Dictionary Learning¶
This example demonstrates the use of class
wbpdndl.WeightedBPDNDictLearn for learning a dictionary
(standard, not convolutional) from a set of training images. The primary
purpose of this example is to demonstrate the use of a dictionary
learning class based on PGM solvers for the sparse coding and dictionary
update stages; the support for a weighted data fidelity term that is
included in wbpdndl.WeightedBPDNDictLearn is not used.
from __future__ import division, print_function
from builtins import input
import numpy as np
from sporco.dictlrn import wbpdndl
from sporco import util
from sporco import array
from sporco import plot
plot.config_notebook_plotting()
Load training images.
exim = util.ExampleImages(scaled=True, zoom=0.25, gray=True)
S1 = exim.image('barbara.png', idxexp=np.s_[10:522, 100:612])
S2 = exim.image('kodim23.png', idxexp=np.s_[:, 60:572])
S3 = exim.image('monarch.png', idxexp=np.s_[:, 160:672])
S4 = exim.image('sail.png', idxexp=np.s_[:, 210:722])
S5 = exim.image('tulips.png', idxexp=np.s_[:, 30:542])
Extract all 8x8 image blocks, reshape, and subtract block means.
S = array.extract_blocks((S1, S2, S3, S4, S5), (8, 8))
S = np.reshape(S, (np.prod(S.shape[0:2]), S.shape[2]))
S -= np.mean(S, axis=0)
Construct initial dictionary.
np.random.seed(12345)
D0 = np.random.randn(S.shape[0], 128)
Set regularization parameter and options for dictionary learning solver.
lmbda = 0.1
opt = wbpdndl.WeightedBPDNDictLearn.Options(
{'Verbose': True, 'MaxMainIter': 150,
'BPDN': {'L': 1e1}, 'CMOD': {'L': 1e3}})
Create solver object and solve.
d = wbpdndl.WeightedBPDNDictLearn(D0, S, lmbda, opt=opt)
d.solve()
print("WeightedBPDNDictLearn solve time: %.2fs" % d.timer.elapsed('solve'))
Itn Fnc DFid ℓ1 Cnstr X_Rsdl X_L D_Rsdl D_L
------------------------------------------------------------------------------------
0 3.58e+04 3.27e+04 3.17e+04 1.05e-06 2.49e+01 1.00e+01 1.27e+00 1.00e+03
1 2.97e+04 2.34e+04 6.29e+04 1.08e-06 2.39e+01 1.00e+01 1.63e+00 1.00e+03
2 2.48e+04 1.61e+04 8.66e+04 1.16e-06 1.35e+01 1.00e+01 9.11e-01 1.00e+03
3 2.23e+04 1.26e+04 9.78e+04 1.06e-06 9.39e+00 1.00e+01 6.09e-01 1.00e+03
4 2.09e+04 1.04e+04 1.05e+05 1.10e-06 6.20e+00 1.00e+01 3.83e-01 1.00e+03
5 2.00e+04 9.19e+03 1.09e+05 1.07e-06 4.95e+00 1.00e+01 2.63e-01 1.00e+03
6 1.95e+04 8.46e+03 1.10e+05 1.05e-06 4.13e+00 1.00e+01 1.86e-01 1.00e+03
7 1.91e+04 8.00e+03 1.11e+05 1.12e-06 3.56e+00 1.00e+01 1.37e-01 1.00e+03
8 1.89e+04 7.70e+03 1.12e+05 1.06e-06 3.12e+00 1.00e+01 1.06e-01 1.00e+03
9 1.87e+04 7.49e+03 1.12e+05 1.09e-06 2.78e+00 1.00e+01 8.52e-02 1.00e+03
10 1.85e+04 7.34e+03 1.12e+05 1.11e-06 2.50e+00 1.00e+01 6.98e-02 1.00e+03
11 1.84e+04 7.22e+03 1.12e+05 1.11e-06 2.26e+00 1.00e+01 5.83e-02 1.00e+03
12 1.83e+04 7.13e+03 1.12e+05 1.12e-06 2.07e+00 1.00e+01 4.92e-02 1.00e+03
13 1.82e+04 7.06e+03 1.11e+05 1.05e-06 1.91e+00 1.00e+01 4.22e-02 1.00e+03
14 1.81e+04 7.01e+03 1.11e+05 1.20e-06 1.77e+00 1.00e+01 3.68e-02 1.00e+03
15 1.81e+04 6.96e+03 1.11e+05 1.12e-06 1.65e+00 1.00e+01 3.26e-02 1.00e+03
16 1.80e+04 6.93e+03 1.11e+05 1.07e-06 1.56e+00 1.00e+01 2.93e-02 1.00e+03
17 1.80e+04 6.90e+03 1.11e+05 1.04e-06 1.47e+00 1.00e+01 2.67e-02 1.00e+03
18 1.79e+04 6.88e+03 1.10e+05 1.01e-06 1.40e+00 1.00e+01 2.47e-02 1.00e+03
19 1.79e+04 6.86e+03 1.10e+05 1.01e-06 1.33e+00 1.00e+01 2.34e-02 1.00e+03
20 1.78e+04 6.84e+03 1.10e+05 1.06e-06 1.27e+00 1.00e+01 2.25e-02 1.00e+03
21 1.78e+04 6.83e+03 1.09e+05 9.06e-07 1.22e+00 1.00e+01 2.19e-02 1.00e+03
22 1.77e+04 6.82e+03 1.09e+05 1.14e-06 1.18e+00 1.00e+01 2.15e-02 1.00e+03
23 1.77e+04 6.80e+03 1.09e+05 1.00e-06 1.14e+00 1.00e+01 2.11e-02 1.00e+03
24 1.77e+04 6.79e+03 1.09e+05 1.06e-06 1.11e+00 1.00e+01 2.06e-02 1.00e+03
25 1.76e+04 6.77e+03 1.09e+05 1.04e-06 1.08e+00 1.00e+01 2.02e-02 1.00e+03
26 1.76e+04 6.76e+03 1.08e+05 1.23e-06 1.06e+00 1.00e+01 1.96e-02 1.00e+03
27 1.76e+04 6.74e+03 1.08e+05 1.05e-06 1.04e+00 1.00e+01 1.92e-02 1.00e+03
28 1.75e+04 6.73e+03 1.08e+05 1.17e-06 1.02e+00 1.00e+01 1.88e-02 1.00e+03
29 1.75e+04 6.71e+03 1.08e+05 1.05e-06 1.01e+00 1.00e+01 1.84e-02 1.00e+03
30 1.75e+04 6.69e+03 1.08e+05 9.84e-07 9.99e-01 1.00e+01 1.81e-02 1.00e+03
31 1.74e+04 6.68e+03 1.07e+05 9.69e-07 9.91e-01 1.00e+01 1.79e-02 1.00e+03
32 1.74e+04 6.66e+03 1.07e+05 1.02e-06 9.85e-01 1.00e+01 1.76e-02 1.00e+03
33 1.74e+04 6.64e+03 1.07e+05 1.15e-06 9.82e-01 1.00e+01 1.73e-02 1.00e+03
34 1.73e+04 6.62e+03 1.07e+05 1.00e-06 9.76e-01 1.00e+01 1.71e-02 1.00e+03
35 1.73e+04 6.60e+03 1.07e+05 1.12e-06 9.68e-01 1.00e+01 1.69e-02 1.00e+03
36 1.73e+04 6.58e+03 1.07e+05 1.08e-06 9.66e-01 1.00e+01 1.66e-02 1.00e+03
37 1.72e+04 6.56e+03 1.07e+05 1.08e-06 9.66e-01 1.00e+01 1.64e-02 1.00e+03
38 1.72e+04 6.54e+03 1.07e+05 9.57e-07 9.70e-01 1.00e+01 1.61e-02 1.00e+03
39 1.72e+04 6.51e+03 1.06e+05 1.13e-06 9.69e-01 1.00e+01 1.59e-02 1.00e+03
40 1.71e+04 6.49e+03 1.06e+05 1.08e-06 9.64e-01 1.00e+01 1.57e-02 1.00e+03
41 1.71e+04 6.47e+03 1.06e+05 1.12e-06 9.71e-01 1.00e+01 1.55e-02 1.00e+03
42 1.71e+04 6.45e+03 1.06e+05 1.01e-06 9.64e-01 1.00e+01 1.53e-02 1.00e+03
43 1.70e+04 6.42e+03 1.06e+05 1.06e-06 9.79e-01 1.00e+01 1.50e-02 1.00e+03
44 1.70e+04 6.40e+03 1.06e+05 1.10e-06 9.70e-01 1.00e+01 1.48e-02 1.00e+03
45 1.70e+04 6.38e+03 1.06e+05 1.09e-06 9.75e-01 1.00e+01 1.45e-02 1.00e+03
46 1.70e+04 6.35e+03 1.06e+05 1.03e-06 9.73e-01 1.00e+01 1.42e-02 1.00e+03
47 1.69e+04 6.33e+03 1.06e+05 1.11e-06 9.70e-01 1.00e+01 1.41e-02 1.00e+03
48 1.69e+04 6.30e+03 1.06e+05 9.67e-07 9.74e-01 1.00e+01 1.39e-02 1.00e+03
49 1.69e+04 6.28e+03 1.06e+05 1.18e-06 9.67e-01 1.00e+01 1.38e-02 1.00e+03
50 1.68e+04 6.26e+03 1.06e+05 1.01e-06 9.71e-01 1.00e+01 1.36e-02 1.00e+03
51 1.68e+04 6.23e+03 1.06e+05 1.10e-06 9.67e-01 1.00e+01 1.35e-02 1.00e+03
52 1.68e+04 6.21e+03 1.06e+05 1.00e-06 9.63e-01 1.00e+01 1.33e-02 1.00e+03
53 1.68e+04 6.19e+03 1.06e+05 1.17e-06 9.63e-01 1.00e+01 1.32e-02 1.00e+03
54 1.67e+04 6.16e+03 1.06e+05 1.11e-06 9.57e-01 1.00e+01 1.31e-02 1.00e+03
55 1.67e+04 6.14e+03 1.06e+05 1.13e-06 9.56e-01 1.00e+01 1.29e-02 1.00e+03
56 1.67e+04 6.12e+03 1.06e+05 9.79e-07 9.51e-01 1.00e+01 1.27e-02 1.00e+03
57 1.67e+04 6.09e+03 1.06e+05 1.14e-06 9.49e-01 1.00e+01 1.26e-02 1.00e+03
58 1.66e+04 6.07e+03 1.06e+05 1.06e-06 9.43e-01 1.00e+01 1.24e-02 1.00e+03
59 1.66e+04 6.05e+03 1.06e+05 1.17e-06 9.38e-01 1.00e+01 1.23e-02 1.00e+03
60 1.66e+04 6.02e+03 1.06e+05 1.15e-06 9.38e-01 1.00e+01 1.21e-02 1.00e+03
61 1.66e+04 6.00e+03 1.06e+05 9.97e-07 9.32e-01 1.00e+01 1.20e-02 1.00e+03
62 1.65e+04 5.98e+03 1.06e+05 1.17e-06 9.27e-01 1.00e+01 1.18e-02 1.00e+03
63 1.65e+04 5.96e+03 1.06e+05 1.14e-06 9.24e-01 1.00e+01 1.17e-02 1.00e+03
64 1.65e+04 5.93e+03 1.06e+05 1.08e-06 9.16e-01 1.00e+01 1.15e-02 1.00e+03
65 1.65e+04 5.91e+03 1.06e+05 1.08e-06 9.09e-01 1.00e+01 1.14e-02 1.00e+03
66 1.65e+04 5.89e+03 1.06e+05 1.11e-06 9.05e-01 1.00e+01 1.13e-02 1.00e+03
67 1.64e+04 5.87e+03 1.06e+05 1.09e-06 8.93e-01 1.00e+01 1.12e-02 1.00e+03
68 1.64e+04 5.85e+03 1.06e+05 1.09e-06 8.89e-01 1.00e+01 1.11e-02 1.00e+03
69 1.64e+04 5.83e+03 1.06e+05 1.03e-06 8.85e-01 1.00e+01 1.10e-02 1.00e+03
70 1.64e+04 5.81e+03 1.06e+05 1.16e-06 8.78e-01 1.00e+01 1.09e-02 1.00e+03
71 1.64e+04 5.79e+03 1.06e+05 1.09e-06 8.76e-01 1.00e+01 1.09e-02 1.00e+03
72 1.64e+04 5.77e+03 1.06e+05 1.14e-06 8.65e-01 1.00e+01 1.08e-02 1.00e+03
73 1.63e+04 5.76e+03 1.06e+05 1.04e-06 8.61e-01 1.00e+01 1.08e-02 1.00e+03
74 1.63e+04 5.74e+03 1.06e+05 1.01e-06 8.47e-01 1.00e+01 1.07e-02 1.00e+03
75 1.63e+04 5.72e+03 1.06e+05 1.24e-06 8.45e-01 1.00e+01 1.07e-02 1.00e+03
76 1.63e+04 5.70e+03 1.06e+05 1.03e-06 8.44e-01 1.00e+01 1.06e-02 1.00e+03
77 1.63e+04 5.69e+03 1.06e+05 1.13e-06 8.30e-01 1.00e+01 1.05e-02 1.00e+03
78 1.63e+04 5.67e+03 1.06e+05 1.07e-06 8.28e-01 1.00e+01 1.04e-02 1.00e+03
79 1.62e+04 5.65e+03 1.06e+05 1.15e-06 8.22e-01 1.00e+01 1.03e-02 1.00e+03
80 1.62e+04 5.64e+03 1.06e+05 1.03e-06 8.16e-01 1.00e+01 1.03e-02 1.00e+03
81 1.62e+04 5.62e+03 1.06e+05 1.15e-06 8.10e-01 1.00e+01 1.02e-02 1.00e+03
82 1.62e+04 5.61e+03 1.06e+05 1.12e-06 8.00e-01 1.00e+01 1.01e-02 1.00e+03
83 1.62e+04 5.60e+03 1.06e+05 1.03e-06 7.86e-01 1.00e+01 1.00e-02 1.00e+03
84 1.62e+04 5.58e+03 1.06e+05 1.10e-06 7.87e-01 1.00e+01 9.87e-03 1.00e+03
85 1.62e+04 5.57e+03 1.06e+05 1.13e-06 7.79e-01 1.00e+01 9.72e-03 1.00e+03
86 1.61e+04 5.56e+03 1.06e+05 9.68e-07 7.74e-01 1.00e+01 9.55e-03 1.00e+03
87 1.61e+04 5.54e+03 1.06e+05 1.25e-06 7.62e-01 1.00e+01 9.39e-03 1.00e+03
88 1.61e+04 5.53e+03 1.06e+05 1.14e-06 7.54e-01 1.00e+01 9.22e-03 1.00e+03
89 1.61e+04 5.52e+03 1.06e+05 1.11e-06 7.46e-01 1.00e+01 9.06e-03 1.00e+03
90 1.61e+04 5.51e+03 1.06e+05 1.24e-06 7.40e-01 1.00e+01 8.91e-03 1.00e+03
91 1.61e+04 5.50e+03 1.06e+05 1.11e-06 7.30e-01 1.00e+01 8.76e-03 1.00e+03
92 1.61e+04 5.49e+03 1.06e+05 1.22e-06 7.22e-01 1.00e+01 8.61e-03 1.00e+03
93 1.61e+04 5.48e+03 1.06e+05 1.19e-06 7.12e-01 1.00e+01 8.45e-03 1.00e+03
94 1.60e+04 5.47e+03 1.06e+05 1.06e-06 7.08e-01 1.00e+01 8.30e-03 1.00e+03
95 1.60e+04 5.46e+03 1.06e+05 1.04e-06 7.03e-01 1.00e+01 8.14e-03 1.00e+03
96 1.60e+04 5.45e+03 1.06e+05 1.06e-06 6.89e-01 1.00e+01 8.00e-03 1.00e+03
97 1.60e+04 5.44e+03 1.06e+05 1.14e-06 6.87e-01 1.00e+01 7.84e-03 1.00e+03
98 1.60e+04 5.43e+03 1.06e+05 1.08e-06 6.79e-01 1.00e+01 7.67e-03 1.00e+03
99 1.60e+04 5.42e+03 1.06e+05 1.04e-06 6.70e-01 1.00e+01 7.49e-03 1.00e+03
100 1.60e+04 5.41e+03 1.06e+05 9.78e-07 6.57e-01 1.00e+01 7.30e-03 1.00e+03
101 1.60e+04 5.41e+03 1.06e+05 1.15e-06 6.50e-01 1.00e+01 7.11e-03 1.00e+03
102 1.60e+04 5.40e+03 1.06e+05 1.22e-06 6.48e-01 1.00e+01 6.91e-03 1.00e+03
103 1.60e+04 5.39e+03 1.06e+05 1.17e-06 6.35e-01 1.00e+01 6.71e-03 1.00e+03
104 1.60e+04 5.39e+03 1.06e+05 1.12e-06 6.24e-01 1.00e+01 6.53e-03 1.00e+03
105 1.60e+04 5.38e+03 1.06e+05 1.12e-06 6.18e-01 1.00e+01 6.35e-03 1.00e+03
106 1.59e+04 5.38e+03 1.06e+05 1.03e-06 6.08e-01 1.00e+01 6.20e-03 1.00e+03
107 1.59e+04 5.37e+03 1.06e+05 1.13e-06 5.95e-01 1.00e+01 6.05e-03 1.00e+03
108 1.59e+04 5.37e+03 1.06e+05 1.07e-06 5.89e-01 1.00e+01 5.92e-03 1.00e+03
109 1.59e+04 5.36e+03 1.06e+05 1.17e-06 5.74e-01 1.00e+01 5.79e-03 1.00e+03
110 1.59e+04 5.36e+03 1.06e+05 1.07e-06 5.71e-01 1.00e+01 5.64e-03 1.00e+03
111 1.59e+04 5.35e+03 1.06e+05 9.60e-07 5.57e-01 1.00e+01 5.48e-03 1.00e+03
112 1.59e+04 5.35e+03 1.06e+05 1.06e-06 5.56e-01 1.00e+01 5.31e-03 1.00e+03
113 1.59e+04 5.34e+03 1.06e+05 1.13e-06 5.43e-01 1.00e+01 5.16e-03 1.00e+03
114 1.59e+04 5.34e+03 1.06e+05 1.18e-06 5.35e-01 1.00e+01 5.02e-03 1.00e+03
115 1.59e+04 5.34e+03 1.06e+05 1.16e-06 5.22e-01 1.00e+01 4.91e-03 1.00e+03
116 1.59e+04 5.33e+03 1.06e+05 1.13e-06 5.16e-01 1.00e+01 4.80e-03 1.00e+03
117 1.59e+04 5.33e+03 1.06e+05 9.80e-07 5.10e-01 1.00e+01 4.70e-03 1.00e+03
118 1.59e+04 5.33e+03 1.06e+05 1.18e-06 5.04e-01 1.00e+01 4.61e-03 1.00e+03
119 1.59e+04 5.32e+03 1.06e+05 1.19e-06 4.97e-01 1.00e+01 4.52e-03 1.00e+03
120 1.59e+04 5.32e+03 1.05e+05 1.17e-06 4.88e-01 1.00e+01 4.44e-03 1.00e+03
121 1.59e+04 5.32e+03 1.05e+05 1.25e-06 4.82e-01 1.00e+01 4.35e-03 1.00e+03
122 1.59e+04 5.32e+03 1.05e+05 1.13e-06 4.69e-01 1.00e+01 4.24e-03 1.00e+03
123 1.59e+04 5.31e+03 1.05e+05 1.20e-06 4.64e-01 1.00e+01 4.15e-03 1.00e+03
124 1.59e+04 5.31e+03 1.05e+05 1.08e-06 4.62e-01 1.00e+01 4.06e-03 1.00e+03
125 1.59e+04 5.31e+03 1.05e+05 1.14e-06 4.57e-01 1.00e+01 3.98e-03 1.00e+03
126 1.58e+04 5.31e+03 1.05e+05 1.15e-06 4.50e-01 1.00e+01 3.91e-03 1.00e+03
127 1.58e+04 5.30e+03 1.05e+05 1.17e-06 4.40e-01 1.00e+01 3.82e-03 1.00e+03
128 1.58e+04 5.30e+03 1.05e+05 1.12e-06 4.34e-01 1.00e+01 3.74e-03 1.00e+03
129 1.58e+04 5.30e+03 1.05e+05 1.10e-06 4.27e-01 1.00e+01 3.67e-03 1.00e+03
130 1.58e+04 5.30e+03 1.05e+05 1.11e-06 4.20e-01 1.00e+01 3.62e-03 1.00e+03
131 1.58e+04 5.29e+03 1.05e+05 1.09e-06 4.12e-01 1.00e+01 3.57e-03 1.00e+03
132 1.58e+04 5.29e+03 1.05e+05 1.25e-06 4.08e-01 1.00e+01 3.52e-03 1.00e+03
133 1.58e+04 5.29e+03 1.05e+05 1.22e-06 4.06e-01 1.00e+01 3.47e-03 1.00e+03
134 1.58e+04 5.29e+03 1.05e+05 1.12e-06 4.00e-01 1.00e+01 3.43e-03 1.00e+03
135 1.58e+04 5.28e+03 1.05e+05 1.15e-06 3.90e-01 1.00e+01 3.39e-03 1.00e+03
136 1.58e+04 5.28e+03 1.05e+05 1.16e-06 3.88e-01 1.00e+01 3.34e-03 1.00e+03
137 1.58e+04 5.28e+03 1.05e+05 1.13e-06 3.88e-01 1.00e+01 3.28e-03 1.00e+03
138 1.58e+04 5.28e+03 1.05e+05 1.16e-06 3.76e-01 1.00e+01 3.21e-03 1.00e+03
139 1.58e+04 5.28e+03 1.05e+05 1.33e-06 3.68e-01 1.00e+01 3.16e-03 1.00e+03
140 1.58e+04 5.27e+03 1.05e+05 1.06e-06 3.67e-01 1.00e+01 3.12e-03 1.00e+03
141 1.58e+04 5.27e+03 1.05e+05 1.23e-06 3.62e-01 1.00e+01 3.09e-03 1.00e+03
142 1.58e+04 5.27e+03 1.05e+05 1.10e-06 3.63e-01 1.00e+01 3.05e-03 1.00e+03
143 1.58e+04 5.27e+03 1.05e+05 1.10e-06 3.60e-01 1.00e+01 3.01e-03 1.00e+03
144 1.58e+04 5.27e+03 1.05e+05 1.13e-06 3.52e-01 1.00e+01 2.95e-03 1.00e+03
145 1.58e+04 5.26e+03 1.05e+05 1.19e-06 3.51e-01 1.00e+01 2.89e-03 1.00e+03
146 1.58e+04 5.26e+03 1.05e+05 1.23e-06 3.42e-01 1.00e+01 2.84e-03 1.00e+03
147 1.58e+04 5.26e+03 1.05e+05 1.08e-06 3.36e-01 1.00e+01 2.78e-03 1.00e+03
148 1.58e+04 5.26e+03 1.05e+05 1.22e-06 3.35e-01 1.00e+01 2.73e-03 1.00e+03
149 1.58e+04 5.26e+03 1.05e+05 9.70e-07 3.28e-01 1.00e+01 2.68e-03 1.00e+03
------------------------------------------------------------------------------------
WeightedBPDNDictLearn solve time: 56.84s
Display initial and final dictionaries.
D1 = d.getdict().reshape((8, 8, D0.shape[1]))
D0 = D0.reshape(8, 8, D0.shape[-1])
fig = plot.figure(figsize=(14, 7))
plot.subplot(1, 2, 1)
plot.imview(util.tiledict(D0), title='D0', fig=fig)
plot.subplot(1, 2, 2)
plot.imview(util.tiledict(D1), title='D1', fig=fig)
fig.show()
Get iterations statistics from solver object and plot functional value and PGM residuals.
its = d.getitstat()
fig = plot.figure(figsize=(20, 5))
plot.subplot(1, 2, 1)
plot.plot(its.ObjFun, xlbl='Iterations', ylbl='Functional', fig=fig)
plot.subplot(1, 2, 2)
plot.plot(np.vstack((its.XRsdl, its.DRsdl)).T, ptyp='semilogy',
xlbl='Iterations', ylbl='Residual', lgnd=['X', 'D'],
fig=fig)
fig.show()
