Dictionary Learning¶
This example demonstrates the use of class
bpdndl.BPDNDictLearn for learning a dictionary (standard,
not convolutional) from a set of training images.
from __future__ import division, print_function
from builtins import input
import numpy as np
from sporco.dictlrn import bpdndl
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 = bpdndl.BPDNDictLearn.Options({'Verbose': True, 'MaxMainIter': 100,
'BPDN': {'rho': 10.0*lmbda + 0.1},
'CMOD': {'rho': S.shape[1] / 1e3}})
Create solver object and solve.
d = bpdndl.BPDNDictLearn(D0, S, lmbda, opt)
d.solve()
print("BPDNDictLearn solve time: %.2fs" % d.timer.elapsed('solve'))
Itn Fnc DFid ℓ1 Cnstr r_X s_X ρ_X r_D s_D ρ_D
--------------------------------------------------------------------------------------------------------
0 2.89e+04 2.00e+04 8.85e+04 4.46e+00 6.01e-01 6.06e-01 1.10e+00 3.07e-01 5.71e-01 7.32e+01
1 2.03e+04 6.75e+03 1.35e+05 2.79e-01 3.45e-01 4.31e-01 1.10e+00 2.84e-02 1.59e-01 7.32e+01
2 1.91e+04 6.44e+03 1.27e+05 4.85e-01 2.13e-01 2.20e-01 1.10e+00 4.22e-02 8.63e-02 7.32e+01
3 1.86e+04 6.64e+03 1.19e+05 5.38e-01 1.54e-01 1.53e-01 1.10e+00 4.66e-02 7.08e-02 7.32e+01
4 1.82e+04 6.39e+03 1.18e+05 3.55e-01 1.15e-01 1.17e-01 1.10e+00 3.19e-02 6.00e-02 7.32e+01
5 1.80e+04 6.38e+03 1.16e+05 3.10e-01 9.63e-02 1.03e-01 1.10e+00 2.85e-02 5.55e-02 7.32e+01
6 1.78e+04 6.36e+03 1.14e+05 2.79e-01 8.15e-02 9.59e-02 1.10e+00 2.61e-02 5.23e-02 7.32e+01
7 1.76e+04 6.32e+03 1.13e+05 2.51e-01 7.35e-02 9.15e-02 1.10e+00 2.38e-02 4.99e-02 7.32e+01
8 1.75e+04 6.27e+03 1.12e+05 2.25e-01 6.62e-02 8.84e-02 1.10e+00 2.17e-02 4.78e-02 7.32e+01
9 1.74e+04 6.22e+03 1.11e+05 2.07e-01 6.19e-02 8.58e-02 1.10e+00 2.01e-02 4.58e-02 7.32e+01
10 1.72e+04 6.17e+03 1.11e+05 1.89e-01 5.77e-02 8.33e-02 1.10e+00 1.85e-02 4.38e-02 7.32e+01
11 1.71e+04 6.12e+03 1.10e+05 1.73e-01 5.48e-02 8.09e-02 1.10e+00 1.71e-02 4.19e-02 7.32e+01
12 1.70e+04 6.06e+03 1.09e+05 1.58e-01 5.18e-02 7.85e-02 1.10e+00 1.57e-02 4.02e-02 7.32e+01
13 1.69e+04 6.01e+03 1.09e+05 1.44e-01 4.95e-02 7.61e-02 1.10e+00 1.45e-02 3.84e-02 7.32e+01
14 1.68e+04 5.96e+03 1.09e+05 1.32e-01 4.72e-02 7.36e-02 1.10e+00 1.33e-02 3.68e-02 7.32e+01
15 1.67e+04 5.91e+03 1.08e+05 1.22e-01 4.52e-02 7.12e-02 1.10e+00 1.23e-02 3.53e-02 7.32e+01
16 1.66e+04 5.86e+03 1.08e+05 1.12e-01 4.32e-02 6.88e-02 1.10e+00 1.14e-02 3.38e-02 7.32e+01
17 1.66e+04 5.81e+03 1.08e+05 1.03e-01 4.14e-02 6.64e-02 1.10e+00 1.06e-02 3.24e-02 7.32e+01
18 1.65e+04 5.77e+03 1.07e+05 9.45e-02 3.96e-02 6.41e-02 1.10e+00 9.77e-03 3.10e-02 7.32e+01
19 1.65e+04 5.72e+03 1.07e+05 8.70e-02 3.79e-02 6.18e-02 1.10e+00 9.07e-03 2.96e-02 7.32e+01
20 1.64e+04 5.68e+03 1.07e+05 8.00e-02 3.62e-02 5.94e-02 1.10e+00 8.41e-03 2.83e-02 7.32e+01
21 1.63e+04 5.64e+03 1.07e+05 7.37e-02 3.46e-02 5.70e-02 1.10e+00 7.82e-03 2.70e-02 7.32e+01
22 1.63e+04 5.61e+03 1.07e+05 6.75e-02 3.30e-02 5.48e-02 1.10e+00 7.25e-03 2.57e-02 7.32e+01
23 1.63e+04 5.57e+03 1.07e+05 6.25e-02 3.15e-02 5.26e-02 1.10e+00 6.77e-03 2.45e-02 7.32e+01
24 1.62e+04 5.54e+03 1.07e+05 5.83e-02 3.01e-02 5.05e-02 1.10e+00 6.37e-03 2.34e-02 7.32e+01
25 1.62e+04 5.52e+03 1.07e+05 5.46e-02 2.87e-02 4.85e-02 1.10e+00 6.00e-03 2.22e-02 7.32e+01
26 1.61e+04 5.49e+03 1.07e+05 5.19e-02 2.75e-02 4.66e-02 1.10e+00 5.71e-03 2.11e-02 7.32e+01
27 1.61e+04 5.47e+03 1.06e+05 5.01e-02 2.63e-02 4.48e-02 1.10e+00 5.50e-03 2.01e-02 7.32e+01
28 1.61e+04 5.45e+03 1.06e+05 4.88e-02 2.51e-02 4.31e-02 1.10e+00 5.32e-03 1.91e-02 7.32e+01
29 1.61e+04 5.43e+03 1.06e+05 4.74e-02 2.40e-02 4.14e-02 1.10e+00 5.14e-03 1.81e-02 7.32e+01
30 1.60e+04 5.42e+03 1.06e+05 4.66e-02 2.29e-02 3.98e-02 1.10e+00 5.00e-03 1.71e-02 7.32e+01
31 1.60e+04 5.40e+03 1.06e+05 4.59e-02 2.19e-02 3.82e-02 1.10e+00 4.88e-03 1.62e-02 7.32e+01
32 1.60e+04 5.39e+03 1.06e+05 4.52e-02 2.09e-02 3.66e-02 1.10e+00 4.78e-03 1.53e-02 7.32e+01
33 1.60e+04 5.37e+03 1.06e+05 4.45e-02 1.99e-02 3.50e-02 1.10e+00 4.67e-03 1.45e-02 7.32e+01
34 1.60e+04 5.36e+03 1.06e+05 4.37e-02 1.89e-02 3.36e-02 1.10e+00 4.56e-03 1.37e-02 7.32e+01
35 1.59e+04 5.35e+03 1.06e+05 4.29e-02 1.81e-02 3.22e-02 1.10e+00 4.45e-03 1.31e-02 7.32e+01
36 1.59e+04 5.34e+03 1.06e+05 4.19e-02 1.73e-02 3.10e-02 1.10e+00 4.34e-03 1.26e-02 7.32e+01
37 1.59e+04 5.33e+03 1.06e+05 4.11e-02 1.66e-02 2.98e-02 1.10e+00 4.23e-03 1.21e-02 7.32e+01
38 1.59e+04 5.32e+03 1.06e+05 4.02e-02 1.60e-02 2.88e-02 1.10e+00 4.13e-03 1.17e-02 7.32e+01
39 1.59e+04 5.31e+03 1.06e+05 3.96e-02 1.54e-02 2.78e-02 1.10e+00 4.05e-03 1.13e-02 7.32e+01
40 1.59e+04 5.31e+03 1.06e+05 3.89e-02 1.48e-02 2.69e-02 1.10e+00 3.96e-03 1.09e-02 7.32e+01
41 1.59e+04 5.30e+03 1.06e+05 3.81e-02 1.43e-02 2.60e-02 1.10e+00 3.86e-03 1.05e-02 7.32e+01
42 1.59e+04 5.29e+03 1.06e+05 3.73e-02 1.38e-02 2.52e-02 1.10e+00 3.76e-03 1.01e-02 7.32e+01
43 1.59e+04 5.29e+03 1.06e+05 3.63e-02 1.34e-02 2.44e-02 1.10e+00 3.66e-03 9.75e-03 7.32e+01
44 1.59e+04 5.28e+03 1.06e+05 3.54e-02 1.29e-02 2.36e-02 1.10e+00 3.55e-03 9.40e-03 7.32e+01
45 1.58e+04 5.28e+03 1.06e+05 3.44e-02 1.25e-02 2.29e-02 1.10e+00 3.45e-03 9.08e-03 7.32e+01
46 1.58e+04 5.27e+03 1.06e+05 3.34e-02 1.21e-02 2.22e-02 1.10e+00 3.35e-03 8.77e-03 7.32e+01
47 1.58e+04 5.27e+03 1.06e+05 3.24e-02 1.17e-02 2.15e-02 1.10e+00 3.24e-03 8.48e-03 7.32e+01
48 1.58e+04 5.26e+03 1.06e+05 3.14e-02 1.13e-02 2.09e-02 1.10e+00 3.15e-03 8.20e-03 7.32e+01
49 1.58e+04 5.26e+03 1.06e+05 3.05e-02 1.09e-02 2.03e-02 1.10e+00 3.06e-03 7.95e-03 7.32e+01
50 1.58e+04 5.25e+03 1.06e+05 2.96e-02 1.06e-02 1.98e-02 1.10e+00 2.97e-03 7.71e-03 7.32e+01
51 1.58e+04 5.25e+03 1.06e+05 2.87e-02 1.03e-02 1.92e-02 1.10e+00 2.88e-03 7.48e-03 7.32e+01
52 1.58e+04 5.25e+03 1.06e+05 2.78e-02 1.00e-02 1.87e-02 1.10e+00 2.79e-03 7.27e-03 7.32e+01
53 1.58e+04 5.24e+03 1.06e+05 2.69e-02 9.72e-03 1.82e-02 1.10e+00 2.70e-03 7.07e-03 7.32e+01
54 1.58e+04 5.24e+03 1.06e+05 2.60e-02 9.46e-03 1.78e-02 1.10e+00 2.62e-03 6.89e-03 7.32e+01
55 1.58e+04 5.24e+03 1.06e+05 2.52e-02 9.22e-03 1.74e-02 1.10e+00 2.54e-03 6.72e-03 7.32e+01
56 1.58e+04 5.23e+03 1.06e+05 2.44e-02 8.99e-03 1.69e-02 1.10e+00 2.47e-03 6.56e-03 7.32e+01
57 1.58e+04 5.23e+03 1.06e+05 2.36e-02 8.78e-03 1.66e-02 1.10e+00 2.39e-03 6.41e-03 7.32e+01
58 1.58e+04 5.23e+03 1.06e+05 2.29e-02 8.58e-03 1.62e-02 1.10e+00 2.32e-03 6.26e-03 7.32e+01
59 1.58e+04 5.23e+03 1.06e+05 2.22e-02 8.39e-03 1.59e-02 1.10e+00 2.26e-03 6.13e-03 7.32e+01
60 1.58e+04 5.22e+03 1.06e+05 2.16e-02 8.21e-03 1.56e-02 1.10e+00 2.20e-03 6.00e-03 7.32e+01
61 1.58e+04 5.22e+03 1.06e+05 2.10e-02 8.05e-03 1.53e-02 1.10e+00 2.15e-03 5.89e-03 7.32e+01
62 1.58e+04 5.22e+03 1.05e+05 2.04e-02 7.90e-03 1.51e-02 1.10e+00 2.09e-03 5.79e-03 7.32e+01
63 1.58e+04 5.22e+03 1.05e+05 1.98e-02 7.76e-03 1.48e-02 1.10e+00 2.04e-03 5.68e-03 7.32e+01
64 1.58e+04 5.21e+03 1.05e+05 1.93e-02 7.62e-03 1.46e-02 1.10e+00 1.99e-03 5.58e-03 7.32e+01
65 1.58e+04 5.21e+03 1.05e+05 1.88e-02 7.49e-03 1.43e-02 1.10e+00 1.95e-03 5.49e-03 7.32e+01
66 1.58e+04 5.21e+03 1.05e+05 1.82e-02 7.37e-03 1.41e-02 1.10e+00 1.90e-03 5.40e-03 7.32e+01
67 1.58e+04 5.21e+03 1.05e+05 1.78e-02 7.25e-03 1.39e-02 1.10e+00 1.86e-03 5.31e-03 7.32e+01
68 1.58e+04 5.21e+03 1.05e+05 1.73e-02 7.14e-03 1.37e-02 1.10e+00 1.82e-03 5.23e-03 7.32e+01
69 1.57e+04 5.21e+03 1.05e+05 1.69e-02 7.03e-03 1.35e-02 1.10e+00 1.78e-03 5.14e-03 7.32e+01
70 1.57e+04 5.20e+03 1.05e+05 1.65e-02 6.93e-03 1.33e-02 1.10e+00 1.75e-03 5.06e-03 7.32e+01
71 1.57e+04 5.20e+03 1.05e+05 1.61e-02 6.83e-03 1.31e-02 1.10e+00 1.71e-03 4.99e-03 7.32e+01
72 1.57e+04 5.20e+03 1.05e+05 1.58e-02 6.73e-03 1.30e-02 1.10e+00 1.68e-03 4.92e-03 7.32e+01
73 1.57e+04 5.20e+03 1.05e+05 1.54e-02 6.64e-03 1.28e-02 1.10e+00 1.65e-03 4.85e-03 7.32e+01
74 1.57e+04 5.20e+03 1.05e+05 1.51e-02 6.56e-03 1.27e-02 1.10e+00 1.62e-03 4.79e-03 7.32e+01
75 1.57e+04 5.20e+03 1.05e+05 1.48e-02 6.48e-03 1.25e-02 1.10e+00 1.60e-03 4.73e-03 7.32e+01
76 1.57e+04 5.20e+03 1.05e+05 1.45e-02 6.40e-03 1.24e-02 1.10e+00 1.58e-03 4.67e-03 7.32e+01
77 1.57e+04 5.19e+03 1.05e+05 1.43e-02 6.33e-03 1.22e-02 1.10e+00 1.55e-03 4.61e-03 7.32e+01
78 1.57e+04 5.19e+03 1.05e+05 1.40e-02 6.26e-03 1.21e-02 1.10e+00 1.53e-03 4.56e-03 7.32e+01
79 1.57e+04 5.19e+03 1.05e+05 1.38e-02 6.19e-03 1.20e-02 1.10e+00 1.51e-03 4.51e-03 7.32e+01
80 1.57e+04 5.19e+03 1.05e+05 1.36e-02 6.12e-03 1.18e-02 1.10e+00 1.49e-03 4.46e-03 7.32e+01
81 1.57e+04 5.19e+03 1.05e+05 1.34e-02 6.05e-03 1.17e-02 1.10e+00 1.47e-03 4.41e-03 7.32e+01
82 1.57e+04 5.19e+03 1.05e+05 1.32e-02 5.99e-03 1.16e-02 1.10e+00 1.46e-03 4.37e-03 7.32e+01
83 1.57e+04 5.19e+03 1.05e+05 1.30e-02 5.93e-03 1.15e-02 1.10e+00 1.44e-03 4.33e-03 7.32e+01
84 1.57e+04 5.18e+03 1.05e+05 1.29e-02 5.87e-03 1.14e-02 1.10e+00 1.43e-03 4.29e-03 7.32e+01
85 1.57e+04 5.18e+03 1.05e+05 1.27e-02 5.82e-03 1.13e-02 1.10e+00 1.41e-03 4.26e-03 7.32e+01
86 1.57e+04 5.18e+03 1.05e+05 1.26e-02 5.77e-03 1.12e-02 1.10e+00 1.40e-03 4.23e-03 7.32e+01
87 1.57e+04 5.18e+03 1.05e+05 1.24e-02 5.71e-03 1.11e-02 1.10e+00 1.39e-03 4.19e-03 7.32e+01
88 1.57e+04 5.18e+03 1.05e+05 1.23e-02 5.66e-03 1.10e-02 1.10e+00 1.37e-03 4.16e-03 7.32e+01
89 1.57e+04 5.18e+03 1.05e+05 1.22e-02 5.61e-03 1.09e-02 1.10e+00 1.36e-03 4.13e-03 7.32e+01
90 1.57e+04 5.18e+03 1.05e+05 1.21e-02 5.57e-03 1.08e-02 1.10e+00 1.35e-03 4.09e-03 7.32e+01
91 1.57e+04 5.18e+03 1.05e+05 1.19e-02 5.52e-03 1.07e-02 1.10e+00 1.34e-03 4.06e-03 7.32e+01
92 1.57e+04 5.18e+03 1.05e+05 1.18e-02 5.47e-03 1.06e-02 1.10e+00 1.33e-03 4.03e-03 7.32e+01
93 1.57e+04 5.17e+03 1.05e+05 1.17e-02 5.42e-03 1.05e-02 1.10e+00 1.31e-03 4.00e-03 7.32e+01
94 1.57e+04 5.17e+03 1.05e+05 1.15e-02 5.37e-03 1.05e-02 1.10e+00 1.30e-03 3.98e-03 7.32e+01
95 1.57e+04 5.17e+03 1.05e+05 1.14e-02 5.33e-03 1.04e-02 1.10e+00 1.29e-03 3.95e-03 7.32e+01
96 1.57e+04 5.17e+03 1.05e+05 1.13e-02 5.28e-03 1.03e-02 1.10e+00 1.28e-03 3.92e-03 7.32e+01
97 1.57e+04 5.17e+03 1.05e+05 1.11e-02 5.24e-03 1.02e-02 1.10e+00 1.26e-03 3.89e-03 7.32e+01
98 1.57e+04 5.17e+03 1.05e+05 1.10e-02 5.19e-03 1.01e-02 1.10e+00 1.25e-03 3.86e-03 7.32e+01
99 1.57e+04 5.17e+03 1.05e+05 1.08e-02 5.14e-03 1.00e-02 1.10e+00 1.23e-03 3.83e-03 7.32e+01
--------------------------------------------------------------------------------------------------------
BPDNDictLearn solve time: 44.22s
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, ADMM primary and dual residuals, and automatically adjusted ADMM penalty parameter against the iteration number.
its = d.getitstat()
fig = plot.figure(figsize=(20, 5))
plot.subplot(1, 3, 1)
plot.plot(its.ObjFun, xlbl='Iterations', ylbl='Functional', fig=fig)
plot.subplot(1, 3, 2)
plot.plot(np.vstack((its.XPrRsdl, its.XDlRsdl, its.DPrRsdl,
its.DDlRsdl)).T, ptyp='semilogy', xlbl='Iterations',
ylbl='Residual', lgnd=['X Primal', 'X Dual', 'D Primal', 'D Dual'],
fig=fig)
plot.subplot(1, 3, 3)
plot.plot(np.vstack((its.XRho, its.DRho)).T, xlbl='Iterations',
ylbl='Penalty Parameter', ptyp='semilogy',
lgnd=['$\\rho_X$', '$\\rho_D$'], fig=fig)
fig.show()
