1
2
3
4
5
6
7
8
9
10
11
12
13
14
15
16
17
18
19
20
21
22
23
24
25
26
27
28
29
30
31
32
33
34
35
36
37
38
39
40
41
42
43
44
45
46
47
48
49
50
51
52
53
54
55
56
57
58
59
60
61
62
63
64
65
66
67
68
69
70
71
72
73
74
75
76
77
78
79
80
81
82
83
84
85
86
87
88
89
90
91
92
93
94
95
96
97
98
99
100
101
102
103
104
105
106
107
108
109
110
111
112
113
114
115
116
117
118
119
120
121
122
123
124
125
126
127
128
129
130
131
132
133
134
135
136
137
138
139
140
141
142
143
144
145
146
147
148
149
150
151
152
153
154
155
156
157
158
159
160
161
162
163
164
165
166
167
168
169
170
171
172
173
174
175
176
177
178
179
180
181
182
183
184
185
186
187
188
189
190
191
192
193
194
195
196
197
198
199
200
201
202
203
204
205
206
207
208
209
210
211
212
213
214
215
216
217
218
219
220
221
222
223
224
225
226
227
228
229
230
231
232
233
234
235
236
237
238
239
240
241
242
243
244
245
246
247
248
249
250
251
252
253
254
255
256
257
258
259
260
261
262
263
264
265
266
267
268
269
|
.. _sphx_glr_auto_examples_plot_otda_d2.py:
===================================================
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.
.. code-block:: python
# Authors: Remi Flamary <remi.flamary@unice.fr>
# Stanislas Chambon <stan.chambon@gmail.com>
#
# License: MIT License
import matplotlib.pylab as pl
import ot
import ot.plot
generate data
-------------
.. code-block:: python
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
-----------------------------------------------------------
.. code-block:: python
# 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
---------------------------------------------------------------------
.. code-block:: python
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()
.. image:: /auto_examples/images/sphx_glr_plot_otda_d2_001.png
:align: center
Fig 2 : plots optimal couplings for the different methods
---------------------------------------------------------
.. code-block:: python
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()
.. image:: /auto_examples/images/sphx_glr_plot_otda_d2_003.png
:align: center
Fig 3 : plot transported samples
--------------------------------
.. code-block:: python
# 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()
.. image:: /auto_examples/images/sphx_glr_plot_otda_d2_006.png
:align: center
**Total running time of the script:** ( 0 minutes 35.515 seconds)
.. only :: html
.. container:: sphx-glr-footer
.. container:: sphx-glr-download
:download:`Download Python source code: plot_otda_d2.py <plot_otda_d2.py>`
.. container:: sphx-glr-download
:download:`Download Jupyter notebook: plot_otda_d2.ipynb <plot_otda_d2.ipynb>`
.. only:: html
.. rst-class:: sphx-glr-signature
`Gallery generated by Sphinx-Gallery <https://sphinx-gallery.readthedocs.io>`_
|
