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
|
# -*- coding: utf-8 -*-
"""
==========================================
2D Optimal transport for different metrics
==========================================
2D OT on empirical distributio with different gound metric.
Stole the figure idea from Fig. 1 and 2 in
https://arxiv.org/pdf/1706.07650.pdf
"""
# Author: Remi Flamary <remi.flamary@unice.fr>
#
# License: MIT License
import numpy as np
import matplotlib.pylab as pl
import ot
import ot.plot
##############################################################################
# Dataset 1 : uniform sampling
# ----------------------------
n = 20 # nb samples
xs = np.zeros((n, 2))
xs[:, 0] = np.arange(n) + 1
xs[:, 1] = (np.arange(n) + 1) * -0.001 # to make it strictly convex...
xt = np.zeros((n, 2))
xt[:, 1] = np.arange(n) + 1
a, b = ot.unif(n), ot.unif(n) # uniform distribution on samples
# loss matrix
M1 = ot.dist(xs, xt, metric='euclidean')
M1 /= M1.max()
# loss matrix
M2 = ot.dist(xs, xt, metric='sqeuclidean')
M2 /= M2.max()
# loss matrix
Mp = np.sqrt(ot.dist(xs, xt, metric='euclidean'))
Mp /= Mp.max()
# Data
pl.figure(1, figsize=(7, 3))
pl.clf()
pl.plot(xs[:, 0], xs[:, 1], '+b', label='Source samples')
pl.plot(xt[:, 0], xt[:, 1], 'xr', label='Target samples')
pl.axis('equal')
pl.title('Source and target distributions')
# Cost matrices
pl.figure(2, figsize=(7, 3))
pl.subplot(1, 3, 1)
pl.imshow(M1, interpolation='nearest')
pl.title('Euclidean cost')
pl.subplot(1, 3, 2)
pl.imshow(M2, interpolation='nearest')
pl.title('Squared Euclidean cost')
pl.subplot(1, 3, 3)
pl.imshow(Mp, interpolation='nearest')
pl.title('Sqrt Euclidean cost')
pl.tight_layout()
##############################################################################
# Dataset 1 : Plot OT Matrices
# ----------------------------
#%% EMD
G1 = ot.emd(a, b, M1)
G2 = ot.emd(a, b, M2)
Gp = ot.emd(a, b, Mp)
# OT matrices
pl.figure(3, figsize=(7, 3))
pl.subplot(1, 3, 1)
ot.plot.plot2D_samples_mat(xs, xt, G1, 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.axis('equal')
# pl.legend(loc=0)
pl.title('OT Euclidean')
pl.subplot(1, 3, 2)
ot.plot.plot2D_samples_mat(xs, xt, G2, 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.axis('equal')
# pl.legend(loc=0)
pl.title('OT squared Euclidean')
pl.subplot(1, 3, 3)
ot.plot.plot2D_samples_mat(xs, xt, Gp, 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.axis('equal')
# pl.legend(loc=0)
pl.title('OT sqrt Euclidean')
pl.tight_layout()
pl.show()
##############################################################################
# Dataset 2 : Partial circle
# --------------------------
n = 50 # nb samples
xtot = np.zeros((n + 1, 2))
xtot[:, 0] = np.cos(
(np.arange(n + 1) + 1.0) * 0.9 / (n + 2) * 2 * np.pi)
xtot[:, 1] = np.sin(
(np.arange(n + 1) + 1.0) * 0.9 / (n + 2) * 2 * np.pi)
xs = xtot[:n, :]
xt = xtot[1:, :]
a, b = ot.unif(n), ot.unif(n) # uniform distribution on samples
# loss matrix
M1 = ot.dist(xs, xt, metric='euclidean')
M1 /= M1.max()
# loss matrix
M2 = ot.dist(xs, xt, metric='sqeuclidean')
M2 /= M2.max()
# loss matrix
Mp = np.sqrt(ot.dist(xs, xt, metric='euclidean'))
Mp /= Mp.max()
# Data
pl.figure(4, figsize=(7, 3))
pl.clf()
pl.plot(xs[:, 0], xs[:, 1], '+b', label='Source samples')
pl.plot(xt[:, 0], xt[:, 1], 'xr', label='Target samples')
pl.axis('equal')
pl.title('Source and traget distributions')
# Cost matrices
pl.figure(5, figsize=(7, 3))
pl.subplot(1, 3, 1)
pl.imshow(M1, interpolation='nearest')
pl.title('Euclidean cost')
pl.subplot(1, 3, 2)
pl.imshow(M2, interpolation='nearest')
pl.title('Squared Euclidean cost')
pl.subplot(1, 3, 3)
pl.imshow(Mp, interpolation='nearest')
pl.title('Sqrt Euclidean cost')
pl.tight_layout()
##############################################################################
# Dataset 2 : Plot OT Matrices
# -----------------------------
#%% EMD
G1 = ot.emd(a, b, M1)
G2 = ot.emd(a, b, M2)
Gp = ot.emd(a, b, Mp)
# OT matrices
pl.figure(6, figsize=(7, 3))
pl.subplot(1, 3, 1)
ot.plot.plot2D_samples_mat(xs, xt, G1, 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.axis('equal')
# pl.legend(loc=0)
pl.title('OT Euclidean')
pl.subplot(1, 3, 2)
ot.plot.plot2D_samples_mat(xs, xt, G2, 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.axis('equal')
# pl.legend(loc=0)
pl.title('OT squared Euclidean')
pl.subplot(1, 3, 3)
ot.plot.plot2D_samples_mat(xs, xt, Gp, 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.axis('equal')
# pl.legend(loc=0)
pl.title('OT sqrt Euclidean')
pl.tight_layout()
pl.show()
|
