10 files changed, 1389 insertions, 0 deletions
diff --git a/examples/domain-adaptation/README.txt b/examples/domain-adaptation/README.txt
new file mode 100644
index 0000000..81dd8d2
--- /dev/null
+++ b/examples/domain-adaptation/README.txt
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+
+
+
+Domain adaptation examples
+--------------------------
+\ No newline at end of file
diff --git a/examples/domain-adaptation/plot_otda_classes.py b/examples/domain-adaptation/plot_otda_classes.py
new file mode 100644
index 0000000..f028022
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+++ b/examples/domain-adaptation/plot_otda_classes.py
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+# -*- 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.make_data_classif('3gauss', n_source_samples)
+Xt, yt = ot.datasets.make_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'}
+
+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/domain-adaptation/plot_otda_color_images.py b/examples/domain-adaptation/plot_otda_color_images.py
new file mode 100644
index 0000000..929365e
--- /dev/null
+++ b/examples/domain-adaptation/plot_otda_color_images.py
@@ -0,0 +1,166 @@
+# -*- coding: utf-8 -*-
+"""
+=============================
+OT for image color adaptation
+=============================
+
+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).
+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
+
+# sphinx_gallery_thumbnail_number = 2
+
+import numpy as np
+import matplotlib.pylab as pl
+import ot
+
+
+r = np.random.RandomState(42)
+
+
+def im2mat(I):
+    """Converts an 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 = pl.imread('../../data/ocean_day.jpg').astype(np.float64) / 256
+I2 = pl.imread('../../data/ocean_sunset.jpg').astype(np.float64) / 256
+
+X1 = im2mat(I1)
+X2 = im2mat(I2)
+
+# training samples
+nb = 1000
+idx1 = r.randint(X1.shape[0], size=(nb,))
+idx2 = r.randint(X2.shape[0], size=(nb,))
+
+Xs = X1[idx1, :]
+Xt = X2[idx2, :]
+
+
+##############################################################################
+# Plot original image
+# -------------------
+
+pl.figure(1, figsize=(6.4, 3))
+
+pl.subplot(1, 2, 1)
+pl.imshow(I1)
+pl.axis('off')
+pl.title('Image 1')
+
+pl.subplot(1, 2, 2)
+pl.imshow(I2)
+pl.axis('off')
+pl.title('Image 2')
+
+
+##############################################################################
+# Scatter plot of colors
+# ----------------------
+
+pl.figure(2, figsize=(6.4, 3))
+
+pl.subplot(1, 2, 1)
+pl.scatter(Xs[:, 0], Xs[:, 2], c=Xs)
+pl.axis([0, 1, 0, 1])
+pl.xlabel('Red')
+pl.ylabel('Blue')
+pl.title('Image 1')
+
+pl.subplot(1, 2, 2)
+pl.scatter(Xt[:, 0], Xt[:, 2], c=Xt)
+pl.axis([0, 1, 0, 1])
+pl.xlabel('Red')
+pl.ylabel('Blue')
+pl.title('Image 2')
+pl.tight_layout()
+
+
+##############################################################################
+# Instantiate the different transport algorithms and fit them
+# -----------------------------------------------------------
+
+# EMDTransport
+ot_emd = ot.da.EMDTransport()
+ot_emd.fit(Xs=Xs, Xt=Xt)
+
+# SinkhornTransport
+ot_sinkhorn = ot.da.SinkhornTransport(reg_e=1e-1)
+ot_sinkhorn.fit(Xs=Xs, Xt=Xt)
+
+# prediction between images (using out of sample prediction as in [6])
+transp_Xs_emd = ot_emd.transform(Xs=X1)
+transp_Xt_emd = ot_emd.inverse_transform(Xt=X2)
+
+transp_Xs_sinkhorn = ot_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))
+
+I1te = minmax(mat2im(transp_Xs_sinkhorn, I1.shape))
+I2te = minmax(mat2im(transp_Xt_sinkhorn, I2.shape))
+
+
+##############################################################################
+# Plot new images
+# ---------------
+
+pl.figure(3, figsize=(8, 4))
+
+pl.subplot(2, 3, 1)
+pl.imshow(I1)
+pl.axis('off')
+pl.title('Image 1')
+
+pl.subplot(2, 3, 2)
+pl.imshow(I1t)
+pl.axis('off')
+pl.title('Image 1 Adapt')
+
+pl.subplot(2, 3, 3)
+pl.imshow(I1te)
+pl.axis('off')
+pl.title('Image 1 Adapt (reg)')
+
+pl.subplot(2, 3, 4)
+pl.imshow(I2)
+pl.axis('off')
+pl.title('Image 2')
+
+pl.subplot(2, 3, 5)
+pl.imshow(I2t)
+pl.axis('off')
+pl.title('Image 2 Adapt')
+
+pl.subplot(2, 3, 6)
+pl.imshow(I2te)
+pl.axis('off')
+pl.title('Image 2 Adapt (reg)')
+pl.tight_layout()
+
+pl.show()
diff --git a/examples/domain-adaptation/plot_otda_d2.py b/examples/domain-adaptation/plot_otda_d2.py
new file mode 100644
index 0000000..d8b2a93
--- /dev/null
+++ b/examples/domain-adaptation/plot_otda_d2.py
@@ -0,0 +1,174 @@
+# -*- coding: utf-8 -*-
+"""
+===================================================
+OT for domain adaptation on empirical distributions
+===================================================
+
+This example introduces a domain adaptation in a 2D setting. It explicits
+the problem of domain adaptation and introduces some optimal transport
+approaches to solve it.
+
+Quantities such as optimal couplings, greater coupling coefficients and
+transported samples are represented in order to give a visual understanding
+of what the transport methods are doing.
+"""
+
+# Authors: Remi Flamary <remi.flamary@unice.fr>
+#          Stanislas Chambon <stan.chambon@gmail.com>
+#
+# License: MIT License
+
+# sphinx_gallery_thumbnail_number = 2
+
+import matplotlib.pylab as pl
+import ot
+import ot.plot
+
+##############################################################################
+# Generate data
+# -------------
+
+n_samples_source = 150
+n_samples_target = 150
+
+Xs, ys = ot.datasets.make_data_classif('3gauss', n_samples_source)
+Xt, yt = ot.datasets.make_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/domain-adaptation/plot_otda_jcpot.py b/examples/domain-adaptation/plot_otda_jcpot.py
new file mode 100644
index 0000000..c495690
--- /dev/null
+++ b/examples/domain-adaptation/plot_otda_jcpot.py
@@ -0,0 +1,171 @@
+# -*- coding: utf-8 -*-
+"""
+========================
+OT for multi-source target shift
+========================
+
+This example introduces a target shift problem with two 2D source and 1 target domain.
+
+"""
+
+# Authors: Remi Flamary <remi.flamary@unice.fr>
+#          Ievgen Redko <ievgen.redko@univ-st-etienne.fr>
+#
+# License: MIT License
+
+import pylab as pl
+import numpy as np
+import ot
+from ot.datasets import make_data_classif
+
+##############################################################################
+# Generate data
+# -------------
+n = 50
+sigma = 0.3
+np.random.seed(1985)
+
+p1 = .2
+dec1 = [0, 2]
+
+p2 = .9
+dec2 = [0, -2]
+
+pt = .4
+dect = [4, 0]
+
+xs1, ys1 = make_data_classif('2gauss_prop', n, nz=sigma, p=p1, bias=dec1)
+xs2, ys2 = make_data_classif('2gauss_prop', n + 1, nz=sigma, p=p2, bias=dec2)
+xt, yt = make_data_classif('2gauss_prop', n, nz=sigma, p=pt, bias=dect)
+
+all_Xr = [xs1, xs2]
+all_Yr = [ys1, ys2]
+# %%
+
+da = 1.5
+
+
+def plot_ax(dec, name):
+    pl.plot([dec[0], dec[0]], [dec[1] - da, dec[1] + da], 'k', alpha=0.5)
+    pl.plot([dec[0] - da, dec[0] + da], [dec[1], dec[1]], 'k', alpha=0.5)
+    pl.text(dec[0] - .5, dec[1] + 2, name)
+
+
+##############################################################################
+# Fig 1 : plots source and target samples
+# ---------------------------------------
+
+pl.figure(1)
+pl.clf()
+plot_ax(dec1, 'Source 1')
+plot_ax(dec2, 'Source 2')
+plot_ax(dect, 'Target')
+pl.scatter(xs1[:, 0], xs1[:, 1], c=ys1, s=35, marker='x', cmap='Set1', vmax=9,
+           label='Source 1 ({:1.2f}, {:1.2f})'.format(1 - p1, p1))
+pl.scatter(xs2[:, 0], xs2[:, 1], c=ys2, s=35, marker='+', cmap='Set1', vmax=9,
+           label='Source 2 ({:1.2f}, {:1.2f})'.format(1 - p2, p2))
+pl.scatter(xt[:, 0], xt[:, 1], c=yt, s=35, marker='o', cmap='Set1', vmax=9,
+           label='Target ({:1.2f}, {:1.2f})'.format(1 - pt, pt))
+pl.title('Data')
+
+pl.legend()
+pl.axis('equal')
+pl.axis('off')
+
+##############################################################################
+# Instantiate Sinkhorn transport algorithm and fit them for all source domains
+# ----------------------------------------------------------------------------
+ot_sinkhorn = ot.da.SinkhornTransport(reg_e=1e-1, metric='sqeuclidean')
+
+
+def print_G(G, xs, ys, xt):
+    for i in range(G.shape[0]):
+        for j in range(G.shape[1]):
+            if G[i, j] > 5e-4:
+                if ys[i]:
+                    c = 'b'
+                else:
+                    c = 'r'
+                pl.plot([xs[i, 0], xt[j, 0]], [xs[i, 1], xt[j, 1]], c, alpha=.2)
+
+
+##############################################################################
+# Fig 2 : plot optimal couplings and transported samples
+# ------------------------------------------------------
+pl.figure(2)
+pl.clf()
+plot_ax(dec1, 'Source 1')
+plot_ax(dec2, 'Source 2')
+plot_ax(dect, 'Target')
+print_G(ot_sinkhorn.fit(Xs=xs1, Xt=xt).coupling_, xs1, ys1, xt)
+print_G(ot_sinkhorn.fit(Xs=xs2, Xt=xt).coupling_, xs2, ys2, xt)
+pl.scatter(xs1[:, 0], xs1[:, 1], c=ys1, s=35, marker='x', cmap='Set1', vmax=9)
+pl.scatter(xs2[:, 0], xs2[:, 1], c=ys2, s=35, marker='+', cmap='Set1', vmax=9)
+pl.scatter(xt[:, 0], xt[:, 1], c=yt, s=35, marker='o', cmap='Set1', vmax=9)
+
+pl.plot([], [], 'r', alpha=.2, label='Mass from Class 1')
+pl.plot([], [], 'b', alpha=.2, label='Mass from Class 2')
+
+pl.title('Independent OT')
+
+pl.legend()
+pl.axis('equal')
+pl.axis('off')
+
+##############################################################################
+# Instantiate JCPOT adaptation algorithm and fit it
+# ----------------------------------------------------------------------------
+otda = ot.da.JCPOTTransport(reg_e=1, max_iter=1000, metric='sqeuclidean', tol=1e-9, verbose=True, log=True)
+otda.fit(all_Xr, all_Yr, xt)
+
+ws1 = otda.proportions_.dot(otda.log_['D2'][0])
+ws2 = otda.proportions_.dot(otda.log_['D2'][1])
+
+pl.figure(3)
+pl.clf()
+plot_ax(dec1, 'Source 1')
+plot_ax(dec2, 'Source 2')
+plot_ax(dect, 'Target')
+print_G(ot.bregman.sinkhorn(ws1, [], otda.log_['M'][0], reg=1e-1), xs1, ys1, xt)
+print_G(ot.bregman.sinkhorn(ws2, [], otda.log_['M'][1], reg=1e-1), xs2, ys2, xt)
+pl.scatter(xs1[:, 0], xs1[:, 1], c=ys1, s=35, marker='x', cmap='Set1', vmax=9)
+pl.scatter(xs2[:, 0], xs2[:, 1], c=ys2, s=35, marker='+', cmap='Set1', vmax=9)
+pl.scatter(xt[:, 0], xt[:, 1], c=yt, s=35, marker='o', cmap='Set1', vmax=9)
+
+pl.plot([], [], 'r', alpha=.2, label='Mass from Class 1')
+pl.plot([], [], 'b', alpha=.2, label='Mass from Class 2')
+
+pl.title('OT with prop estimation ({:1.3f},{:1.3f})'.format(otda.proportions_[0], otda.proportions_[1]))
+
+pl.legend()
+pl.axis('equal')
+pl.axis('off')
+
+##############################################################################
+# Run oracle transport algorithm with known proportions
+# ----------------------------------------------------------------------------
+h_res = np.array([1 - pt, pt])
+
+ws1 = h_res.dot(otda.log_['D2'][0])
+ws2 = h_res.dot(otda.log_['D2'][1])
+
+pl.figure(4)
+pl.clf()
+plot_ax(dec1, 'Source 1')
+plot_ax(dec2, 'Source 2')
+plot_ax(dect, 'Target')
+print_G(ot.bregman.sinkhorn(ws1, [], otda.log_['M'][0], reg=1e-1), xs1, ys1, xt)
+print_G(ot.bregman.sinkhorn(ws2, [], otda.log_['M'][1], reg=1e-1), xs2, ys2, xt)
+pl.scatter(xs1[:, 0], xs1[:, 1], c=ys1, s=35, marker='x', cmap='Set1', vmax=9)
+pl.scatter(xs2[:, 0], xs2[:, 1], c=ys2, s=35, marker='+', cmap='Set1', vmax=9)
+pl.scatter(xt[:, 0], xt[:, 1], c=yt, s=35, marker='o', cmap='Set1', vmax=9)
+
+pl.plot([], [], 'r', alpha=.2, label='Mass from Class 1')
+pl.plot([], [], 'b', alpha=.2, label='Mass from Class 2')
+
+pl.title('OT with known proportion ({:1.1f},{:1.1f})'.format(h_res[0], h_res[1]))
+
+pl.legend()
+pl.axis('equal')
+pl.axis('off')
+pl.show()
diff --git a/examples/domain-adaptation/plot_otda_laplacian.py b/examples/domain-adaptation/plot_otda_laplacian.py
new file mode 100644
index 0000000..67c8f67
--- /dev/null
+++ b/examples/domain-adaptation/plot_otda_laplacian.py
@@ -0,0 +1,127 @@
+# -*- coding: utf-8 -*-
+"""
+======================================================
+OT with Laplacian regularization for domain adaptation
+======================================================
+
+This example introduces a domain adaptation in a 2D setting and OTDA
+approach with Laplacian regularization.
+
+"""
+
+# Authors: Ievgen Redko <ievgen.redko@univ-st-etienne.fr>
+
+# License: MIT License
+
+import matplotlib.pylab as pl
+import ot
+
+##############################################################################
+# Generate data
+# -------------
+
+n_source_samples = 150
+n_target_samples = 150
+
+Xs, ys = ot.datasets.make_data_classif('3gauss', n_source_samples)
+Xt, yt = ot.datasets.make_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=.01)
+ot_sinkhorn.fit(Xs=Xs, Xt=Xt)
+
+# EMD Transport with Laplacian regularization
+ot_emd_laplace = ot.da.EMDLaplaceTransport(reg_lap=100, reg_src=1)
+ot_emd_laplace.fit(Xs=Xs, 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_emd_laplace = ot_emd_laplace.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'}
+
+pl.figure(2, figsize=(15, 8))
+pl.subplot(2, 3, 1)
+pl.imshow(ot_emd.coupling_, **param_img)
+pl.xticks([])
+pl.yticks([])
+pl.title('Optimal coupling\nEMDTransport')
+
+pl.figure(2, figsize=(15, 8))
+pl.subplot(2, 3, 2)
+pl.imshow(ot_sinkhorn.coupling_, **param_img)
+pl.xticks([])
+pl.yticks([])
+pl.title('Optimal coupling\nSinkhornTransport')
+
+pl.subplot(2, 3, 3)
+pl.imshow(ot_emd_laplace.coupling_, **param_img)
+pl.xticks([])
+pl.yticks([])
+pl.title('Optimal coupling\nEMDLaplaceTransport')
+
+pl.subplot(2, 3, 4)
+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, 3, 5)
+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, 3, 6)
+pl.scatter(Xt[:, 0], Xt[:, 1], c=yt, marker='o',
+           label='Target samples', alpha=0.3)
+pl.scatter(transp_Xs_emd_laplace[:, 0], transp_Xs_emd_laplace[:, 1], c=ys,
+           marker='+', label='Transp samples', s=30)
+pl.xticks([])
+pl.yticks([])
+pl.title('Transported samples\nEMDLaplaceTransport')
+pl.tight_layout()
+
+pl.show()
diff --git a/examples/domain-adaptation/plot_otda_linear_mapping.py b/examples/domain-adaptation/plot_otda_linear_mapping.py
new file mode 100644
index 0000000..dbf16b8
--- /dev/null
+++ b/examples/domain-adaptation/plot_otda_linear_mapping.py
@@ -0,0 +1,146 @@
+#!/usr/bin/env python3
+# -*- coding: utf-8 -*-
+"""
+============================
+Linear OT mapping estimation
+============================
+
+
+"""
+
+# Author: Remi Flamary <remi.flamary@unice.fr>
+#
+# License: MIT License
+
+# sphinx_gallery_thumbnail_number = 2
+
+import numpy as np
+import pylab as pl
+import ot
+
+##############################################################################
+# Generate data
+# -------------
+
+n = 1000
+d = 2
+sigma = .1
+
+# source samples
+angles = np.random.rand(n, 1) * 2 * np.pi
+xs = np.concatenate((np.sin(angles), np.cos(angles)),
+                    axis=1) + sigma * np.random.randn(n, 2)
+xs[:n // 2, 1] += 2
+
+
+# target samples
+anglet = np.random.rand(n, 1) * 2 * np.pi
+xt = np.concatenate((np.sin(anglet), np.cos(anglet)),
+                    axis=1) + sigma * np.random.randn(n, 2)
+xt[:n // 2, 1] += 2
+
+
+A = np.array([[1.5, .7], [.7, 1.5]])
+b = np.array([[4, 2]])
+xt = xt.dot(A) + b
+
+##############################################################################
+# Plot data
+# ---------
+
+pl.figure(1, (5, 5))
+pl.plot(xs[:, 0], xs[:, 1], '+')
+pl.plot(xt[:, 0], xt[:, 1], 'o')
+
+
+##############################################################################
+# Estimate linear mapping and transport
+# -------------------------------------
+
+Ae, be = ot.da.OT_mapping_linear(xs, xt)
+
+xst = xs.dot(Ae) + be
+
+
+##############################################################################
+# Plot transported samples
+# ------------------------
+
+pl.figure(1, (5, 5))
+pl.clf()
+pl.plot(xs[:, 0], xs[:, 1], '+')
+pl.plot(xt[:, 0], xt[:, 1], 'o')
+pl.plot(xst[:, 0], xst[:, 1], '+')
+
+pl.show()
+
+##############################################################################
+# Load image data
+# ---------------
+
+
+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)
+
+
+# Loading images
+I1 = pl.imread('../../data/ocean_day.jpg').astype(np.float64) / 256
+I2 = pl.imread('../../data/ocean_sunset.jpg').astype(np.float64) / 256
+
+
+X1 = im2mat(I1)
+X2 = im2mat(I2)
+
+##############################################################################
+# Estimate mapping and adapt
+# ----------------------------
+
+mapping = ot.da.LinearTransport()
+
+mapping.fit(Xs=X1, Xt=X2)
+
+
+xst = mapping.transform(Xs=X1)
+xts = mapping.inverse_transform(Xt=X2)
+
+I1t = minmax(mat2im(xst, I1.shape))
+I2t = minmax(mat2im(xts, I2.shape))
+
+# %%
+
+
+##############################################################################
+# Plot transformed images
+# -----------------------
+
+pl.figure(2, figsize=(10, 7))
+
+pl.subplot(2, 2, 1)
+pl.imshow(I1)
+pl.axis('off')
+pl.title('Im. 1')
+
+pl.subplot(2, 2, 2)
+pl.imshow(I2)
+pl.axis('off')
+pl.title('Im. 2')
+
+pl.subplot(2, 2, 3)
+pl.imshow(I1t)
+pl.axis('off')
+pl.title('Mapping Im. 1')
+
+pl.subplot(2, 2, 4)
+pl.imshow(I2t)
+pl.axis('off')
+pl.title('Inverse mapping Im. 2')
diff --git a/examples/domain-adaptation/plot_otda_mapping.py b/examples/domain-adaptation/plot_otda_mapping.py
new file mode 100644
index 0000000..d21d3c9
--- /dev/null
+++ b/examples/domain-adaptation/plot_otda_mapping.py
@@ -0,0 +1,127 @@
+# -*- coding: utf-8 -*-
+"""
+===========================================
+OT mapping estimation for domain adaptation
+===========================================
+
+This example presents how to use MappingTransport to estimate at the same
+time both the coupling transport and approximate the transport map with either
+a linear or a kernelized mapping as introduced in [8].
+
+[8] M. Perrot, N. Courty, R. Flamary, A. Habrard,
+"Mapping estimation for discrete optimal transport",
+Neural Information Processing Systems (NIPS), 2016.
+"""
+
+# Authors: Remi Flamary <remi.flamary@unice.fr>
+#          Stanislas Chambon <stan.chambon@gmail.com>
+#
+# License: MIT License
+
+# sphinx_gallery_thumbnail_number = 2
+
+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.make_data_classif(
+    'gaussrot', n_source_samples, nz=noise_level)
+Xs_new, _ = ot.datasets.make_data_classif(
+    'gaussrot', n_source_samples, nz=noise_level)
+Xt, yt = ot.datasets.make_data_classif(
+    'gaussrot', n_target_samples, theta=theta, nz=noise_level)
+
+# one of the target mode changes its variance (no linear mapping)
+Xt[yt == 2] *= 3
+Xt = Xt + 4
+
+##############################################################################
+# Plot data
+# ---------
+
+pl.figure(1, (10, 5))
+pl.clf()
+pl.scatter(Xs[:, 0], Xs[:, 1], c=ys, marker='+', label='Source samples')
+pl.scatter(Xt[:, 0], Xt[:, 1], c=yt, marker='o', label='Target samples')
+pl.legend(loc=0)
+pl.title('Source and target distributions')
+
+
+##############################################################################
+# Instantiate the different transport algorithms and fit them
+# -----------------------------------------------------------
+
+# MappingTransport with linear kernel
+ot_mapping_linear = ot.da.MappingTransport(
+    kernel="linear", mu=1e0, eta=1e-8, bias=True,
+    max_iter=20, verbose=True)
+
+ot_mapping_linear.fit(Xs=Xs, Xt=Xt)
+
+# for original source samples, transform applies barycentric mapping
+transp_Xs_linear = ot_mapping_linear.transform(Xs=Xs)
+
+# for out of source samples, transform applies the linear mapping
+transp_Xs_linear_new = ot_mapping_linear.transform(Xs=Xs_new)
+
+
+# MappingTransport with gaussian kernel
+ot_mapping_gaussian = ot.da.MappingTransport(
+    kernel="gaussian", eta=1e-5, mu=1e-1, bias=True, sigma=1,
+    max_iter=10, verbose=True)
+ot_mapping_gaussian.fit(Xs=Xs, Xt=Xt)
+
+# for original source samples, transform applies barycentric mapping
+transp_Xs_gaussian = ot_mapping_gaussian.transform(Xs=Xs)
+
+# for out of source samples, transform applies the gaussian mapping
+transp_Xs_gaussian_new = ot_mapping_gaussian.transform(Xs=Xs_new)
+
+
+##############################################################################
+# Plot transported samples
+# ------------------------
+
+pl.figure(2)
+pl.clf()
+pl.subplot(2, 2, 1)
+pl.scatter(Xt[:, 0], Xt[:, 1], c=yt, marker='o',
+           label='Target samples', alpha=.2)
+pl.scatter(transp_Xs_linear[:, 0], transp_Xs_linear[:, 1], c=ys, marker='+',
+           label='Mapped source samples')
+pl.title("Bary. mapping (linear)")
+pl.legend(loc=0)
+
+pl.subplot(2, 2, 2)
+pl.scatter(Xt[:, 0], Xt[:, 1], c=yt, marker='o',
+           label='Target samples', alpha=.2)
+pl.scatter(transp_Xs_linear_new[:, 0], transp_Xs_linear_new[:, 1],
+           c=ys, marker='+', label='Learned mapping')
+pl.title("Estim. mapping (linear)")
+
+pl.subplot(2, 2, 3)
+pl.scatter(Xt[:, 0], Xt[:, 1], c=yt, marker='o',
+           label='Target samples', alpha=.2)
+pl.scatter(transp_Xs_gaussian[:, 0], transp_Xs_gaussian[:, 1], c=ys,
+           marker='+', label='barycentric mapping')
+pl.title("Bary. mapping (kernel)")
+
+pl.subplot(2, 2, 4)
+pl.scatter(Xt[:, 0], Xt[:, 1], c=yt, marker='o',
+           label='Target samples', alpha=.2)
+pl.scatter(transp_Xs_gaussian_new[:, 0], transp_Xs_gaussian_new[:, 1], c=ys,
+           marker='+', label='Learned mapping')
+pl.title("Estim. mapping (kernel)")
+pl.tight_layout()
+
+pl.show()
diff --git a/examples/domain-adaptation/plot_otda_mapping_colors_images.py b/examples/domain-adaptation/plot_otda_mapping_colors_images.py
new file mode 100644
index 0000000..ee5c8b0
--- /dev/null
+++ b/examples/domain-adaptation/plot_otda_mapping_colors_images.py
@@ -0,0 +1,174 @@
+# -*- coding: utf-8 -*-
+"""
+=====================================================
+OT for image color adaptation with mapping estimation
+=====================================================
+
+OT for domain adaptation with image color adaptation [6] with mapping
+estimation [8].
+
+[6] Ferradans, S., Papadakis, N., Peyre, G., & Aujol, J. F. (2014). Regularized
+discrete optimal transport. SIAM Journal on Imaging Sciences, 7(3), 1853-1882.
+
+[8] M. Perrot, N. Courty, R. Flamary, A. Habrard, "Mapping estimation for
+discrete optimal transport", Neural Information Processing Systems (NIPS), 2016.
+
+"""
+
+# Authors: Remi Flamary <remi.flamary@unice.fr>
+#          Stanislas Chambon <stan.chambon@gmail.com>
+#
+# License: MIT License
+
+# sphinx_gallery_thumbnail_number = 3
+
+import numpy as np
+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 = pl.imread('../../data/ocean_day.jpg').astype(np.float64) / 256
+I2 = pl.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_sinkhorn.transform(Xs=X1)
+Image_sinkhorn = minmax(mat2im(transp_Xs_sinkhorn, I1.shape))
+
+ot_mapping_linear = ot.da.MappingTransport(
+    mu=1e0, eta=1e-8, bias=True, max_iter=20, verbose=True)
+ot_mapping_linear.fit(Xs=Xs, Xt=Xt)
+
+X1tl = ot_mapping_linear.transform(Xs=X1)
+Image_mapping_linear = minmax(mat2im(X1tl, I1.shape))
+
+ot_mapping_gaussian = ot.da.MappingTransport(
+    mu=1e0, eta=1e-2, sigma=1, bias=False, max_iter=10, verbose=True)
+ot_mapping_gaussian.fit(Xs=Xs, Xt=Xt)
+
+X1tn = ot_mapping_gaussian.transform(Xs=X1)  # use the estimated mapping
+Image_mapping_gaussian = minmax(mat2im(X1tn, I1.shape))
+
+
+##############################################################################
+# Plot original images
+# --------------------
+
+pl.figure(1, figsize=(6.4, 3))
+pl.subplot(1, 2, 1)
+pl.imshow(I1)
+pl.axis('off')
+pl.title('Image 1')
+
+pl.subplot(1, 2, 2)
+pl.imshow(I2)
+pl.axis('off')
+pl.title('Image 2')
+pl.tight_layout()
+
+
+##############################################################################
+# Plot pixel values distribution
+# ------------------------------
+
+pl.figure(2, figsize=(6.4, 5))
+
+pl.subplot(1, 2, 1)
+pl.scatter(Xs[:, 0], Xs[:, 2], c=Xs)
+pl.axis([0, 1, 0, 1])
+pl.xlabel('Red')
+pl.ylabel('Blue')
+pl.title('Image 1')
+
+pl.subplot(1, 2, 2)
+pl.scatter(Xt[:, 0], Xt[:, 2], c=Xt)
+pl.axis([0, 1, 0, 1])
+pl.xlabel('Red')
+pl.ylabel('Blue')
+pl.title('Image 2')
+pl.tight_layout()
+
+
+##############################################################################
+# Plot transformed images
+# -----------------------
+
+pl.figure(2, figsize=(10, 5))
+
+pl.subplot(2, 3, 1)
+pl.imshow(I1)
+pl.axis('off')
+pl.title('Im. 1')
+
+pl.subplot(2, 3, 4)
+pl.imshow(I2)
+pl.axis('off')
+pl.title('Im. 2')
+
+pl.subplot(2, 3, 2)
+pl.imshow(Image_emd)
+pl.axis('off')
+pl.title('EmdTransport')
+
+pl.subplot(2, 3, 5)
+pl.imshow(Image_sinkhorn)
+pl.axis('off')
+pl.title('SinkhornTransport')
+
+pl.subplot(2, 3, 3)
+pl.imshow(Image_mapping_linear)
+pl.axis('off')
+pl.title('MappingTransport (linear)')
+
+pl.subplot(2, 3, 6)
+pl.imshow(Image_mapping_gaussian)
+pl.axis('off')
+pl.title('MappingTransport (gaussian)')
+pl.tight_layout()
+
+pl.show()
diff --git a/examples/domain-adaptation/plot_otda_semi_supervised.py b/examples/domain-adaptation/plot_otda_semi_supervised.py
new file mode 100644
index 0000000..478c3b8
--- /dev/null
+++ b/examples/domain-adaptation/plot_otda_semi_supervised.py
@@ -0,0 +1,150 @@
+# -*- 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 <remi.flamary@unice.fr>
+#          Stanislas Chambon <stan.chambon@gmail.com>
+#
+# License: MIT License
+
+# sphinx_gallery_thumbnail_number = 3
+
+import matplotlib.pylab as pl
+import ot
+
+
+##############################################################################
+# Generate data
+# -------------
+
+n_samples_source = 150
+n_samples_target = 150
+
+Xs, ys = ot.datasets.make_data_classif('3gauss', n_samples_source)
+Xt, yt = ot.datasets.make_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()