl.legend(loc=0)
+pl.title('Target samples')
+
+pl.subplot(2, 2, 3)
+pl.imshow(M, interpolation='nearest')
+pl.xticks([])
+pl.yticks([])
+pl.title('Matrix of pairwise distances')
+pl.tight_layout()
+
+
+##############################################################################
+# Fig 2 : plots optimal couplings for the different methods
+##############################################################################
+
+pl.figure(2, figsize=(10, 6))
+
+pl.subplot(2, 3, 1)
+pl.imshow(ot_emd.coupling_, interpolation='nearest')
+pl.xticks([])
+pl.yticks([])
+pl.title('Optimal coupling\nEMDTransport')
+
+pl.subplot(2, 3, 2)
+pl.imshow(ot_sinkhorn.coupling_, interpolation='nearest')
+pl.xticks([])
+pl.yticks([])
+pl.title('Optimal coupling\nSinkhornTransport')
+
+pl.subplot(2, 3, 3)
+pl.imshow(ot_lpl1.coupling_, interpolation='nearest')
+pl.xticks([])
+pl.yticks([])
+pl.title('Optimal coupling\nSinkhornLpl1Transport')
+
+pl.subplot(2, 3, 4)
+ot.plot.plot2D_samples_mat(Xs, Xt, ot_emd.coupling_, c=[.5, .5, 1])
+pl.scatter(Xs[:, 0], Xs[:, 1], c=ys, marker='+', label='Source samples')
+pl.scatter(Xt[:, 0], Xt[:, 1], c=yt, marker='o', label='Target samples')
+pl.xticks([])
+pl.yticks([])
+pl.title('Main coupling coefficients\nEMDTransport')
+
+pl.subplot(2, 3, 5)
+ot.plot.plot2D_samples_mat(Xs, Xt, ot_sinkhorn.coupling_, c=[.5, .5, 1])
+pl.scatter(Xs[:, 0], Xs[:, 1], c=ys, marker='+', label='Source samples')
+pl.scatter(Xt[:, 0], Xt[:, 1], c=yt, marker='o', label='Target samples')
+pl.xticks([])
+pl.yticks([])
+pl.title('Main coupling coefficients\nSinkhornTransport')
+
+pl.subplot(2, 3, 6)
+ot.plot.plot2D_samples_mat(Xs, Xt, ot_lpl1.coupling_, c=[.5, .5, 1])
+pl.scatter(Xs[:, 0], Xs[:, 1], c=ys, marker='+', label='Source samples')
+pl.scatter(Xt[:, 0], Xt[:, 1], c=yt, marker='o', label='Target samples')
+pl.xticks([])
+pl.yticks([])
+pl.title('Main coupling coefficients\nSinkhornLpl1Transport')
+pl.tight_layout()
+
+
+##############################################################################
+# Fig 3 : plot transported samples
+##############################################################################
+
+# display transported samples
+pl.figure(4, figsize=(10, 4))
+pl.subplot(1, 3, 1)
+pl.scatter(Xt[:, 0], Xt[:, 1], c=yt, marker='o',
+           label='Target samples', alpha=0.5)
+pl.scatter(transp_Xs_emd[:, 0], transp_Xs_emd[:, 1], c=ys,
+           marker='+', label='Transp samples', s=30)
+pl.title('Transported samples\nEmdTransport')
+pl.legend(loc=0)
+pl.xticks([])
+pl.yticks([])
+
+pl.subplot(1, 3, 2)
+pl.scatter(Xt[:, 0], Xt[:, 1], c=yt, marker='o',
+           label='Target samples', alpha=0.5)
+pl.scatter(transp_Xs_sinkhorn[:, 0], transp_Xs_sinkhorn[:, 1], c=ys,
+           marker='+', label='Transp samples', s=30)
+pl.title('Transported samples\nSinkhornTransport')
+pl.xticks([])
+pl.yticks([])
+
+pl.subplot(1, 3, 3)
+pl.scatter(Xt[:, 0], Xt[:, 1], c=yt, marker='o',
+           label='Target samples', alpha=0.5)
+pl.scatter(transp_Xs_lpl1[:, 0], transp_Xs_lpl1[:, 1], c=ys,
+           marker='+', label='Transp samples', s=30)
+pl.title('Transported samples\nSinkhornLpl1Transport')
+pl.xticks([])
+pl.yticks([])
+
+pl.tight_layout()
+pl.show()
diff --git a/examples/plot_otda_mapping.py b/examples/plot_otda_mapping.py
new file mode 100644
index 0000000..09d2cb4
--- /dev/null
+++ b/examples/plot_otda_mapping.py
@@ -0,0 +1,126 @@
+# -*- coding: utf-8 -*-
+"""
+===============================================
+OT mapping estimation for domain adaptation [8]
+===============================================
+
+This example presents how to use MappingTransport to estimate at the same
+time both the coupling transport and approximate the transport map with either
+a linear or a kernelized mapping as introduced in [8]
+
+[8] M. Perrot, N. Courty, R. Flamary, A. Habrard,
+    "Mapping estimation for discrete optimal transport",
+    Neural Information Processing Systems (NIPS), 2016.
+"""
+
+# Authors: Remi Flamary <remi.flamary@unice.fr>
+#          Stanislas Chambon <stan.chambon@gmail.com>
+#
+# License: MIT License
+
+import numpy as np
+import matplotlib.pylab as pl
+import ot
+
+
+##############################################################################
+# generate data
+##############################################################################
+
+n_source_samples = 100
+n_target_samples = 100
+theta = 2 * np.pi / 20
+noise_level = 0.1
+
+Xs, ys = ot.datasets.get_data_classif(
+    'gaussrot', n_source_samples, nz=noise_level)
+Xs_new, _ = ot.datasets.get_data_classif(
+    'gaussrot', n_source_samples, nz=noise_level)
+Xt, yt = ot.datasets.get_data_classif(
+    'gaussrot', n_target_samples, theta=theta, nz=noise_level)
+
+# one of the target mode changes its variance (no linear mapping)
+Xt[yt == 2] *= 3
+Xt = Xt + 4
+
+
+##############################################################################
+# Instantiate the different transport algorithms and fit them
+##############################################################################
+
+# MappingTransport with linear kernel
+ot_mapping_linear = ot.da.MappingTransport(
+    kernel="linear", mu=1e0, eta=1e-8, bias=True,
+    max_iter=20, verbose=True)
+
+ot_mapping_linear.fit(Xs=Xs, Xt=Xt)
+
+# for original source samples, transform applies barycentric mapping
+transp_Xs_linear = ot_mapping_linear.transform(Xs=Xs)
+
+# for out of source samples, transform applies the linear mapping
+transp_Xs_linear_new = ot_mapping_linear.transform(Xs=Xs_new)
+
+
+# MappingTransport with gaussian kernel
+ot_mapping_gaussian = ot.da.MappingTransport(
+    kernel="gaussian", eta=1e-5, mu=1e-1, bias=True, sigma=1,
+    max_iter=10, verbose=True)
+ot_mapping_gaussian.fit(Xs=Xs, Xt=Xt)
+
+# for original source samples, transform applies barycentric mapping
+transp_Xs_gaussian = ot_mapping_gaussian.transform(Xs=Xs)
+
+# for out of source samples, transform applies the gaussian mapping
+transp_Xs_gaussian_new = ot_mapping_gaussian.transform(Xs=Xs_new)
+
+
+##############################################################################
+# plot data
+##############################################################################
+
+pl.figure(1, (10, 5))
+pl.clf()
+pl.scatter(Xs[:, 0], Xs[:, 1], c=ys, marker='+', label='Source samples')
+pl.scatter(Xt[:, 0], Xt[:, 1], c=yt, marker='o', label='Target samples')
+pl.legend(loc=0)
+pl.title('Source and target distributions')
+
+
+##############################################################################
+# plot transported samples
+##############################################################################
+
+pl.figure(2)
+pl.clf()
+pl.subplot(2, 2, 1)
+pl.scatter(Xt[:, 0], Xt[:, 1], c=yt, marker='o',
+           label='Target samples', alpha=.2)
+pl.scatter(transp_Xs_linear[:, 0], transp_Xs_linear[:, 1], c=ys, marker='+',
+           label='Mapped source samples')
+pl.title("Bary. mapping (linear)")
+pl.legend(loc=0)
+
+pl.subplot(2, 2, 2)
+pl.scatter(Xt[:, 0], Xt[:, 1], c=yt, marker='o',
+           label='Target samples', alpha=.2)
+pl.scatter(transp_Xs_linear_new[:, 0], transp_Xs_linear_new[:, 1],
+           c=ys, marker='+', label='Learned mapping')
+pl.title("Estim. mapping (linear)")
+
+pl.subplot(2, 2, 3)
+pl.scatter(Xt[:, 0], Xt[:, 1], c=yt, marker='o',
+           label='Target samples', alpha=.2)
+pl.scatter(transp_Xs_gaussian[:, 0], transp_Xs_gaussian[:, 1], c=ys,
+           marker='+', label='barycentric mapping')
+pl.title("Bary. mapping (kernel)")
+
+pl.subplot(2, 2, 4)
+pl.scatter(Xt[:, 0], Xt[:, 1], c=yt, marker='o',
+           label='Target samples', alpha=.2)
+pl.scatter(transp_Xs_gaussian_new[:, 0], transp_Xs_gaussian_new[:, 1], c=ys,
+           marker='+', label='Learned mapping')
+pl.title("Estim. mapping (kernel)")
+pl.tight_layout()
+
+pl.show()
diff --git a/examples/plot_otda_mapping_colors_images.py b/examples/plot_otda_mapping_colors_images.py
new file mode 100644
index 0000000..936206c
--- /dev/null
+++ b/examples/plot_otda_mapping_colors_images.py
@@ -0,0 +1,171 @@
+# -*- coding: utf-8 -*-
+"""
+====================================================================================
+OT for domain adaptation with image color adaptation [6] with mapping estimation [8]
+====================================================================================
+
+[6] Ferradans, S., Papadakis, N., Peyre, G., & Aujol, J. F. (2014). Regularized
+    discrete optimal transport. SIAM Journal on Imaging Sciences, 7(3),
+    1853-1882.
+[8] M. Perrot, N. Courty, R. Flamary, A. Habrard, "Mapping estimation for
+    discrete optimal transport", Neural Information Processing Systems (NIPS),
+    2016.
+
+"""
+
+# Authors: Remi Flamary <remi.flamary@unice.fr>
+#          Stanislas Chambon <stan.chambon@gmail.com>
+#
+# License: MIT License
+
+import numpy as np
+from scipy import ndimage
+import matplotlib.pylab as pl
+import ot
+
+r = np.random.RandomState(42)
+
+
+def im2mat(I):
+    """Converts and image to matrix (one pixel per line)"""
+    return I.reshape((I.shape[0] * I.shape[1], I.shape[2]))
+
+
+def mat2im(X, shape):
+    """Converts back a matrix to an image"""
+    return X.reshape(shape)
+
+
+def minmax(I):
+    return np.clip(I, 0, 1)
+
+
+##############################################################################
+# Generate data
+##############################################################################
+
+# Loading images
+I1 = ndimage.imread('../data/ocean_day.jpg').astype(np.float64) / 256
+I2 = ndimage.imread('../data/ocean_sunset.jpg').astype(np.float64) / 256
+
+
+X1 = im2mat(I1)
+X2 = im2mat(I2)
+
+# training samples
+nb = 1000
+idx1 = r.randint(X1.shape[0], size=(nb,))
+idx2 = r.randint(X2.shape[0], size=(nb,))
+
+Xs = X1[idx1, :]
+Xt = X2[idx2, :]
+
+
+##############################################################################
+# Domain adaptation for pixel distribution transfer
+##############################################################################
+
+# EMDTransport
+ot_emd = ot.da.EMDTransport()
+ot_emd.fit(Xs=Xs, Xt=Xt)
+transp_Xs_emd = ot_emd.transform(Xs=X1)
+Image_emd = minmax(mat2im(transp_Xs_emd, I1.shape))
+
+# SinkhornTransport
+ot_sinkhorn = ot.da.SinkhornTransport(reg_e=1e-1)
+ot_sinkhorn.fit(Xs=Xs, Xt=Xt)
+transp_Xs_sinkhorn = ot_emd.transform(Xs=X1)
+Image_sinkhorn = minmax(mat2im(transp_Xs_sinkhorn, I1.shape))
+
+ot_mapping_linear = ot.da.MappingTransport(
+    mu=1e0, eta=1e-8, bias=True, max_iter=20, verbose=True)
+ot_mapping_linear.fit(Xs=Xs, Xt=Xt)
+
+X1tl = ot_mapping_linear.transform(Xs=X1)
+Image_mapping_linear = minmax(mat2im(X1tl, I1.shape))
+
+ot_mapping_gaussian = ot.da.MappingTransport(
+    mu=1e0, eta=1e-2, sigma=1, bias=False, max_iter=10, verbose=True)
+ot_mapping_gaussian.fit(Xs=Xs, Xt=Xt)
+
+X1tn = ot_mapping_gaussian.transform(Xs=X1)  # use the estimated mapping
+Image_mapping_gaussian = minmax(mat2im(X1tn, I1.shape))
+
+
+##############################################################################
+# plot original images
+##############################################################################
+
+pl.figure(1, figsize=(6.4, 3))
+pl.subplot(1, 2, 1)
+pl.imshow(I1)
+pl.axis('off')
+pl.title('Image 1')
+
+pl.subplot(1, 2, 2)
+pl.imshow(I2)
+pl.axis('off')
+pl.title('Image 2')
+pl.tight_layout()
+
+
+##############################################################################
+# plot pixel values distribution
+##############################################################################
+
+pl.figure(2, figsize=(6.4, 5))
+
+pl.subplot(1, 2, 1)
+pl.scatter(Xs[:, 0], Xs[:, 2], c=Xs)
+pl.axis([0, 1, 0, 1])
+pl.xlabel('Red')
+pl.ylabel('Blue')
+pl.title('Image 1')
+
+pl.subplot(1, 2, 2)
+pl.scatter(Xt[:, 0], Xt[:, 2], c=Xt)
+pl.axis([0, 1, 0, 1])
+pl.xlabel('Red')
+pl.ylabel('Blue')
+pl.title('Image 2')
+pl.tight_layout()
+
+
+##############################################################################
+# plot transformed images
+##############################################################################
+
+pl.figure(2, figsize=(10, 5))
+
+pl.subplot(2, 3, 1)
+pl.imshow(I1)
+pl.axis('off')
+pl.title('Im. 1')
+
+pl.subplot(2, 3, 4)
+pl.imshow(I2)
+pl.axis('off')
+pl.title('Im. 2')
+
+pl.subplot(2, 3, 2)
+pl.imshow(Image_emd)
+pl.axis('off')
+pl.title('EmdTransport')
+
+pl.subplot(2, 3, 5)
+pl.imshow(Image_sinkhorn)
+pl.axis('off')
+pl.title('SinkhornTransport')
+
+pl.subplot(2, 3, 3)
+pl.imshow(Image_mapping_linear)
+pl.axis('off')
+pl.title('MappingTransport (linear)')
+
+pl.subplot(2, 3, 6)
+pl.imshow(Image_mapping_gaussian)
+pl.axis('off')
+pl.title('MappingTransport (gaussian)')
+pl.tight_layout()
+
+pl.show()