/
plot_compute_emd.py
132 lines (103 loc) · 3.3 KB
/
plot_compute_emd.py
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
# -*- coding: utf-8 -*-
"""
==================
OT distances in 1D
==================
Shows how to compute multiple Wassersein and Sinkhorn with two different
ground metrics and plot their values for different distributions.
"""
# Author: Remi Flamary <remi.flamary@unice.fr>
#
# License: MIT License
# sphinx_gallery_thumbnail_number = 2
import numpy as np
import matplotlib.pylab as pl
import ot
from ot.datasets import make_1D_gauss as gauss
##############################################################################
# Generate data
# -------------
#%% parameters
n = 100 # nb bins
n_target = 20 # nb target distributions
# bin positions
x = np.arange(n, dtype=np.float64)
lst_m = np.linspace(20, 90, n_target)
# Gaussian distributions
a = gauss(n, m=20, s=5) # m= mean, s= std
B = np.zeros((n, n_target))
for i, m in enumerate(lst_m):
B[:, i] = gauss(n, m=m, s=5)
# loss matrix and normalization
M = ot.dist(x.reshape((n, 1)), x.reshape((n, 1)), 'euclidean')
M /= M.max() * 0.1
M2 = ot.dist(x.reshape((n, 1)), x.reshape((n, 1)), 'sqeuclidean')
M2 /= M2.max() * 0.1
##############################################################################
# Plot data
# ---------
#%% plot the distributions
pl.figure(1)
pl.subplot(2, 1, 1)
pl.plot(x, a, 'r', label='Source distribution')
pl.title('Source distribution')
pl.subplot(2, 1, 2)
for i in range(n_target):
pl.plot(x, B[:, i], 'b', alpha=i / n_target)
pl.plot(x, B[:, -1], 'b', label='Target distributions')
pl.title('Target distributions')
pl.tight_layout()
##############################################################################
# Compute EMD for the different losses
# ------------------------------------
#%% Compute and plot distributions and loss matrix
d_emd = ot.emd2(a, B, M) # direct computation of OT loss
d_emd2 = ot.emd2(a, B, M2) # direct computation of OT loss with metrixc M2
d_tv = [np.sum(abs(a - B[:, i])) for i in range(n_target)]
pl.figure(2)
pl.subplot(2, 1, 1)
pl.plot(x, a, 'r', label='Source distribution')
pl.title('Distributions')
for i in range(n_target):
pl.plot(x, B[:, i], 'b', alpha=i / n_target)
pl.plot(x, B[:, -1], 'b', label='Target distributions')
pl.ylim((-.01, 0.13))
pl.xticks(())
pl.legend()
pl.subplot(2, 1, 2)
pl.plot(d_emd, label='Euclidean OT')
pl.plot(d_emd2, label='Squared Euclidean OT')
pl.plot(d_tv, label='Total Variation (TV)')
#pl.xlim((-7,23))
pl.xlabel('Displacement')
pl.title('Divergences')
pl.legend()
##############################################################################
# Compute Sinkhorn for the different losses
# -----------------------------------------
#%%
reg = 1e-1
d_sinkhorn = ot.sinkhorn2(a, B, M, reg)
d_sinkhorn2 = ot.sinkhorn2(a, B, M2, reg)
pl.figure(3)
pl.clf()
pl.subplot(2, 1, 1)
pl.plot(x, a, 'r', label='Source distribution')
pl.title('Distributions')
for i in range(n_target):
pl.plot(x, B[:, i], 'b', alpha=i / n_target)
pl.plot(x, B[:, -1], 'b', label='Target distributions')
pl.ylim((-.01, 0.13))
pl.xticks(())
pl.legend()
pl.subplot(2, 1, 2)
pl.plot(d_emd, label='Euclidean OT')
pl.plot(d_emd2, label='Squared Euclidean OT')
pl.plot(d_sinkhorn, '+', label='Euclidean Sinkhorn')
pl.plot(d_sinkhorn2, '+', label='Squared Euclidean Sinkhorn')
pl.plot(d_tv, label='Total Variation (TV)')
#pl.xlim((-7,23))
pl.xlabel('Displacement')
pl.title('Divergences')
pl.legend()
pl.show()