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
|
# -*- coding: utf-8 -*-
"""
====================================================
2D Optimal transport between empirical distributions
====================================================
Illustration of 2D optimal transport between discributions that are weighted
sum of diracs. The OT matrix is plotted with the samples.
"""
# Author: Remi Flamary <remi.flamary@unice.fr>
# Kilian Fatras <kilian.fatras@irisa.fr>
#
# License: MIT License
# sphinx_gallery_thumbnail_number = 4
import numpy as np
import matplotlib.pylab as pl
import ot
import ot.plot
##############################################################################
# Generate data
# -------------
#%% parameters and data generation
n = 50 # nb samples
mu_s = np.array([0, 0])
cov_s = np.array([[1, 0], [0, 1]])
mu_t = np.array([4, 4])
cov_t = np.array([[1, -.8], [-.8, 1]])
xs = ot.datasets.make_2D_samples_gauss(n, mu_s, cov_s)
xt = ot.datasets.make_2D_samples_gauss(n, mu_t, cov_t)
a, b = np.ones((n,)) / n, np.ones((n,)) / n # uniform distribution on samples
# loss matrix
M = ot.dist(xs, xt)
M /= M.max()
##############################################################################
# Plot data
# ---------
#%% plot samples
pl.figure(1)
pl.plot(xs[:, 0], xs[:, 1], '+b', label='Source samples')
pl.plot(xt[:, 0], xt[:, 1], 'xr', label='Target samples')
pl.legend(loc=0)
pl.title('Source and target distributions')
pl.figure(2)
pl.imshow(M, interpolation='nearest')
pl.title('Cost matrix M')
##############################################################################
# Compute EMD
# -----------
#%% EMD
G0 = ot.emd(a, b, M)
pl.figure(3)
pl.imshow(G0, interpolation='nearest')
pl.title('OT matrix G0')
pl.figure(4)
ot.plot.plot2D_samples_mat(xs, xt, G0, c=[.5, .5, 1])
pl.plot(xs[:, 0], xs[:, 1], '+b', label='Source samples')
pl.plot(xt[:, 0], xt[:, 1], 'xr', label='Target samples')
pl.legend(loc=0)
pl.title('OT matrix with samples')
##############################################################################
# Compute Sinkhorn
# ----------------
#%% sinkhorn
# reg term
lambd = 1e-3
Gs = ot.sinkhorn(a, b, M, lambd)
pl.figure(5)
pl.imshow(Gs, interpolation='nearest')
pl.title('OT matrix sinkhorn')
pl.figure(6)
ot.plot.plot2D_samples_mat(xs, xt, Gs, color=[.5, .5, 1])
pl.plot(xs[:, 0], xs[:, 1], '+b', label='Source samples')
pl.plot(xt[:, 0], xt[:, 1], 'xr', label='Target samples')
pl.legend(loc=0)
pl.title('OT matrix Sinkhorn with samples')
pl.show()
##############################################################################
# Emprirical Sinkhorn
# ----------------
#%% sinkhorn
# reg term
lambd = 1e-3
Ges = ot.bregman.empirical_sinkhorn(xs, xt, lambd)
pl.figure(7)
pl.imshow(Ges, interpolation='nearest')
pl.title('OT matrix empirical sinkhorn')
pl.figure(8)
ot.plot.plot2D_samples_mat(xs, xt, Ges, color=[.5, .5, 1])
pl.plot(xs[:, 0], xs[:, 1], '+b', label='Source samples')
pl.plot(xt[:, 0], xt[:, 1], 'xr', label='Target samples')
pl.legend(loc=0)
pl.title('OT matrix Sinkhorn from samples')
pl.show()
|
