-
Notifications
You must be signed in to change notification settings - Fork 81
/
Copy pathplot_faces_decomposition.html
620 lines (574 loc) · 65.8 KB
/
plot_faces_decomposition.html
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
133
134
135
136
137
138
139
140
141
142
143
144
145
146
147
148
149
150
151
152
153
154
155
156
157
158
159
160
161
162
163
164
165
166
167
168
169
170
171
172
173
174
175
176
177
178
179
180
181
182
183
184
185
186
187
188
189
190
191
192
193
194
195
196
197
198
199
200
201
202
203
204
205
206
207
208
209
210
211
212
213
214
215
216
217
218
219
220
221
222
223
224
225
226
227
228
229
230
231
232
233
234
235
236
237
238
239
240
241
242
243
244
245
246
247
248
249
250
251
252
253
254
255
256
257
258
259
260
261
262
263
264
265
266
267
268
269
270
271
272
273
274
275
276
277
278
279
280
281
282
283
284
285
286
287
288
289
290
291
292
293
294
295
296
297
298
299
300
301
302
303
304
305
306
307
308
309
310
311
312
313
314
315
316
317
318
319
320
321
322
323
324
325
326
327
328
329
330
331
332
333
334
335
336
337
338
339
340
341
342
343
344
345
346
347
348
349
350
351
352
353
354
355
356
357
358
359
360
361
362
363
364
365
366
367
368
369
370
371
372
373
374
375
376
377
378
379
380
381
382
383
384
385
386
387
388
389
390
391
392
393
394
395
396
397
398
399
400
401
402
403
404
405
406
407
408
409
410
411
412
413
414
415
416
417
418
419
420
421
422
423
424
425
426
427
428
429
430
431
432
433
434
435
436
437
438
439
440
441
442
443
444
445
446
447
448
449
450
451
452
453
454
455
456
457
458
459
460
461
462
463
464
465
466
467
468
469
470
471
472
473
474
475
476
477
478
479
480
481
482
483
484
485
486
487
488
489
490
491
492
493
494
495
496
497
498
499
500
501
502
503
504
505
506
507
508
509
510
511
512
513
514
515
516
517
518
519
520
521
522
523
524
525
526
527
528
529
530
531
532
533
534
535
536
537
538
539
540
541
542
543
544
545
546
547
548
549
550
551
552
553
554
555
556
557
558
559
560
561
562
563
564
565
566
567
568
569
570
571
572
573
574
575
576
577
578
579
580
581
582
583
584
585
586
587
588
589
590
591
592
593
594
595
596
597
598
599
600
601
602
603
604
605
606
607
608
609
610
611
612
613
614
615
616
617
618
619
620
<!DOCTYPE html>
<!-- data-theme below is forced to be "light" but should be changed if we use pydata-theme-sphinx in the future -->
<!--[if IE 8]><html class="no-js lt-ie9" lang="en" data-content_root="../../" data-theme="light"> <![endif]-->
<!--[if gt IE 8]><!--> <html class="no-js" lang="en" data-content_root="../../" data-theme="light"> <!--<![endif]-->
<head>
<meta charset="utf-8">
<meta name="viewport" content="width=device-width, initial-scale=1" />
<meta property="og:title" content="Faces dataset decompositions" />
<meta property="og:type" content="website" />
<meta property="og:url" content="https://scikit-learn/stable/auto_examples/decomposition/plot_faces_decomposition.html" />
<meta property="og:site_name" content="scikit-learn" />
<meta property="og:description" content="This example applies to The Olivetti faces dataset different unsupervised matrix decomposition (dimension reduction) methods from the module sklearn.decomposition(see the documentation chapter Deco..." />
<meta property="og:image" content="https://scikit-learn.org/stable/_static/scikit-learn-logo-small.png" />
<meta property="og:image:alt" content="scikit-learn" />
<meta name="description" content="This example applies to The Olivetti faces dataset different unsupervised matrix decomposition (dimension reduction) methods from the module sklearn.decomposition(see the documentation chapter Deco..." />
<meta name="viewport" content="width=device-width, initial-scale=1.0">
<title>Faces dataset decompositions — scikit-learn 1.4.2 documentation</title>
<link rel="canonical" href="https://scikit-learn.org/stable/auto_examples/decomposition/plot_faces_decomposition.html" />
<link rel="shortcut icon" href="../../_static/favicon.ico"/>
<link rel="stylesheet" href="../../_static/css/vendor/bootstrap.min.css" type="text/css" />
<link rel="stylesheet" href="../../_static/pygments.css" type="text/css" />
<link rel="stylesheet" href="../../_static/css/theme.css" type="text/css" />
<link rel="stylesheet" href="../../_static/copybutton.css" type="text/css" />
<link rel="stylesheet" href="../../_static/plot_directive.css" type="text/css" />
<link rel="stylesheet" href="../../https://fonts.googleapis.com/css?family=Vibur" type="text/css" />
<link rel="stylesheet" href="../../_static/jupyterlite_sphinx.css" type="text/css" />
<link rel="stylesheet" href="../../_static/sg_gallery.css" type="text/css" />
<link rel="stylesheet" href="../../_static/sg_gallery-binder.css" type="text/css" />
<link rel="stylesheet" href="../../_static/sg_gallery-dataframe.css" type="text/css" />
<link rel="stylesheet" href="../../_static/sg_gallery-rendered-html.css" type="text/css" />
<link rel="stylesheet" href="../../_static/css/theme.css" type="text/css" />
<script id="documentation_options" data-url_root="../../" src="../../_static/documentation_options.js"></script>
<script src="../../_static/js/vendor/jquery-3.6.3.slim.min.js"></script>
<script src="../../_static/js/details-permalink.js"></script>
</head>
<body>
<nav id="navbar" class="sk-docs-navbar navbar navbar-expand-md navbar-light bg-light py-0">
<div class="container-fluid sk-docs-container px-0">
<a class="navbar-brand py-0" href="../../index.html">
<img
class="sk-brand-img"
src="../../_static/scikit-learn-logo-small.png"
alt="logo"/>
</a>
<button
id="sk-navbar-toggler"
class="navbar-toggler"
type="button"
data-toggle="collapse"
data-target="#navbarSupportedContent"
aria-controls="navbarSupportedContent"
aria-expanded="false"
aria-label="Toggle navigation"
>
<span class="navbar-toggler-icon"></span>
</button>
<div class="sk-navbar-collapse collapse navbar-collapse" id="navbarSupportedContent">
<ul class="navbar-nav mr-auto">
<li class="nav-item">
<a class="sk-nav-link nav-link" href="../../install.html">Install</a>
</li>
<li class="nav-item">
<a class="sk-nav-link nav-link" href="../../user_guide.html">User Guide</a>
</li>
<li class="nav-item">
<a class="sk-nav-link nav-link" href="../../modules/classes.html">API</a>
</li>
<li class="nav-item">
<a class="sk-nav-link nav-link" href="../index.html">Examples</a>
</li>
<li class="nav-item">
<a class="sk-nav-link nav-link" target="_blank" rel="noopener noreferrer" href="https://blog.scikit-learn.org/">Community</a>
</li>
<li class="nav-item">
<a class="sk-nav-link nav-link nav-more-item-mobile-items" href="../../getting_started.html" >Getting Started</a>
</li>
<li class="nav-item">
<a class="sk-nav-link nav-link nav-more-item-mobile-items" href="../../tutorial/index.html" >Tutorial</a>
</li>
<li class="nav-item">
<a class="sk-nav-link nav-link nav-more-item-mobile-items" href="../../whats_new/v1.4.html" >What's new</a>
</li>
<li class="nav-item">
<a class="sk-nav-link nav-link nav-more-item-mobile-items" href="../../glossary.html" >Glossary</a>
</li>
<li class="nav-item">
<a class="sk-nav-link nav-link nav-more-item-mobile-items" href="https://scikit-learn.org/dev/developers/index.html" target="_blank" rel="noopener noreferrer">Development</a>
</li>
<li class="nav-item">
<a class="sk-nav-link nav-link nav-more-item-mobile-items" href="../../faq.html" >FAQ</a>
</li>
<li class="nav-item">
<a class="sk-nav-link nav-link nav-more-item-mobile-items" href="../../support.html" >Support</a>
</li>
<li class="nav-item">
<a class="sk-nav-link nav-link nav-more-item-mobile-items" href="../../related_projects.html" >Related packages</a>
</li>
<li class="nav-item">
<a class="sk-nav-link nav-link nav-more-item-mobile-items" href="../../roadmap.html" >Roadmap</a>
</li>
<li class="nav-item">
<a class="sk-nav-link nav-link nav-more-item-mobile-items" href="../../governance.html" >Governance</a>
</li>
<li class="nav-item">
<a class="sk-nav-link nav-link nav-more-item-mobile-items" href="../../about.html" >About us</a>
</li>
<li class="nav-item">
<a class="sk-nav-link nav-link nav-more-item-mobile-items" href="https://github.com/scikit-learn/scikit-learn" >GitHub</a>
</li>
<li class="nav-item">
<a class="sk-nav-link nav-link nav-more-item-mobile-items" href="https://scikit-learn.org/dev/versions.html" >Other Versions and Download</a>
</li>
<li class="nav-item dropdown nav-more-item-dropdown">
<a class="sk-nav-link nav-link dropdown-toggle" href="#" id="navbarDropdown" role="button" data-toggle="dropdown" aria-haspopup="true" aria-expanded="false">More</a>
<div class="dropdown-menu" aria-labelledby="navbarDropdown">
<a class="sk-nav-dropdown-item dropdown-item" href="../../getting_started.html" >Getting Started</a>
<a class="sk-nav-dropdown-item dropdown-item" href="../../tutorial/index.html" >Tutorial</a>
<a class="sk-nav-dropdown-item dropdown-item" href="../../whats_new/v1.4.html" >What's new</a>
<a class="sk-nav-dropdown-item dropdown-item" href="../../glossary.html" >Glossary</a>
<a class="sk-nav-dropdown-item dropdown-item" href="https://scikit-learn.org/dev/developers/index.html" target="_blank" rel="noopener noreferrer">Development</a>
<a class="sk-nav-dropdown-item dropdown-item" href="../../faq.html" >FAQ</a>
<a class="sk-nav-dropdown-item dropdown-item" href="../../support.html" >Support</a>
<a class="sk-nav-dropdown-item dropdown-item" href="../../related_projects.html" >Related packages</a>
<a class="sk-nav-dropdown-item dropdown-item" href="../../roadmap.html" >Roadmap</a>
<a class="sk-nav-dropdown-item dropdown-item" href="../../governance.html" >Governance</a>
<a class="sk-nav-dropdown-item dropdown-item" href="../../about.html" >About us</a>
<a class="sk-nav-dropdown-item dropdown-item" href="https://github.com/scikit-learn/scikit-learn" >GitHub</a>
<a class="sk-nav-dropdown-item dropdown-item" href="https://scikit-learn.org/dev/versions.html" >Other Versions and Download</a>
</div>
</li>
</ul>
<div id="searchbox" role="search">
<div class="searchformwrapper">
<form class="search" action="../../search.html" method="get">
<input class="sk-search-text-input" type="text" name="q" aria-labelledby="searchlabel" />
<input class="sk-search-text-btn" type="submit" value="Go" />
</form>
</div>
</div>
</div>
</div>
</nav>
<div class="d-flex" id="sk-doc-wrapper">
<input type="checkbox" name="sk-toggle-checkbox" id="sk-toggle-checkbox">
<label id="sk-sidemenu-toggle" class="sk-btn-toggle-toc btn sk-btn-primary" for="sk-toggle-checkbox">Toggle Menu</label>
<div id="sk-sidebar-wrapper" class="border-right">
<div class="sk-sidebar-toc-wrapper">
<div class="btn-group w-100 mb-2" role="group" aria-label="rellinks">
<a href="plot_pca_vs_lda.html" role="button" class="btn sk-btn-rellink py-1" sk-rellink-tooltip="Comparison of LDA and PCA 2D projection of Iris dataset">Prev</a><a href="index.html" role="button" class="btn sk-btn-rellink py-1" sk-rellink-tooltip="Decomposition">Up</a>
<a href="plot_varimax_fa.html" role="button" class="btn sk-btn-rellink py-1" sk-rellink-tooltip="Factor Analysis (with rotation) to visualize patterns">Next</a>
</div>
<div class="alert alert-danger p-1 mb-2" role="alert">
<p class="text-center mb-0">
<strong>scikit-learn 1.4.2</strong><br/>
<a href="https://scikit-learn.org/dev/versions.html">Other versions</a>
</p>
</div>
<div class="alert alert-warning p-1 mb-2" role="alert">
<p class="text-center mb-0">
Please <a class="font-weight-bold" href="../../about.html#citing-scikit-learn"><string>cite us</string></a> if you use the software.
</p>
</div>
<div class="sk-sidebar-toc">
<ul>
<li><a class="reference internal" href="#">Faces dataset decompositions</a><ul>
<li><a class="reference internal" href="#dataset-preparation">Dataset preparation</a></li>
<li><a class="reference internal" href="#decomposition">Decomposition</a><ul>
<li><a class="reference internal" href="#eigenfaces-pca-using-randomized-svd">Eigenfaces - PCA using randomized SVD</a></li>
<li><a class="reference internal" href="#non-negative-components-nmf">Non-negative components - NMF</a></li>
<li><a class="reference internal" href="#independent-components-fastica">Independent components - FastICA</a></li>
<li><a class="reference internal" href="#sparse-components-minibatchsparsepca">Sparse components - MiniBatchSparsePCA</a></li>
<li><a class="reference internal" href="#dictionary-learning">Dictionary learning</a></li>
<li><a class="reference internal" href="#cluster-centers-minibatchkmeans">Cluster centers - MiniBatchKMeans</a></li>
<li><a class="reference internal" href="#factor-analysis-components-fa">Factor Analysis components - FA</a></li>
</ul>
</li>
<li><a class="reference internal" href="#decomposition-dictionary-learning">Decomposition: Dictionary learning</a><ul>
<li><a class="reference internal" href="#dictionary-learning-positive-dictionary">Dictionary learning - positive dictionary</a></li>
<li><a class="reference internal" href="#dictionary-learning-positive-code">Dictionary learning - positive code</a></li>
<li><a class="reference internal" href="#dictionary-learning-positive-dictionary-code">Dictionary learning - positive dictionary & code</a></li>
</ul>
</li>
</ul>
</li>
</ul>
</div>
</div>
</div>
<div id="sk-page-content-wrapper">
<div class="sk-page-content container-fluid body px-md-3" role="main">
<div class="sphx-glr-download-link-note admonition note">
<p class="admonition-title">Note</p>
<p><a class="reference internal" href="#sphx-glr-download-auto-examples-decomposition-plot-faces-decomposition-py"><span class="std std-ref">Go to the end</span></a>
to download the full example code or to run this example in your browser via JupyterLite or Binder</p>
</div>
<section class="sphx-glr-example-title" id="faces-dataset-decompositions">
<span id="sphx-glr-auto-examples-decomposition-plot-faces-decomposition-py"></span><h1>Faces dataset decompositions<a class="headerlink" href="#faces-dataset-decompositions" title="Link to this heading">¶</a></h1>
<p>This example applies to <a class="reference internal" href="../../datasets/real_world.html#olivetti-faces-dataset"><span class="std std-ref">The Olivetti faces dataset</span></a> different unsupervised
matrix decomposition (dimension reduction) methods from the module
<a class="reference internal" href="../../modules/classes.html#module-sklearn.decomposition" title="sklearn.decomposition"><code class="xref py py-mod docutils literal notranslate"><span class="pre">sklearn.decomposition</span></code></a> (see the documentation chapter
<a class="reference internal" href="../../modules/decomposition.html#decompositions"><span class="std std-ref">Decomposing signals in components (matrix factorization problems)</span></a>).</p>
<ul class="simple">
<li><p>Authors: Vlad Niculae, Alexandre Gramfort</p></li>
<li><p>License: BSD 3 clause</p></li>
</ul>
<section id="dataset-preparation">
<h2>Dataset preparation<a class="headerlink" href="#dataset-preparation" title="Link to this heading">¶</a></h2>
<p>Loading and preprocessing the Olivetti faces dataset.</p>
<div class="highlight-Python notranslate"><div class="highlight"><pre><span></span><span class="kn">import</span> <span class="nn">logging</span>
<span class="kn">import</span> <span class="nn">matplotlib.pyplot</span> <span class="k">as</span> <span class="nn">plt</span>
<span class="kn">from</span> <span class="nn">numpy.random</span> <span class="kn">import</span> <a href="https://numpy.org/doc/stable/reference/random/legacy.html#numpy.random.RandomState" title="numpy.random.RandomState" class="sphx-glr-backref-module-numpy-random sphx-glr-backref-type-py-class sphx-glr-backref-instance"><span class="n">RandomState</span></a>
<span class="kn">from</span> <span class="nn">sklearn</span> <span class="kn">import</span> <span class="n">cluster</span><span class="p">,</span> <span class="n">decomposition</span>
<span class="kn">from</span> <span class="nn">sklearn.datasets</span> <span class="kn">import</span> <a href="../../modules/generated/sklearn.datasets.fetch_olivetti_faces.html#sklearn.datasets.fetch_olivetti_faces" title="sklearn.datasets.fetch_olivetti_faces" class="sphx-glr-backref-module-sklearn-datasets sphx-glr-backref-type-py-function"><span class="n">fetch_olivetti_faces</span></a>
<span class="n">rng</span> <span class="o">=</span> <a href="https://numpy.org/doc/stable/reference/random/legacy.html#numpy.random.RandomState" title="numpy.random.RandomState" class="sphx-glr-backref-module-numpy-random sphx-glr-backref-type-py-class sphx-glr-backref-instance"><span class="n">RandomState</span></a><span class="p">(</span><span class="mi">0</span><span class="p">)</span>
<span class="c1"># Display progress logs on stdout</span>
<a href="https://docs.python.org/3/library/logging.html#logging.basicConfig" title="logging.basicConfig" class="sphx-glr-backref-module-logging sphx-glr-backref-type-py-function"><span class="n">logging</span><span class="o">.</span><span class="n">basicConfig</span></a><span class="p">(</span><span class="n">level</span><span class="o">=</span><a href="https://docs.python.org/3/library/logging.html#logging.INFO" title="logging.INFO" class="sphx-glr-backref-module-logging sphx-glr-backref-type-py-data"><span class="n">logging</span><span class="o">.</span><span class="n">INFO</span></a><span class="p">,</span> <span class="nb">format</span><span class="o">=</span><span class="s2">"</span><span class="si">%(asctime)s</span><span class="s2"> </span><span class="si">%(levelname)s</span><span class="s2"> </span><span class="si">%(message)s</span><span class="s2">"</span><span class="p">)</span>
<span class="n">faces</span><span class="p">,</span> <span class="n">_</span> <span class="o">=</span> <a href="../../modules/generated/sklearn.datasets.fetch_olivetti_faces.html#sklearn.datasets.fetch_olivetti_faces" title="sklearn.datasets.fetch_olivetti_faces" class="sphx-glr-backref-module-sklearn-datasets sphx-glr-backref-type-py-function"><span class="n">fetch_olivetti_faces</span></a><span class="p">(</span><span class="n">return_X_y</span><span class="o">=</span><span class="kc">True</span><span class="p">,</span> <span class="n">shuffle</span><span class="o">=</span><span class="kc">True</span><span class="p">,</span> <span class="n">random_state</span><span class="o">=</span><span class="n">rng</span><span class="p">)</span>
<span class="n">n_samples</span><span class="p">,</span> <span class="n">n_features</span> <span class="o">=</span> <span class="n">faces</span><span class="o">.</span><span class="n">shape</span>
<span class="c1"># Global centering (focus on one feature, centering all samples)</span>
<span class="n">faces_centered</span> <span class="o">=</span> <span class="n">faces</span> <span class="o">-</span> <span class="n">faces</span><span class="o">.</span><span class="n">mean</span><span class="p">(</span><span class="n">axis</span><span class="o">=</span><span class="mi">0</span><span class="p">)</span>
<span class="c1"># Local centering (focus on one sample, centering all features)</span>
<span class="n">faces_centered</span> <span class="o">-=</span> <span class="n">faces_centered</span><span class="o">.</span><span class="n">mean</span><span class="p">(</span><span class="n">axis</span><span class="o">=</span><span class="mi">1</span><span class="p">)</span><span class="o">.</span><span class="n">reshape</span><span class="p">(</span><span class="n">n_samples</span><span class="p">,</span> <span class="o">-</span><span class="mi">1</span><span class="p">)</span>
<span class="nb">print</span><span class="p">(</span><span class="s2">"Dataset consists of </span><span class="si">%d</span><span class="s2"> faces"</span> <span class="o">%</span> <span class="n">n_samples</span><span class="p">)</span>
</pre></div>
</div>
<div class="sphx-glr-script-out highlight-none notranslate"><div class="highlight"><pre><span></span>Dataset consists of 400 faces
</pre></div>
</div>
<p>Define a base function to plot the gallery of faces.</p>
<div class="highlight-Python notranslate"><div class="highlight"><pre><span></span><span class="n">n_row</span><span class="p">,</span> <span class="n">n_col</span> <span class="o">=</span> <span class="mi">2</span><span class="p">,</span> <span class="mi">3</span>
<span class="n">n_components</span> <span class="o">=</span> <span class="n">n_row</span> <span class="o">*</span> <span class="n">n_col</span>
<span class="n">image_shape</span> <span class="o">=</span> <span class="p">(</span><span class="mi">64</span><span class="p">,</span> <span class="mi">64</span><span class="p">)</span>
<span class="k">def</span> <span class="nf">plot_gallery</span><span class="p">(</span><span class="n">title</span><span class="p">,</span> <span class="n">images</span><span class="p">,</span> <span class="n">n_col</span><span class="o">=</span><span class="n">n_col</span><span class="p">,</span> <span class="n">n_row</span><span class="o">=</span><span class="n">n_row</span><span class="p">,</span> <span class="n">cmap</span><span class="o">=</span><span class="n">plt</span><span class="o">.</span><span class="n">cm</span><span class="o">.</span><span class="n">gray</span><span class="p">):</span>
<span class="n">fig</span><span class="p">,</span> <span class="n">axs</span> <span class="o">=</span> <a href="https://matplotlib.org/stable/api/_as_gen/matplotlib.pyplot.subplots.html#matplotlib.pyplot.subplots" title="matplotlib.pyplot.subplots" class="sphx-glr-backref-module-matplotlib-pyplot sphx-glr-backref-type-py-function"><span class="n">plt</span><span class="o">.</span><span class="n">subplots</span></a><span class="p">(</span>
<span class="n">nrows</span><span class="o">=</span><span class="n">n_row</span><span class="p">,</span>
<span class="n">ncols</span><span class="o">=</span><span class="n">n_col</span><span class="p">,</span>
<span class="n">figsize</span><span class="o">=</span><span class="p">(</span><span class="mf">2.0</span> <span class="o">*</span> <span class="n">n_col</span><span class="p">,</span> <span class="mf">2.3</span> <span class="o">*</span> <span class="n">n_row</span><span class="p">),</span>
<span class="n">facecolor</span><span class="o">=</span><span class="s2">"white"</span><span class="p">,</span>
<span class="n">constrained_layout</span><span class="o">=</span><span class="kc">True</span><span class="p">,</span>
<span class="p">)</span>
<span class="n">fig</span><span class="o">.</span><span class="n">set_constrained_layout_pads</span><span class="p">(</span><span class="n">w_pad</span><span class="o">=</span><span class="mf">0.01</span><span class="p">,</span> <span class="n">h_pad</span><span class="o">=</span><span class="mf">0.02</span><span class="p">,</span> <span class="n">hspace</span><span class="o">=</span><span class="mi">0</span><span class="p">,</span> <span class="n">wspace</span><span class="o">=</span><span class="mi">0</span><span class="p">)</span>
<span class="n">fig</span><span class="o">.</span><span class="n">set_edgecolor</span><span class="p">(</span><span class="s2">"black"</span><span class="p">)</span>
<span class="n">fig</span><span class="o">.</span><span class="n">suptitle</span><span class="p">(</span><span class="n">title</span><span class="p">,</span> <span class="n">size</span><span class="o">=</span><span class="mi">16</span><span class="p">)</span>
<span class="k">for</span> <span class="n">ax</span><span class="p">,</span> <span class="n">vec</span> <span class="ow">in</span> <span class="nb">zip</span><span class="p">(</span><span class="n">axs</span><span class="o">.</span><span class="n">flat</span><span class="p">,</span> <span class="n">images</span><span class="p">):</span>
<span class="n">vmax</span> <span class="o">=</span> <span class="nb">max</span><span class="p">(</span><span class="n">vec</span><span class="o">.</span><span class="n">max</span><span class="p">(),</span> <span class="o">-</span><span class="n">vec</span><span class="o">.</span><span class="n">min</span><span class="p">())</span>
<span class="n">im</span> <span class="o">=</span> <span class="n">ax</span><span class="o">.</span><span class="n">imshow</span><span class="p">(</span>
<span class="n">vec</span><span class="o">.</span><span class="n">reshape</span><span class="p">(</span><span class="n">image_shape</span><span class="p">),</span>
<span class="n">cmap</span><span class="o">=</span><span class="n">cmap</span><span class="p">,</span>
<span class="n">interpolation</span><span class="o">=</span><span class="s2">"nearest"</span><span class="p">,</span>
<span class="n">vmin</span><span class="o">=-</span><span class="n">vmax</span><span class="p">,</span>
<span class="n">vmax</span><span class="o">=</span><span class="n">vmax</span><span class="p">,</span>
<span class="p">)</span>
<span class="n">ax</span><span class="o">.</span><span class="n">axis</span><span class="p">(</span><span class="s2">"off"</span><span class="p">)</span>
<span class="n">fig</span><span class="o">.</span><span class="n">colorbar</span><span class="p">(</span><span class="n">im</span><span class="p">,</span> <span class="n">ax</span><span class="o">=</span><span class="n">axs</span><span class="p">,</span> <span class="n">orientation</span><span class="o">=</span><span class="s2">"horizontal"</span><span class="p">,</span> <span class="n">shrink</span><span class="o">=</span><span class="mf">0.99</span><span class="p">,</span> <span class="n">aspect</span><span class="o">=</span><span class="mi">40</span><span class="p">,</span> <span class="n">pad</span><span class="o">=</span><span class="mf">0.01</span><span class="p">)</span>
<a href="https://matplotlib.org/stable/api/_as_gen/matplotlib.pyplot.show.html#matplotlib.pyplot.show" title="matplotlib.pyplot.show" class="sphx-glr-backref-module-matplotlib-pyplot sphx-glr-backref-type-py-function"><span class="n">plt</span><span class="o">.</span><span class="n">show</span></a><span class="p">()</span>
</pre></div>
</div>
<p>Let’s take a look at our data. Gray color indicates negative values,
white indicates positive values.</p>
<div class="highlight-Python notranslate"><div class="highlight"><pre><span></span><span class="n">plot_gallery</span><span class="p">(</span><span class="s2">"Faces from dataset"</span><span class="p">,</span> <span class="n">faces_centered</span><span class="p">[:</span><span class="n">n_components</span><span class="p">])</span>
</pre></div>
</div>
<img src="../../_images/sphx_glr_plot_faces_decomposition_001.png" srcset="../../_images/sphx_glr_plot_faces_decomposition_001.png" alt="Faces from dataset" class = "sphx-glr-single-img"/></section>
<section id="decomposition">
<h2>Decomposition<a class="headerlink" href="#decomposition" title="Link to this heading">¶</a></h2>
<p>Initialise different estimators for decomposition and fit each
of them on all images and plot some results. Each estimator extracts
6 components as vectors <span class="math notranslate nohighlight">\(h \in \mathbb{R}^{4096}\)</span>.
We just displayed these vectors in human-friendly visualisation as 64x64 pixel images.</p>
<p>Read more in the <a class="reference internal" href="../../modules/decomposition.html#decompositions"><span class="std std-ref">User Guide</span></a>.</p>
<section id="eigenfaces-pca-using-randomized-svd">
<h3>Eigenfaces - PCA using randomized SVD<a class="headerlink" href="#eigenfaces-pca-using-randomized-svd" title="Link to this heading">¶</a></h3>
<p>Linear dimensionality reduction using Singular Value Decomposition (SVD) of the data
to project it to a lower dimensional space.</p>
<div class="admonition note">
<p class="admonition-title">Note</p>
<p>The Eigenfaces estimator, via the <a class="reference internal" href="../../modules/generated/sklearn.decomposition.PCA.html#sklearn.decomposition.PCA" title="sklearn.decomposition.PCA"><code class="xref py py-mod docutils literal notranslate"><span class="pre">sklearn.decomposition.PCA</span></code></a>,
also provides a scalar <code class="docutils literal notranslate"><span class="pre">noise_variance_</span></code> (the mean of pixelwise variance)
that cannot be displayed as an image.</p>
</div>
<div class="highlight-Python notranslate"><div class="highlight"><pre><span></span><span class="n">pca_estimator</span> <span class="o">=</span> <a href="../../modules/generated/sklearn.decomposition.PCA.html#sklearn.decomposition.PCA" title="sklearn.decomposition.PCA" class="sphx-glr-backref-module-sklearn-decomposition sphx-glr-backref-type-py-class sphx-glr-backref-instance"><span class="n">decomposition</span><span class="o">.</span><span class="n">PCA</span></a><span class="p">(</span>
<span class="n">n_components</span><span class="o">=</span><span class="n">n_components</span><span class="p">,</span> <span class="n">svd_solver</span><span class="o">=</span><span class="s2">"randomized"</span><span class="p">,</span> <span class="n">whiten</span><span class="o">=</span><span class="kc">True</span>
<span class="p">)</span>
<span class="n">pca_estimator</span><span class="o">.</span><span class="n">fit</span><span class="p">(</span><span class="n">faces_centered</span><span class="p">)</span>
<span class="n">plot_gallery</span><span class="p">(</span>
<span class="s2">"Eigenfaces - PCA using randomized SVD"</span><span class="p">,</span> <span class="n">pca_estimator</span><span class="o">.</span><span class="n">components_</span><span class="p">[:</span><span class="n">n_components</span><span class="p">]</span>
<span class="p">)</span>
</pre></div>
</div>
<img src="../../_images/sphx_glr_plot_faces_decomposition_002.png" srcset="../../_images/sphx_glr_plot_faces_decomposition_002.png" alt="Eigenfaces - PCA using randomized SVD" class = "sphx-glr-single-img"/></section>
<section id="non-negative-components-nmf">
<h3>Non-negative components - NMF<a class="headerlink" href="#non-negative-components-nmf" title="Link to this heading">¶</a></h3>
<p>Estimate non-negative original data as production of two non-negative matrices.</p>
<div class="highlight-Python notranslate"><div class="highlight"><pre><span></span><span class="n">nmf_estimator</span> <span class="o">=</span> <a href="../../modules/generated/sklearn.decomposition.NMF.html#sklearn.decomposition.NMF" title="sklearn.decomposition.NMF" class="sphx-glr-backref-module-sklearn-decomposition sphx-glr-backref-type-py-class sphx-glr-backref-instance"><span class="n">decomposition</span><span class="o">.</span><span class="n">NMF</span></a><span class="p">(</span><span class="n">n_components</span><span class="o">=</span><span class="n">n_components</span><span class="p">,</span> <span class="n">tol</span><span class="o">=</span><span class="mf">5e-3</span><span class="p">)</span>
<span class="n">nmf_estimator</span><span class="o">.</span><span class="n">fit</span><span class="p">(</span><span class="n">faces</span><span class="p">)</span> <span class="c1"># original non- negative dataset</span>
<span class="n">plot_gallery</span><span class="p">(</span><span class="s2">"Non-negative components - NMF"</span><span class="p">,</span> <span class="n">nmf_estimator</span><span class="o">.</span><span class="n">components_</span><span class="p">[:</span><span class="n">n_components</span><span class="p">])</span>
</pre></div>
</div>
<img src="../../_images/sphx_glr_plot_faces_decomposition_003.png" srcset="../../_images/sphx_glr_plot_faces_decomposition_003.png" alt="Non-negative components - NMF" class = "sphx-glr-single-img"/></section>
<section id="independent-components-fastica">
<h3>Independent components - FastICA<a class="headerlink" href="#independent-components-fastica" title="Link to this heading">¶</a></h3>
<p>Independent component analysis separates a multivariate vectors into additive
subcomponents that are maximally independent.</p>
<div class="highlight-Python notranslate"><div class="highlight"><pre><span></span><span class="n">ica_estimator</span> <span class="o">=</span> <a href="../../modules/generated/sklearn.decomposition.FastICA.html#sklearn.decomposition.FastICA" title="sklearn.decomposition.FastICA" class="sphx-glr-backref-module-sklearn-decomposition sphx-glr-backref-type-py-class sphx-glr-backref-instance"><span class="n">decomposition</span><span class="o">.</span><span class="n">FastICA</span></a><span class="p">(</span>
<span class="n">n_components</span><span class="o">=</span><span class="n">n_components</span><span class="p">,</span> <span class="n">max_iter</span><span class="o">=</span><span class="mi">400</span><span class="p">,</span> <span class="n">whiten</span><span class="o">=</span><span class="s2">"arbitrary-variance"</span><span class="p">,</span> <span class="n">tol</span><span class="o">=</span><span class="mf">15e-5</span>
<span class="p">)</span>
<span class="n">ica_estimator</span><span class="o">.</span><span class="n">fit</span><span class="p">(</span><span class="n">faces_centered</span><span class="p">)</span>
<span class="n">plot_gallery</span><span class="p">(</span>
<span class="s2">"Independent components - FastICA"</span><span class="p">,</span> <span class="n">ica_estimator</span><span class="o">.</span><span class="n">components_</span><span class="p">[:</span><span class="n">n_components</span><span class="p">]</span>
<span class="p">)</span>
</pre></div>
</div>
<img src="../../_images/sphx_glr_plot_faces_decomposition_004.png" srcset="../../_images/sphx_glr_plot_faces_decomposition_004.png" alt="Independent components - FastICA" class = "sphx-glr-single-img"/></section>
<section id="sparse-components-minibatchsparsepca">
<h3>Sparse components - MiniBatchSparsePCA<a class="headerlink" href="#sparse-components-minibatchsparsepca" title="Link to this heading">¶</a></h3>
<p>Mini-batch sparse PCA (<a class="reference internal" href="../../modules/generated/sklearn.decomposition.MiniBatchSparsePCA.html#sklearn.decomposition.MiniBatchSparsePCA" title="sklearn.decomposition.MiniBatchSparsePCA"><code class="xref py py-class docutils literal notranslate"><span class="pre">MiniBatchSparsePCA</span></code></a>)
extracts the set of sparse components that best reconstruct the data. This
variant is faster but less accurate than the similar
<a class="reference internal" href="../../modules/generated/sklearn.decomposition.SparsePCA.html#sklearn.decomposition.SparsePCA" title="sklearn.decomposition.SparsePCA"><code class="xref py py-class docutils literal notranslate"><span class="pre">SparsePCA</span></code></a>.</p>
<div class="highlight-Python notranslate"><div class="highlight"><pre><span></span><span class="n">batch_pca_estimator</span> <span class="o">=</span> <a href="../../modules/generated/sklearn.decomposition.MiniBatchSparsePCA.html#sklearn.decomposition.MiniBatchSparsePCA" title="sklearn.decomposition.MiniBatchSparsePCA" class="sphx-glr-backref-module-sklearn-decomposition sphx-glr-backref-type-py-class sphx-glr-backref-instance"><span class="n">decomposition</span><span class="o">.</span><span class="n">MiniBatchSparsePCA</span></a><span class="p">(</span>
<span class="n">n_components</span><span class="o">=</span><span class="n">n_components</span><span class="p">,</span> <span class="n">alpha</span><span class="o">=</span><span class="mf">0.1</span><span class="p">,</span> <span class="n">max_iter</span><span class="o">=</span><span class="mi">100</span><span class="p">,</span> <span class="n">batch_size</span><span class="o">=</span><span class="mi">3</span><span class="p">,</span> <span class="n">random_state</span><span class="o">=</span><span class="n">rng</span>
<span class="p">)</span>
<span class="n">batch_pca_estimator</span><span class="o">.</span><span class="n">fit</span><span class="p">(</span><span class="n">faces_centered</span><span class="p">)</span>
<span class="n">plot_gallery</span><span class="p">(</span>
<span class="s2">"Sparse components - MiniBatchSparsePCA"</span><span class="p">,</span>
<span class="n">batch_pca_estimator</span><span class="o">.</span><span class="n">components_</span><span class="p">[:</span><span class="n">n_components</span><span class="p">],</span>
<span class="p">)</span>
</pre></div>
</div>
<img src="../../_images/sphx_glr_plot_faces_decomposition_005.png" srcset="../../_images/sphx_glr_plot_faces_decomposition_005.png" alt="Sparse components - MiniBatchSparsePCA" class = "sphx-glr-single-img"/></section>
<section id="dictionary-learning">
<h3>Dictionary learning<a class="headerlink" href="#dictionary-learning" title="Link to this heading">¶</a></h3>
<p>By default, <a class="reference internal" href="../../modules/generated/sklearn.decomposition.MiniBatchDictionaryLearning.html#sklearn.decomposition.MiniBatchDictionaryLearning" title="sklearn.decomposition.MiniBatchDictionaryLearning"><code class="xref py py-class docutils literal notranslate"><span class="pre">MiniBatchDictionaryLearning</span></code></a>
divides the data into mini-batches and optimizes in an online manner by
cycling over the mini-batches for the specified number of iterations.</p>
<div class="highlight-Python notranslate"><div class="highlight"><pre><span></span><span class="n">batch_dict_estimator</span> <span class="o">=</span> <a href="../../modules/generated/sklearn.decomposition.MiniBatchDictionaryLearning.html#sklearn.decomposition.MiniBatchDictionaryLearning" title="sklearn.decomposition.MiniBatchDictionaryLearning" class="sphx-glr-backref-module-sklearn-decomposition sphx-glr-backref-type-py-class sphx-glr-backref-instance"><span class="n">decomposition</span><span class="o">.</span><span class="n">MiniBatchDictionaryLearning</span></a><span class="p">(</span>
<span class="n">n_components</span><span class="o">=</span><span class="n">n_components</span><span class="p">,</span> <span class="n">alpha</span><span class="o">=</span><span class="mf">0.1</span><span class="p">,</span> <span class="n">max_iter</span><span class="o">=</span><span class="mi">50</span><span class="p">,</span> <span class="n">batch_size</span><span class="o">=</span><span class="mi">3</span><span class="p">,</span> <span class="n">random_state</span><span class="o">=</span><span class="n">rng</span>
<span class="p">)</span>
<span class="n">batch_dict_estimator</span><span class="o">.</span><span class="n">fit</span><span class="p">(</span><span class="n">faces_centered</span><span class="p">)</span>
<span class="n">plot_gallery</span><span class="p">(</span><span class="s2">"Dictionary learning"</span><span class="p">,</span> <span class="n">batch_dict_estimator</span><span class="o">.</span><span class="n">components_</span><span class="p">[:</span><span class="n">n_components</span><span class="p">])</span>
</pre></div>
</div>
<img src="../../_images/sphx_glr_plot_faces_decomposition_006.png" srcset="../../_images/sphx_glr_plot_faces_decomposition_006.png" alt="Dictionary learning" class = "sphx-glr-single-img"/></section>
<section id="cluster-centers-minibatchkmeans">
<h3>Cluster centers - MiniBatchKMeans<a class="headerlink" href="#cluster-centers-minibatchkmeans" title="Link to this heading">¶</a></h3>
<p><a class="reference internal" href="../../modules/generated/sklearn.cluster.MiniBatchKMeans.html#sklearn.cluster.MiniBatchKMeans" title="sklearn.cluster.MiniBatchKMeans"><code class="xref py py-class docutils literal notranslate"><span class="pre">sklearn.cluster.MiniBatchKMeans</span></code></a> is computationally efficient and
implements on-line learning with a
<a class="reference internal" href="../../modules/generated/sklearn.cluster.MiniBatchKMeans.html#sklearn.cluster.MiniBatchKMeans.partial_fit" title="sklearn.cluster.MiniBatchKMeans.partial_fit"><code class="xref py py-meth docutils literal notranslate"><span class="pre">partial_fit</span></code></a> method. That is
why it could be beneficial to enhance some time-consuming algorithms with
<a class="reference internal" href="../../modules/generated/sklearn.cluster.MiniBatchKMeans.html#sklearn.cluster.MiniBatchKMeans" title="sklearn.cluster.MiniBatchKMeans"><code class="xref py py-class docutils literal notranslate"><span class="pre">MiniBatchKMeans</span></code></a>.</p>
<div class="highlight-Python notranslate"><div class="highlight"><pre><span></span><span class="n">kmeans_estimator</span> <span class="o">=</span> <a href="../../modules/generated/sklearn.cluster.MiniBatchKMeans.html#sklearn.cluster.MiniBatchKMeans" title="sklearn.cluster.MiniBatchKMeans" class="sphx-glr-backref-module-sklearn-cluster sphx-glr-backref-type-py-class sphx-glr-backref-instance"><span class="n">cluster</span><span class="o">.</span><span class="n">MiniBatchKMeans</span></a><span class="p">(</span>
<span class="n">n_clusters</span><span class="o">=</span><span class="n">n_components</span><span class="p">,</span>
<span class="n">tol</span><span class="o">=</span><span class="mf">1e-3</span><span class="p">,</span>
<span class="n">batch_size</span><span class="o">=</span><span class="mi">20</span><span class="p">,</span>
<span class="n">max_iter</span><span class="o">=</span><span class="mi">50</span><span class="p">,</span>
<span class="n">random_state</span><span class="o">=</span><span class="n">rng</span><span class="p">,</span>
<span class="p">)</span>
<span class="n">kmeans_estimator</span><span class="o">.</span><span class="n">fit</span><span class="p">(</span><span class="n">faces_centered</span><span class="p">)</span>
<span class="n">plot_gallery</span><span class="p">(</span>
<span class="s2">"Cluster centers - MiniBatchKMeans"</span><span class="p">,</span>
<span class="n">kmeans_estimator</span><span class="o">.</span><span class="n">cluster_centers_</span><span class="p">[:</span><span class="n">n_components</span><span class="p">],</span>
<span class="p">)</span>
</pre></div>
</div>
<img src="../../_images/sphx_glr_plot_faces_decomposition_007.png" srcset="../../_images/sphx_glr_plot_faces_decomposition_007.png" alt="Cluster centers - MiniBatchKMeans" class = "sphx-glr-single-img"/></section>
<section id="factor-analysis-components-fa">
<h3>Factor Analysis components - FA<a class="headerlink" href="#factor-analysis-components-fa" title="Link to this heading">¶</a></h3>
<p><a class="reference internal" href="../../modules/generated/sklearn.decomposition.FactorAnalysis.html#sklearn.decomposition.FactorAnalysis" title="sklearn.decomposition.FactorAnalysis"><code class="xref py py-class docutils literal notranslate"><span class="pre">FactorAnalysis</span></code></a> is similar to
<a class="reference internal" href="../../modules/generated/sklearn.decomposition.PCA.html#sklearn.decomposition.PCA" title="sklearn.decomposition.PCA"><code class="xref py py-class docutils literal notranslate"><span class="pre">PCA</span></code></a> but has the advantage of modelling the
variance in every direction of the input space independently (heteroscedastic
noise). Read more in the <a class="reference internal" href="../../modules/decomposition.html#fa"><span class="std std-ref">User Guide</span></a>.</p>
<div class="highlight-Python notranslate"><div class="highlight"><pre><span></span><span class="n">fa_estimator</span> <span class="o">=</span> <a href="../../modules/generated/sklearn.decomposition.FactorAnalysis.html#sklearn.decomposition.FactorAnalysis" title="sklearn.decomposition.FactorAnalysis" class="sphx-glr-backref-module-sklearn-decomposition sphx-glr-backref-type-py-class sphx-glr-backref-instance"><span class="n">decomposition</span><span class="o">.</span><span class="n">FactorAnalysis</span></a><span class="p">(</span><span class="n">n_components</span><span class="o">=</span><span class="n">n_components</span><span class="p">,</span> <span class="n">max_iter</span><span class="o">=</span><span class="mi">20</span><span class="p">)</span>
<span class="n">fa_estimator</span><span class="o">.</span><span class="n">fit</span><span class="p">(</span><span class="n">faces_centered</span><span class="p">)</span>
<span class="n">plot_gallery</span><span class="p">(</span><span class="s2">"Factor Analysis (FA)"</span><span class="p">,</span> <span class="n">fa_estimator</span><span class="o">.</span><span class="n">components_</span><span class="p">[:</span><span class="n">n_components</span><span class="p">])</span>
<span class="c1"># --- Pixelwise variance</span>
<a href="https://matplotlib.org/stable/api/_as_gen/matplotlib.pyplot.figure.html#matplotlib.pyplot.figure" title="matplotlib.pyplot.figure" class="sphx-glr-backref-module-matplotlib-pyplot sphx-glr-backref-type-py-function"><span class="n">plt</span><span class="o">.</span><span class="n">figure</span></a><span class="p">(</span><span class="n">figsize</span><span class="o">=</span><span class="p">(</span><span class="mf">3.2</span><span class="p">,</span> <span class="mf">3.6</span><span class="p">),</span> <span class="n">facecolor</span><span class="o">=</span><span class="s2">"white"</span><span class="p">,</span> <span class="n">tight_layout</span><span class="o">=</span><span class="kc">True</span><span class="p">)</span>
<span class="n">vec</span> <span class="o">=</span> <span class="n">fa_estimator</span><span class="o">.</span><span class="n">noise_variance_</span>
<span class="n">vmax</span> <span class="o">=</span> <span class="nb">max</span><span class="p">(</span><span class="n">vec</span><span class="o">.</span><span class="n">max</span><span class="p">(),</span> <span class="o">-</span><span class="n">vec</span><span class="o">.</span><span class="n">min</span><span class="p">())</span>
<a href="https://matplotlib.org/stable/api/_as_gen/matplotlib.pyplot.imshow.html#matplotlib.pyplot.imshow" title="matplotlib.pyplot.imshow" class="sphx-glr-backref-module-matplotlib-pyplot sphx-glr-backref-type-py-function"><span class="n">plt</span><span class="o">.</span><span class="n">imshow</span></a><span class="p">(</span>
<span class="n">vec</span><span class="o">.</span><span class="n">reshape</span><span class="p">(</span><span class="n">image_shape</span><span class="p">),</span>
<span class="n">cmap</span><span class="o">=</span><span class="n">plt</span><span class="o">.</span><span class="n">cm</span><span class="o">.</span><span class="n">gray</span><span class="p">,</span>
<span class="n">interpolation</span><span class="o">=</span><span class="s2">"nearest"</span><span class="p">,</span>
<span class="n">vmin</span><span class="o">=-</span><span class="n">vmax</span><span class="p">,</span>
<span class="n">vmax</span><span class="o">=</span><span class="n">vmax</span><span class="p">,</span>
<span class="p">)</span>
<a href="https://matplotlib.org/stable/api/_as_gen/matplotlib.pyplot.axis.html#matplotlib.pyplot.axis" title="matplotlib.pyplot.axis" class="sphx-glr-backref-module-matplotlib-pyplot sphx-glr-backref-type-py-function"><span class="n">plt</span><span class="o">.</span><span class="n">axis</span></a><span class="p">(</span><span class="s2">"off"</span><span class="p">)</span>
<a href="https://matplotlib.org/stable/api/_as_gen/matplotlib.pyplot.title.html#matplotlib.pyplot.title" title="matplotlib.pyplot.title" class="sphx-glr-backref-module-matplotlib-pyplot sphx-glr-backref-type-py-function"><span class="n">plt</span><span class="o">.</span><span class="n">title</span></a><span class="p">(</span><span class="s2">"Pixelwise variance from </span><span class="se">\n</span><span class="s2"> Factor Analysis (FA)"</span><span class="p">,</span> <span class="n">size</span><span class="o">=</span><span class="mi">16</span><span class="p">,</span> <span class="n">wrap</span><span class="o">=</span><span class="kc">True</span><span class="p">)</span>
<a href="https://matplotlib.org/stable/api/_as_gen/matplotlib.pyplot.colorbar.html#matplotlib.pyplot.colorbar" title="matplotlib.pyplot.colorbar" class="sphx-glr-backref-module-matplotlib-pyplot sphx-glr-backref-type-py-function"><span class="n">plt</span><span class="o">.</span><span class="n">colorbar</span></a><span class="p">(</span><span class="n">orientation</span><span class="o">=</span><span class="s2">"horizontal"</span><span class="p">,</span> <span class="n">shrink</span><span class="o">=</span><span class="mf">0.8</span><span class="p">,</span> <span class="n">pad</span><span class="o">=</span><span class="mf">0.03</span><span class="p">)</span>
<a href="https://matplotlib.org/stable/api/_as_gen/matplotlib.pyplot.show.html#matplotlib.pyplot.show" title="matplotlib.pyplot.show" class="sphx-glr-backref-module-matplotlib-pyplot sphx-glr-backref-type-py-function"><span class="n">plt</span><span class="o">.</span><span class="n">show</span></a><span class="p">()</span>
</pre></div>
</div>
<ul class="sphx-glr-horizontal">
<li><img src="../../_images/sphx_glr_plot_faces_decomposition_008.png" srcset="../../_images/sphx_glr_plot_faces_decomposition_008.png" alt="Factor Analysis (FA)" class = "sphx-glr-multi-img"/></li>
<li><img src="../../_images/sphx_glr_plot_faces_decomposition_009.png" srcset="../../_images/sphx_glr_plot_faces_decomposition_009.png" alt="Pixelwise variance from Factor Analysis (FA)" class = "sphx-glr-multi-img"/></li>
</ul>
</section>
</section>
<section id="decomposition-dictionary-learning">
<h2>Decomposition: Dictionary learning<a class="headerlink" href="#decomposition-dictionary-learning" title="Link to this heading">¶</a></h2>
<p>In the further section, let’s consider <a class="reference internal" href="../../modules/decomposition.html#dictionarylearning"><span class="std std-ref">Dictionary Learning</span></a> more precisely.
Dictionary learning is a problem that amounts to finding a sparse representation
of the input data as a combination of simple elements. These simple elements form
a dictionary. It is possible to constrain the dictionary and/or coding coefficients
to be positive to match constraints that may be present in the data.</p>
<p><a class="reference internal" href="../../modules/generated/sklearn.decomposition.MiniBatchDictionaryLearning.html#sklearn.decomposition.MiniBatchDictionaryLearning" title="sklearn.decomposition.MiniBatchDictionaryLearning"><code class="xref py py-class docutils literal notranslate"><span class="pre">MiniBatchDictionaryLearning</span></code></a> implements a
faster, but less accurate version of the dictionary learning algorithm that
is better suited for large datasets. Read more in the <a class="reference internal" href="../../modules/decomposition.html#minibatchdictionarylearning"><span class="std std-ref">User Guide</span></a>.</p>
<p>Plot the same samples from our dataset but with another colormap.
Red indicates negative values, blue indicates positive values,
and white represents zeros.</p>
<div class="highlight-Python notranslate"><div class="highlight"><pre><span></span><span class="n">plot_gallery</span><span class="p">(</span><span class="s2">"Faces from dataset"</span><span class="p">,</span> <span class="n">faces_centered</span><span class="p">[:</span><span class="n">n_components</span><span class="p">],</span> <span class="n">cmap</span><span class="o">=</span><span class="n">plt</span><span class="o">.</span><span class="n">cm</span><span class="o">.</span><span class="n">RdBu</span><span class="p">)</span>
</pre></div>
</div>
<img src="../../_images/sphx_glr_plot_faces_decomposition_010.png" srcset="../../_images/sphx_glr_plot_faces_decomposition_010.png" alt="Faces from dataset" class = "sphx-glr-single-img"/><p>Similar to the previous examples, we change parameters and train
<a class="reference internal" href="../../modules/generated/sklearn.decomposition.MiniBatchDictionaryLearning.html#sklearn.decomposition.MiniBatchDictionaryLearning" title="sklearn.decomposition.MiniBatchDictionaryLearning"><code class="xref py py-class docutils literal notranslate"><span class="pre">MiniBatchDictionaryLearning</span></code></a> estimator on all
images. Generally, the dictionary learning and sparse encoding decompose
input data into the dictionary and the coding coefficients matrices. <span class="math notranslate nohighlight">\(X
\approx UV\)</span>, where <span class="math notranslate nohighlight">\(X = [x_1, . . . , x_n]\)</span>, <span class="math notranslate nohighlight">\(X \in
\mathbb{R}^{m×n}\)</span>, dictionary <span class="math notranslate nohighlight">\(U \in \mathbb{R}^{m×k}\)</span>, coding
coefficients <span class="math notranslate nohighlight">\(V \in \mathbb{R}^{k×n}\)</span>.</p>
<p>Also below are the results when the dictionary and coding
coefficients are positively constrained.</p>
<section id="dictionary-learning-positive-dictionary">
<h3>Dictionary learning - positive dictionary<a class="headerlink" href="#dictionary-learning-positive-dictionary" title="Link to this heading">¶</a></h3>
<p>In the following section we enforce positivity when finding the dictionary.</p>
<div class="highlight-Python notranslate"><div class="highlight"><pre><span></span><span class="n">dict_pos_dict_estimator</span> <span class="o">=</span> <a href="../../modules/generated/sklearn.decomposition.MiniBatchDictionaryLearning.html#sklearn.decomposition.MiniBatchDictionaryLearning" title="sklearn.decomposition.MiniBatchDictionaryLearning" class="sphx-glr-backref-module-sklearn-decomposition sphx-glr-backref-type-py-class sphx-glr-backref-instance"><span class="n">decomposition</span><span class="o">.</span><span class="n">MiniBatchDictionaryLearning</span></a><span class="p">(</span>
<span class="n">n_components</span><span class="o">=</span><span class="n">n_components</span><span class="p">,</span>
<span class="n">alpha</span><span class="o">=</span><span class="mf">0.1</span><span class="p">,</span>
<span class="n">max_iter</span><span class="o">=</span><span class="mi">50</span><span class="p">,</span>
<span class="n">batch_size</span><span class="o">=</span><span class="mi">3</span><span class="p">,</span>
<span class="n">random_state</span><span class="o">=</span><span class="n">rng</span><span class="p">,</span>
<span class="n">positive_dict</span><span class="o">=</span><span class="kc">True</span><span class="p">,</span>
<span class="p">)</span>
<span class="n">dict_pos_dict_estimator</span><span class="o">.</span><span class="n">fit</span><span class="p">(</span><span class="n">faces_centered</span><span class="p">)</span>
<span class="n">plot_gallery</span><span class="p">(</span>
<span class="s2">"Dictionary learning - positive dictionary"</span><span class="p">,</span>
<span class="n">dict_pos_dict_estimator</span><span class="o">.</span><span class="n">components_</span><span class="p">[:</span><span class="n">n_components</span><span class="p">],</span>
<span class="n">cmap</span><span class="o">=</span><span class="n">plt</span><span class="o">.</span><span class="n">cm</span><span class="o">.</span><span class="n">RdBu</span><span class="p">,</span>
<span class="p">)</span>
</pre></div>
</div>
<img src="../../_images/sphx_glr_plot_faces_decomposition_011.png" srcset="../../_images/sphx_glr_plot_faces_decomposition_011.png" alt="Dictionary learning - positive dictionary" class = "sphx-glr-single-img"/></section>
<section id="dictionary-learning-positive-code">
<h3>Dictionary learning - positive code<a class="headerlink" href="#dictionary-learning-positive-code" title="Link to this heading">¶</a></h3>
<p>Below we constrain the coding coefficients as a positive matrix.</p>
<div class="highlight-Python notranslate"><div class="highlight"><pre><span></span><span class="n">dict_pos_code_estimator</span> <span class="o">=</span> <a href="../../modules/generated/sklearn.decomposition.MiniBatchDictionaryLearning.html#sklearn.decomposition.MiniBatchDictionaryLearning" title="sklearn.decomposition.MiniBatchDictionaryLearning" class="sphx-glr-backref-module-sklearn-decomposition sphx-glr-backref-type-py-class sphx-glr-backref-instance"><span class="n">decomposition</span><span class="o">.</span><span class="n">MiniBatchDictionaryLearning</span></a><span class="p">(</span>
<span class="n">n_components</span><span class="o">=</span><span class="n">n_components</span><span class="p">,</span>
<span class="n">alpha</span><span class="o">=</span><span class="mf">0.1</span><span class="p">,</span>
<span class="n">max_iter</span><span class="o">=</span><span class="mi">50</span><span class="p">,</span>
<span class="n">batch_size</span><span class="o">=</span><span class="mi">3</span><span class="p">,</span>
<span class="n">fit_algorithm</span><span class="o">=</span><span class="s2">"cd"</span><span class="p">,</span>
<span class="n">random_state</span><span class="o">=</span><span class="n">rng</span><span class="p">,</span>
<span class="n">positive_code</span><span class="o">=</span><span class="kc">True</span><span class="p">,</span>
<span class="p">)</span>
<span class="n">dict_pos_code_estimator</span><span class="o">.</span><span class="n">fit</span><span class="p">(</span><span class="n">faces_centered</span><span class="p">)</span>
<span class="n">plot_gallery</span><span class="p">(</span>
<span class="s2">"Dictionary learning - positive code"</span><span class="p">,</span>
<span class="n">dict_pos_code_estimator</span><span class="o">.</span><span class="n">components_</span><span class="p">[:</span><span class="n">n_components</span><span class="p">],</span>
<span class="n">cmap</span><span class="o">=</span><span class="n">plt</span><span class="o">.</span><span class="n">cm</span><span class="o">.</span><span class="n">RdBu</span><span class="p">,</span>
<span class="p">)</span>
</pre></div>
</div>
<img src="../../_images/sphx_glr_plot_faces_decomposition_012.png" srcset="../../_images/sphx_glr_plot_faces_decomposition_012.png" alt="Dictionary learning - positive code" class = "sphx-glr-single-img"/></section>
<section id="dictionary-learning-positive-dictionary-code">
<h3>Dictionary learning - positive dictionary & code<a class="headerlink" href="#dictionary-learning-positive-dictionary-code" title="Link to this heading">¶</a></h3>
<p>Also below are the results if the dictionary values and coding
coefficients are positively constrained.</p>
<div class="highlight-Python notranslate"><div class="highlight"><pre><span></span><span class="n">dict_pos_estimator</span> <span class="o">=</span> <a href="../../modules/generated/sklearn.decomposition.MiniBatchDictionaryLearning.html#sklearn.decomposition.MiniBatchDictionaryLearning" title="sklearn.decomposition.MiniBatchDictionaryLearning" class="sphx-glr-backref-module-sklearn-decomposition sphx-glr-backref-type-py-class sphx-glr-backref-instance"><span class="n">decomposition</span><span class="o">.</span><span class="n">MiniBatchDictionaryLearning</span></a><span class="p">(</span>
<span class="n">n_components</span><span class="o">=</span><span class="n">n_components</span><span class="p">,</span>
<span class="n">alpha</span><span class="o">=</span><span class="mf">0.1</span><span class="p">,</span>
<span class="n">max_iter</span><span class="o">=</span><span class="mi">50</span><span class="p">,</span>
<span class="n">batch_size</span><span class="o">=</span><span class="mi">3</span><span class="p">,</span>
<span class="n">fit_algorithm</span><span class="o">=</span><span class="s2">"cd"</span><span class="p">,</span>
<span class="n">random_state</span><span class="o">=</span><span class="n">rng</span><span class="p">,</span>
<span class="n">positive_dict</span><span class="o">=</span><span class="kc">True</span><span class="p">,</span>
<span class="n">positive_code</span><span class="o">=</span><span class="kc">True</span><span class="p">,</span>
<span class="p">)</span>
<span class="n">dict_pos_estimator</span><span class="o">.</span><span class="n">fit</span><span class="p">(</span><span class="n">faces_centered</span><span class="p">)</span>
<span class="n">plot_gallery</span><span class="p">(</span>
<span class="s2">"Dictionary learning - positive dictionary & code"</span><span class="p">,</span>
<span class="n">dict_pos_estimator</span><span class="o">.</span><span class="n">components_</span><span class="p">[:</span><span class="n">n_components</span><span class="p">],</span>
<span class="n">cmap</span><span class="o">=</span><span class="n">plt</span><span class="o">.</span><span class="n">cm</span><span class="o">.</span><span class="n">RdBu</span><span class="p">,</span>
<span class="p">)</span>
</pre></div>
</div>
<img src="../../_images/sphx_glr_plot_faces_decomposition_013.png" srcset="../../_images/sphx_glr_plot_faces_decomposition_013.png" alt="Dictionary learning - positive dictionary & code" class = "sphx-glr-single-img"/><p class="sphx-glr-timing"><strong>Total running time of the script:</strong> (0 minutes 9.027 seconds)</p>
<div class="sphx-glr-footer sphx-glr-footer-example docutils container" id="sphx-glr-download-auto-examples-decomposition-plot-faces-decomposition-py">
<div class="binder-badge docutils container">
<a class="reference external image-reference" href="https://mybinder.org/v2/gh/scikit-learn/scikit-learn/1.4.X?urlpath=lab/tree/notebooks/auto_examples/decomposition/plot_faces_decomposition.ipynb"><img alt="Launch binder" src="../../_images/binder_badge_logo9.svg" width="150px" /></a>
</div>
<div class="lite-badge docutils container">
<a class="reference external image-reference" href="../../lite/lab/?path=auto_examples/decomposition/plot_faces_decomposition.ipynb"><img alt="Launch JupyterLite" src="../../_images/jupyterlite_badge_logo9.svg" width="150px" /></a>
</div>
<div class="sphx-glr-download sphx-glr-download-jupyter docutils container">
<p><a class="reference download internal" download="" href="../../_downloads/fcae36814d8e700024ca855a1eb87ca9/plot_faces_decomposition.ipynb"><code class="xref download docutils literal notranslate"><span class="pre">Download</span> <span class="pre">Jupyter</span> <span class="pre">notebook:</span> <span class="pre">plot_faces_decomposition.ipynb</span></code></a></p>
</div>
<div class="sphx-glr-download sphx-glr-download-python docutils container">
<p><a class="reference download internal" download="" href="../../_downloads/4825fc8223d1af0f3b61080c3dea3a62/plot_faces_decomposition.py"><code class="xref download docutils literal notranslate"><span class="pre">Download</span> <span class="pre">Python</span> <span class="pre">source</span> <span class="pre">code:</span> <span class="pre">plot_faces_decomposition.py</span></code></a></p>
</div>
</div>
<p class="rubric">Related examples</p>
<div class="sphx-glr-thumbnails"><div class="sphx-glr-thumbcontainer" tooltip="This example uses a large dataset of faces to learn a set of 20 x 20 images patches that consti..."><img alt="" src="../../_images/sphx_glr_plot_dict_face_patches_thumb.png" />
<p><a class="reference internal" href="../cluster/plot_dict_face_patches.html#sphx-glr-auto-examples-cluster-plot-dict-face-patches-py"><span class="std std-ref">Online learning of a dictionary of parts of faces</span></a></p>
<div class="sphx-glr-thumbnail-title">Online learning of a dictionary of parts of faces</div>
</div><div class="sphx-glr-thumbcontainer" tooltip="Transform a signal as a sparse combination of Ricker wavelets. This example visually compares d..."><img alt="" src="../../_images/sphx_glr_plot_sparse_coding_thumb.png" />
<p><a class="reference internal" href="plot_sparse_coding.html#sphx-glr-auto-examples-decomposition-plot-sparse-coding-py"><span class="std std-ref">Sparse coding with a precomputed dictionary</span></a></p>
<div class="sphx-glr-thumbnail-title">Sparse coding with a precomputed dictionary</div>
</div><div class="sphx-glr-thumbcontainer" tooltip="The dataset used in this example is a preprocessed excerpt of the "Labeled Faces in the Wild", ..."><img alt="" src="../../_images/sphx_glr_plot_face_recognition_thumb.png" />
<p><a class="reference internal" href="../applications/plot_face_recognition.html#sphx-glr-auto-examples-applications-plot-face-recognition-py"><span class="std std-ref">Faces recognition example using eigenfaces and SVMs</span></a></p>
<div class="sphx-glr-thumbnail-title">Faces recognition example using eigenfaces and SVMs</div>
</div><div class="sphx-glr-thumbcontainer" tooltip="Probabilistic PCA and Factor Analysis are probabilistic models. The consequence is that the lik..."><img alt="" src="../../_images/sphx_glr_plot_pca_vs_fa_model_selection_thumb.png" />
<p><a class="reference internal" href="plot_pca_vs_fa_model_selection.html#sphx-glr-auto-examples-decomposition-plot-pca-vs-fa-model-selection-py"><span class="std std-ref">Model selection with Probabilistic PCA and Factor Analysis (FA)</span></a></p>
<div class="sphx-glr-thumbnail-title">Model selection with Probabilistic PCA and Factor Analysis (FA)</div>
</div><div class="sphx-glr-thumbcontainer" tooltip="Investigating the Iris dataset, we see that sepal length, petal length and petal width are high..."><img alt="" src="../../_images/sphx_glr_plot_varimax_fa_thumb.png" />
<p><a class="reference internal" href="plot_varimax_fa.html#sphx-glr-auto-examples-decomposition-plot-varimax-fa-py"><span class="std std-ref">Factor Analysis (with rotation) to visualize patterns</span></a></p>
<div class="sphx-glr-thumbnail-title">Factor Analysis (with rotation) to visualize patterns</div>
</div></div><p class="sphx-glr-signature"><a class="reference external" href="https://sphinx-gallery.github.io">Gallery generated by Sphinx-Gallery</a></p>
</section>
</section>
</section>
</div>
<div class="container">
<footer class="sk-content-footer">
© 2007 - 2024, scikit-learn developers (BSD License).
<a href="../../_sources/auto_examples/decomposition/plot_faces_decomposition.rst.txt" rel="nofollow">Show this page source</a>
</footer>
</div>
</div>
</div>
<script src="../../_static/js/vendor/bootstrap.min.js"></script>
<script>
window.ga=window.ga||function(){(ga.q=ga.q||[]).push(arguments)};ga.l=+new Date;
ga('create', 'UA-22606712-2', 'auto');
ga('set', 'anonymizeIp', true);
ga('send', 'pageview');
</script>
<script async src='https://www.google-analytics.com/analytics.js'></script>
<script defer data-domain="scikit-learn.org" src="https://views.scientific-python.org/js/script.js">
</script>
<script src="../../_static/clipboard.min.js"></script>
<script src="../../_static/copybutton.js"></script>
<script>
$(document).ready(function() {
/* Add a [>>>] button on the top-right corner of code samples to hide
* the >>> and ... prompts and the output and thus make the code
* copyable. */
var div = $('.highlight-python .highlight,' +
'.highlight-python3 .highlight,' +
'.highlight-pycon .highlight,' +
'.highlight-default .highlight')
var pre = div.find('pre');
// get the styles from the current theme
pre.parent().parent().css('position', 'relative');
// create and add the button to all the code blocks that contain >>>
div.each(function(index) {
var jthis = $(this);
// tracebacks (.gt) contain bare text elements that need to be
// wrapped in a span to work with .nextUntil() (see later)
jthis.find('pre:has(.gt)').contents().filter(function() {
return ((this.nodeType == 3) && (this.data.trim().length > 0));
}).wrap('<span>');
});
/*** Add permalink buttons next to glossary terms ***/
$('dl.glossary > dt[id]').append(function() {
return ('<a class="headerlink" href="#' +
this.getAttribute('id') +
'" title="Permalink to this term">¶</a>');
});
});
</script>
<script id="MathJax-script" async src="https://cdn.jsdelivr.net/npm/mathjax@3/es5/tex-chtml.js"></script>
<script src="https://scikit-learn.org/versionwarning.js"></script>
</body>
</html>