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
|
# -*- coding: utf-8 -*-
r"""
===================================================
Row and column alignments with CO-Optimal Transport
===================================================
This example is designed to show how to use the CO-Optimal Transport [47]_ in POT.
CO-Optimal Transport allows to calculate the distance between two **arbitrary-size**
matrices, and to align their rows and columns. In this example, we consider two
random matrices :math:`X_1` and :math:`X_2` defined by
:math:`(X_1)_{i,j} = \cos(\frac{i}{n_1} \pi) + \cos(\frac{j}{d_1} \pi) + \sigma \mathcal N(0,1)`
and :math:`(X_2)_{i,j} = \cos(\frac{i}{n_2} \pi) + \cos(\frac{j}{d_2} \pi) + \sigma \mathcal N(0,1)`.
.. [49] Redko, I., Vayer, T., Flamary, R., and Courty, N. (2020).
`CO-Optimal Transport <https://proceedings.neurips.cc/paper/2020/file/cc384c68ad503482fb24e6d1e3b512ae-Paper.pdf>`_.
Advances in Neural Information Processing Systems, 33.
"""
# Author: Remi Flamary <remi.flamary@unice.fr>
# Quang Huy Tran <quang-huy.tran@univ-ubs.fr>
# License: MIT License
from matplotlib.patches import ConnectionPatch
import matplotlib.pylab as pl
import numpy as np
from ot.coot import co_optimal_transport as coot
from ot.coot import co_optimal_transport2 as coot2
# %%
# Generating two random matrices
n1 = 20
n2 = 10
d1 = 16
d2 = 8
sigma = 0.2
X1 = (
np.cos(np.arange(n1) * np.pi / n1)[:, None] +
np.cos(np.arange(d1) * np.pi / d1)[None, :] +
sigma * np.random.randn(n1, d1)
)
X2 = (
np.cos(np.arange(n2) * np.pi / n2)[:, None] +
np.cos(np.arange(d2) * np.pi / d2)[None, :] +
sigma * np.random.randn(n2, d2)
)
# %%
# Visualizing the matrices
pl.figure(1, (8, 5))
pl.subplot(1, 2, 1)
pl.imshow(X1)
pl.title('$X_1$')
pl.subplot(1, 2, 2)
pl.imshow(X2)
pl.title("$X_2$")
pl.tight_layout()
# %%
# Visualizing the alignments of rows and columns, and calculating the CO-Optimal Transport distance
pi_sample, pi_feature, log = coot(X1, X2, log=True, verbose=True)
coot_distance = coot2(X1, X2)
print('CO-Optimal Transport distance = {:.5f}'.format(coot_distance))
fig = pl.figure(4, (9, 7))
pl.clf()
ax1 = pl.subplot(2, 2, 3)
pl.imshow(X1)
pl.xlabel('$X_1$')
ax2 = pl.subplot(2, 2, 2)
ax2.yaxis.tick_right()
pl.imshow(np.transpose(X2))
pl.title("Transpose($X_2$)")
ax2.xaxis.tick_top()
for i in range(n1):
j = np.argmax(pi_sample[i, :])
xyA = (d1 - .5, i)
xyB = (j, d2 - .5)
con = ConnectionPatch(xyA=xyA, xyB=xyB, coordsA=ax1.transData,
coordsB=ax2.transData, color="black")
fig.add_artist(con)
for i in range(d1):
j = np.argmax(pi_feature[i, :])
xyA = (i, -.5)
xyB = (-.5, j)
con = ConnectionPatch(
xyA=xyA, xyB=xyB, coordsA=ax1.transData, coordsB=ax2.transData, color="blue")
fig.add_artist(con)
|
