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
|
# -*- coding: utf-8 -*-
"""
===============================================
OT mapping estimation for domain adaptation [8]
===============================================
[8] M. Perrot, N. Courty, R. Flamary, A. Habrard,
"Mapping estimation for discrete optimal transport",
Neural Information Processing Systems (NIPS), 2016.
"""
import numpy as np
import matplotlib.pylab as pl
import ot
#%% dataset generation
np.random.seed(0) # makes example reproducible
n = 100 # nb samples in source and target datasets
theta = 2 * np.pi / 20
nz = 0.1
xs, ys = ot.datasets.get_data_classif('gaussrot', n, nz=nz)
xt, yt = ot.datasets.get_data_classif('gaussrot', n, theta=theta, nz=nz)
# one of the target mode changes its variance (no linear mapping)
xt[yt == 2] *= 3
xt = xt + 4
#%% plot samples
pl.figure(1, (6.4, 3))
pl.clf()
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.legend(loc=0)
pl.title('Source and target distributions')
#%% OT linear mapping estimation
eta = 1e-8 # quadratic regularization for regression
mu = 1e0 # weight of the OT linear term
bias = True # estimate a bias
ot_mapping = ot.da.OTDA_mapping_linear()
ot_mapping.fit(xs, xt, mu=mu, eta=eta, bias=bias, numItermax=20, verbose=True)
xst = ot_mapping.predict(xs) # use the estimated mapping
xst0 = ot_mapping.interp() # use barycentric mapping
pl.figure(2)
pl.clf()
pl.subplot(2, 2, 1)
pl.scatter(xt[:, 0], xt[:, 1], c=yt, marker='o',
label='Target samples', alpha=.3)
pl.scatter(xst0[:, 0], xst0[:, 1], c=ys,
marker='+', label='barycentric mapping')
pl.title("barycentric mapping")
pl.subplot(2, 2, 2)
pl.scatter(xt[:, 0], xt[:, 1], c=yt, marker='o',
label='Target samples', alpha=.3)
pl.scatter(xst[:, 0], xst[:, 1], c=ys, marker='+', label='Learned mapping')
pl.title("Learned mapping")
pl.tight_layout()
#%% Kernel mapping estimation
eta = 1e-5 # quadratic regularization for regression
mu = 1e-1 # weight of the OT linear term
bias = True # estimate a bias
sigma = 1 # sigma bandwidth fot gaussian kernel
ot_mapping_kernel = ot.da.OTDA_mapping_kernel()
ot_mapping_kernel.fit(
xs, xt, mu=mu, eta=eta, sigma=sigma, bias=bias, numItermax=10, verbose=True)
xst_kernel = ot_mapping_kernel.predict(xs) # use the estimated mapping
xst0_kernel = ot_mapping_kernel.interp() # use barycentric mapping
#%% Plotting the mapped samples
pl.figure(2)
pl.clf()
pl.subplot(2, 2, 1)
pl.scatter(xt[:, 0], xt[:, 1], c=yt, marker='o',
label='Target samples', alpha=.2)
pl.scatter(xst0[:, 0], xst0[:, 1], c=ys, marker='+',
label='Mapped source samples')
pl.title("Bary. mapping (linear)")
pl.legend(loc=0)
pl.subplot(2, 2, 2)
pl.scatter(xt[:, 0], xt[:, 1], c=yt, marker='o',
label='Target samples', alpha=.2)
pl.scatter(xst[:, 0], xst[:, 1], c=ys, marker='+', label='Learned mapping')
pl.title("Estim. mapping (linear)")
pl.subplot(2, 2, 3)
pl.scatter(xt[:, 0], xt[:, 1], c=yt, marker='o',
label='Target samples', alpha=.2)
pl.scatter(xst0_kernel[:, 0], xst0_kernel[:, 1], c=ys,
marker='+', label='barycentric mapping')
pl.title("Bary. mapping (kernel)")
pl.subplot(2, 2, 4)
pl.scatter(xt[:, 0], xt[:, 1], c=yt, marker='o',
label='Target samples', alpha=.2)
pl.scatter(xst_kernel[:, 0], xst_kernel[:, 1], c=ys,
marker='+', label='Learned mapping')
pl.title("Estim. mapping (kernel)")
pl.tight_layout()
pl.show()
|
