forked from scikit-learn/scikit-learn.github.io
-
Notifications
You must be signed in to change notification settings - Fork 0
/
Copy pathsklearn.cluster.KMeans.html
749 lines (705 loc) · 49.8 KB
/
sklearn.cluster.KMeans.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
621
622
623
624
625
626
627
628
629
630
631
632
633
634
635
636
637
638
639
640
641
642
643
644
645
646
647
648
649
650
651
652
653
654
655
656
657
658
659
660
661
662
663
664
665
666
667
668
669
670
671
672
673
674
675
676
677
678
679
680
681
682
683
684
685
686
687
688
689
690
691
692
693
694
695
696
697
698
699
700
701
702
703
704
705
706
707
708
709
710
711
712
713
714
715
716
717
718
719
720
721
722
723
724
725
726
727
728
729
730
731
732
733
734
735
736
737
738
739
740
741
742
743
744
745
746
747
748
749
<!DOCTYPE html>
<!--[if IE 8]><html class="no-js lt-ie9" lang="en" > <![endif]-->
<!--[if gt IE 8]><!--> <html class="no-js" lang="en" > <!--<![endif]-->
<head>
<meta charset="utf-8">
<meta name="viewport" content="width=device-width, initial-scale=1.0">
<title>sklearn.cluster.KMeans — scikit-learn 1.0.dev0 documentation</title>
<link rel="canonical" href="http://scikit-learn.org/stable/modules/generated/sklearn.cluster.KMeans.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/gallery.css" type="text/css" />
<link rel="stylesheet" href="../../_static/gallery-binder.css" type="text/css" />
<link rel="stylesheet" href="../../_static/gallery-dataframe.css" type="text/css" />
<link rel="stylesheet" href="../../_static/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/jquery.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="../classes.html">API</a>
</li>
<li class="nav-item">
<a class="sk-nav-link nav-link" href="../../auto_examples/index.html">Examples</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/v1.0.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="../../developers/index.html">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="../../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/v1.0.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="../../developers/index.html">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="../../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="sk-sidebar-toc-logo">
<a href="../../index.html">
<img
class="sk-brand-img"
src="../../_static/scikit-learn-logo-small.png"
alt="logo"/>
</a>
</div>
<div class="btn-group w-100 mb-2" role="group" aria-label="rellinks">
<a href="sklearn.cluster.FeatureAgglomeration.html" role="button" class="btn sk-btn-rellink py-1" sk-rellink-tooltip="sklearn.cluster.FeatureAgglomeration">Prev</a><a href="../classes.html" role="button" class="btn sk-btn-rellink py-1" sk-rellink-tooltip="API Reference">Up</a>
<a href="sklearn.cluster.MiniBatchKMeans.html" role="button" class="btn sk-btn-rellink py-1" sk-rellink-tooltip="sklearn.cluster.MiniBatchKMeans">Next</a>
</div>
<div class="alert alert-danger p-1 mb-2" role="alert">
<p class="text-center mb-0">
<strong>scikit-learn 1.0.dev0</strong><br/>
<a href="http://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="#"><code class="xref py py-mod docutils literal notranslate"><span class="pre">sklearn.cluster</span></code>.KMeans</a><ul>
<li><a class="reference internal" href="#examples-using-sklearn-cluster-kmeans">Examples using <code class="docutils literal notranslate"><span class="pre">sklearn.cluster.KMeans</span></code></a></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="section" id="sklearn-cluster-kmeans">
<h1><a class="reference internal" href="../classes.html#module-sklearn.cluster" title="sklearn.cluster"><code class="xref py py-mod docutils literal notranslate"><span class="pre">sklearn.cluster</span></code></a>.KMeans<a class="headerlink" href="#sklearn-cluster-kmeans" title="Permalink to this headline">¶</a></h1>
<dl class="py class">
<dt id="sklearn.cluster.KMeans">
<em class="property">class </em><code class="sig-prename descclassname">sklearn.cluster.</code><code class="sig-name descname">KMeans</code><span class="sig-paren">(</span><em class="sig-param"><span class="n">n_clusters</span><span class="o">=</span><span class="default_value">8</span></em>, <em class="sig-param"><span class="o">*</span></em>, <em class="sig-param"><span class="n">init</span><span class="o">=</span><span class="default_value">'k-means++'</span></em>, <em class="sig-param"><span class="n">n_init</span><span class="o">=</span><span class="default_value">10</span></em>, <em class="sig-param"><span class="n">max_iter</span><span class="o">=</span><span class="default_value">300</span></em>, <em class="sig-param"><span class="n">tol</span><span class="o">=</span><span class="default_value">0.0001</span></em>, <em class="sig-param"><span class="n">precompute_distances</span><span class="o">=</span><span class="default_value">'deprecated'</span></em>, <em class="sig-param"><span class="n">verbose</span><span class="o">=</span><span class="default_value">0</span></em>, <em class="sig-param"><span class="n">random_state</span><span class="o">=</span><span class="default_value">None</span></em>, <em class="sig-param"><span class="n">copy_x</span><span class="o">=</span><span class="default_value">True</span></em>, <em class="sig-param"><span class="n">n_jobs</span><span class="o">=</span><span class="default_value">'deprecated'</span></em>, <em class="sig-param"><span class="n">algorithm</span><span class="o">=</span><span class="default_value">'auto'</span></em><span class="sig-paren">)</span><a class="reference external" href="https://github.com/scikit-learn/scikit-learn/blob/23d876161/sklearn/cluster/_kmeans.py#L605"><span class="viewcode-link">[source]</span></a><a class="headerlink" href="#sklearn.cluster.KMeans" title="Permalink to this definition">¶</a></dt>
<dd><p>K-Means clustering.</p>
<p>Read more in the <a class="reference internal" href="../clustering.html#k-means"><span class="std std-ref">User Guide</span></a>.</p>
<dl class="field-list">
<dt class="field-odd">Parameters</dt>
<dd class="field-odd"><dl>
<dt><strong>n_clusters</strong><span class="classifier">int, default=8</span></dt><dd><p>The number of clusters to form as well as the number of
centroids to generate.</p>
</dd>
<dt><strong>init</strong><span class="classifier">{‘k-means++’, ‘random’}, callable or array-like of shape (n_clusters, n_features), default=’k-means++’</span></dt><dd><p>Method for initialization:</p>
<p>‘k-means++’ : selects initial cluster centers for k-mean
clustering in a smart way to speed up convergence. See section
Notes in k_init for more details.</p>
<p>‘random’: choose <code class="docutils literal notranslate"><span class="pre">n_clusters</span></code> observations (rows) at random from data
for the initial centroids.</p>
<p>If an array is passed, it should be of shape (n_clusters, n_features)
and gives the initial centers.</p>
<p>If a callable is passed, it should take arguments X, n_clusters and a
random state and return an initialization.</p>
</dd>
<dt><strong>n_init</strong><span class="classifier">int, default=10</span></dt><dd><p>Number of time the k-means algorithm will be run with different
centroid seeds. The final results will be the best output of
n_init consecutive runs in terms of inertia.</p>
</dd>
<dt><strong>max_iter</strong><span class="classifier">int, default=300</span></dt><dd><p>Maximum number of iterations of the k-means algorithm for a
single run.</p>
</dd>
<dt><strong>tol</strong><span class="classifier">float, default=1e-4</span></dt><dd><p>Relative tolerance with regards to Frobenius norm of the difference
in the cluster centers of two consecutive iterations to declare
convergence.</p>
</dd>
<dt><strong>precompute_distances</strong><span class="classifier">{‘auto’, True, False}, default=’auto’</span></dt><dd><p>Precompute distances (faster but takes more memory).</p>
<p>‘auto’ : do not precompute distances if n_samples * n_clusters > 12
million. This corresponds to about 100MB overhead per job using
double precision.</p>
<p>True : always precompute distances.</p>
<p>False : never precompute distances.</p>
<div class="deprecated">
<p><span class="versionmodified deprecated">Deprecated since version 0.23: </span>‘precompute_distances’ was deprecated in version 0.22 and will be
removed in 1.0 (renaming of 0.25). It has no effect.</p>
</div>
</dd>
<dt><strong>verbose</strong><span class="classifier">int, default=0</span></dt><dd><p>Verbosity mode.</p>
</dd>
<dt><strong>random_state</strong><span class="classifier">int, RandomState instance or None, default=None</span></dt><dd><p>Determines random number generation for centroid initialization. Use
an int to make the randomness deterministic.
See <a class="reference internal" href="../../glossary.html#term-random_state"><span class="xref std std-term">Glossary</span></a>.</p>
</dd>
<dt><strong>copy_x</strong><span class="classifier">bool, default=True</span></dt><dd><p>When pre-computing distances it is more numerically accurate to center
the data first. If copy_x is True (default), then the original data is
not modified. If False, the original data is modified, and put back
before the function returns, but small numerical differences may be
introduced by subtracting and then adding the data mean. Note that if
the original data is not C-contiguous, a copy will be made even if
copy_x is False. If the original data is sparse, but not in CSR format,
a copy will be made even if copy_x is False.</p>
</dd>
<dt><strong>n_jobs</strong><span class="classifier">int, default=None</span></dt><dd><p>The number of OpenMP threads to use for the computation. Parallelism is
sample-wise on the main cython loop which assigns each sample to its
closest center.</p>
<p><code class="docutils literal notranslate"><span class="pre">None</span></code> or <code class="docutils literal notranslate"><span class="pre">-1</span></code> means using all processors.</p>
<div class="deprecated">
<p><span class="versionmodified deprecated">Deprecated since version 0.23: </span><code class="docutils literal notranslate"><span class="pre">n_jobs</span></code> was deprecated in version 0.23 and will be removed in
1.0 (renaming of 0.25).</p>
</div>
</dd>
<dt><strong>algorithm</strong><span class="classifier">{“auto”, “full”, “elkan”}, default=”auto”</span></dt><dd><p>K-means algorithm to use. The classical EM-style algorithm is “full”.
The “elkan” variation is more efficient on data with well-defined
clusters, by using the triangle inequality. However it’s more memory
intensive due to the allocation of an extra array of shape
(n_samples, n_clusters).</p>
<p>For now “auto” (kept for backward compatibiliy) chooses “elkan” but it
might change in the future for a better heuristic.</p>
<div class="versionchanged">
<p><span class="versionmodified changed">Changed in version 0.18: </span>Added Elkan algorithm</p>
</div>
</dd>
</dl>
</dd>
<dt class="field-even">Attributes</dt>
<dd class="field-even"><dl class="simple">
<dt><strong>cluster_centers_</strong><span class="classifier">ndarray of shape (n_clusters, n_features)</span></dt><dd><p>Coordinates of cluster centers. If the algorithm stops before fully
converging (see <code class="docutils literal notranslate"><span class="pre">tol</span></code> and <code class="docutils literal notranslate"><span class="pre">max_iter</span></code>), these will not be
consistent with <code class="docutils literal notranslate"><span class="pre">labels_</span></code>.</p>
</dd>
<dt><strong>labels_</strong><span class="classifier">ndarray of shape (n_samples,)</span></dt><dd><p>Labels of each point</p>
</dd>
<dt><strong>inertia_</strong><span class="classifier">float</span></dt><dd><p>Sum of squared distances of samples to their closest cluster center.</p>
</dd>
<dt><strong>n_iter_</strong><span class="classifier">int</span></dt><dd><p>Number of iterations run.</p>
</dd>
</dl>
</dd>
</dl>
<div class="admonition seealso">
<p class="admonition-title">See also</p>
<dl class="simple">
<dt><a class="reference internal" href="sklearn.cluster.MiniBatchKMeans.html#sklearn.cluster.MiniBatchKMeans" title="sklearn.cluster.MiniBatchKMeans"><code class="xref py py-obj docutils literal notranslate"><span class="pre">MiniBatchKMeans</span></code></a></dt><dd><p>Alternative online implementation that does incremental updates of the centers positions using mini-batches. For large scale learning (say n_samples > 10k) MiniBatchKMeans is probably much faster than the default batch implementation.</p>
</dd>
</dl>
</div>
<p class="rubric">Notes</p>
<p>The k-means problem is solved using either Lloyd’s or Elkan’s algorithm.</p>
<p>The average complexity is given by O(k n T), were n is the number of
samples and T is the number of iteration.</p>
<p>The worst case complexity is given by O(n^(k+2/p)) with
n = n_samples, p = n_features. (D. Arthur and S. Vassilvitskii,
‘How slow is the k-means method?’ SoCG2006)</p>
<p>In practice, the k-means algorithm is very fast (one of the fastest
clustering algorithms available), but it falls in local minima. That’s why
it can be useful to restart it several times.</p>
<p>If the algorithm stops before fully converging (because of <code class="docutils literal notranslate"><span class="pre">tol</span></code> or
<code class="docutils literal notranslate"><span class="pre">max_iter</span></code>), <code class="docutils literal notranslate"><span class="pre">labels_</span></code> and <code class="docutils literal notranslate"><span class="pre">cluster_centers_</span></code> will not be consistent,
i.e. the <code class="docutils literal notranslate"><span class="pre">cluster_centers_</span></code> will not be the means of the points in each
cluster. Also, the estimator will reassign <code class="docutils literal notranslate"><span class="pre">labels_</span></code> after the last
iteration to make <code class="docutils literal notranslate"><span class="pre">labels_</span></code> consistent with <code class="docutils literal notranslate"><span class="pre">predict</span></code> on the training
set.</p>
<p class="rubric">Examples</p>
<div class="doctest highlight-default notranslate"><div class="highlight"><pre><span></span><span class="gp">>>> </span><span class="kn">from</span> <span class="nn">sklearn.cluster</span> <span class="kn">import</span> <span class="n">KMeans</span>
<span class="gp">>>> </span><span class="kn">import</span> <span class="nn">numpy</span> <span class="k">as</span> <span class="nn">np</span>
<span class="gp">>>> </span><span class="n">X</span> <span class="o">=</span> <span class="n">np</span><span class="o">.</span><span class="n">array</span><span class="p">([[</span><span class="mi">1</span><span class="p">,</span> <span class="mi">2</span><span class="p">],</span> <span class="p">[</span><span class="mi">1</span><span class="p">,</span> <span class="mi">4</span><span class="p">],</span> <span class="p">[</span><span class="mi">1</span><span class="p">,</span> <span class="mi">0</span><span class="p">],</span>
<span class="gp">... </span> <span class="p">[</span><span class="mi">10</span><span class="p">,</span> <span class="mi">2</span><span class="p">],</span> <span class="p">[</span><span class="mi">10</span><span class="p">,</span> <span class="mi">4</span><span class="p">],</span> <span class="p">[</span><span class="mi">10</span><span class="p">,</span> <span class="mi">0</span><span class="p">]])</span>
<span class="gp">>>> </span><span class="n">kmeans</span> <span class="o">=</span> <span class="n">KMeans</span><span class="p">(</span><span class="n">n_clusters</span><span class="o">=</span><span class="mi">2</span><span class="p">,</span> <span class="n">random_state</span><span class="o">=</span><span class="mi">0</span><span class="p">)</span><span class="o">.</span><span class="n">fit</span><span class="p">(</span><span class="n">X</span><span class="p">)</span>
<span class="gp">>>> </span><span class="n">kmeans</span><span class="o">.</span><span class="n">labels_</span>
<span class="go">array([1, 1, 1, 0, 0, 0], dtype=int32)</span>
<span class="gp">>>> </span><span class="n">kmeans</span><span class="o">.</span><span class="n">predict</span><span class="p">([[</span><span class="mi">0</span><span class="p">,</span> <span class="mi">0</span><span class="p">],</span> <span class="p">[</span><span class="mi">12</span><span class="p">,</span> <span class="mi">3</span><span class="p">]])</span>
<span class="go">array([1, 0], dtype=int32)</span>
<span class="gp">>>> </span><span class="n">kmeans</span><span class="o">.</span><span class="n">cluster_centers_</span>
<span class="go">array([[10., 2.],</span>
<span class="go"> [ 1., 2.]])</span>
</pre></div>
</div>
<p class="rubric">Methods</p>
<table class="longtable docutils align-default">
<colgroup>
<col style="width: 10%" />
<col style="width: 90%" />
</colgroup>
<tbody>
<tr class="row-odd"><td><p><a class="reference internal" href="#sklearn.cluster.KMeans.fit" title="sklearn.cluster.KMeans.fit"><code class="xref py py-obj docutils literal notranslate"><span class="pre">fit</span></code></a>(X[, y, sample_weight])</p></td>
<td><p>Compute k-means clustering.</p></td>
</tr>
<tr class="row-even"><td><p><a class="reference internal" href="#sklearn.cluster.KMeans.fit_predict" title="sklearn.cluster.KMeans.fit_predict"><code class="xref py py-obj docutils literal notranslate"><span class="pre">fit_predict</span></code></a>(X[, y, sample_weight])</p></td>
<td><p>Compute cluster centers and predict cluster index for each sample.</p></td>
</tr>
<tr class="row-odd"><td><p><a class="reference internal" href="#sklearn.cluster.KMeans.fit_transform" title="sklearn.cluster.KMeans.fit_transform"><code class="xref py py-obj docutils literal notranslate"><span class="pre">fit_transform</span></code></a>(X[, y, sample_weight])</p></td>
<td><p>Compute clustering and transform X to cluster-distance space.</p></td>
</tr>
<tr class="row-even"><td><p><a class="reference internal" href="#sklearn.cluster.KMeans.get_params" title="sklearn.cluster.KMeans.get_params"><code class="xref py py-obj docutils literal notranslate"><span class="pre">get_params</span></code></a>([deep])</p></td>
<td><p>Get parameters for this estimator.</p></td>
</tr>
<tr class="row-odd"><td><p><a class="reference internal" href="#sklearn.cluster.KMeans.predict" title="sklearn.cluster.KMeans.predict"><code class="xref py py-obj docutils literal notranslate"><span class="pre">predict</span></code></a>(X[, sample_weight])</p></td>
<td><p>Predict the closest cluster each sample in X belongs to.</p></td>
</tr>
<tr class="row-even"><td><p><a class="reference internal" href="#sklearn.cluster.KMeans.score" title="sklearn.cluster.KMeans.score"><code class="xref py py-obj docutils literal notranslate"><span class="pre">score</span></code></a>(X[, y, sample_weight])</p></td>
<td><p>Opposite of the value of X on the K-means objective.</p></td>
</tr>
<tr class="row-odd"><td><p><a class="reference internal" href="#sklearn.cluster.KMeans.set_params" title="sklearn.cluster.KMeans.set_params"><code class="xref py py-obj docutils literal notranslate"><span class="pre">set_params</span></code></a>(**params)</p></td>
<td><p>Set the parameters of this estimator.</p></td>
</tr>
<tr class="row-even"><td><p><a class="reference internal" href="#sklearn.cluster.KMeans.transform" title="sklearn.cluster.KMeans.transform"><code class="xref py py-obj docutils literal notranslate"><span class="pre">transform</span></code></a>(X)</p></td>
<td><p>Transform X to a cluster-distance space.</p></td>
</tr>
</tbody>
</table>
<dl class="py method">
<dt id="sklearn.cluster.KMeans.fit">
<code class="sig-name descname">fit</code><span class="sig-paren">(</span><em class="sig-param"><span class="n">X</span></em>, <em class="sig-param"><span class="n">y</span><span class="o">=</span><span class="default_value">None</span></em>, <em class="sig-param"><span class="n">sample_weight</span><span class="o">=</span><span class="default_value">None</span></em><span class="sig-paren">)</span><a class="reference external" href="https://github.com/scikit-learn/scikit-learn/blob/23d876161/sklearn/cluster/_kmeans.py#L954"><span class="viewcode-link">[source]</span></a><a class="headerlink" href="#sklearn.cluster.KMeans.fit" title="Permalink to this definition">¶</a></dt>
<dd><p>Compute k-means clustering.</p>
<dl class="field-list">
<dt class="field-odd">Parameters</dt>
<dd class="field-odd"><dl>
<dt><strong>X</strong><span class="classifier">{array-like, sparse matrix} of shape (n_samples, n_features)</span></dt><dd><p>Training instances to cluster. It must be noted that the data
will be converted to C ordering, which will cause a memory
copy if the given data is not C-contiguous.
If a sparse matrix is passed, a copy will be made if it’s not in
CSR format.</p>
</dd>
<dt><strong>y</strong><span class="classifier">Ignored</span></dt><dd><p>Not used, present here for API consistency by convention.</p>
</dd>
<dt><strong>sample_weight</strong><span class="classifier">array-like of shape (n_samples,), default=None</span></dt><dd><p>The weights for each observation in X. If None, all observations
are assigned equal weight.</p>
<div class="versionadded">
<p><span class="versionmodified added">New in version 0.20.</span></p>
</div>
</dd>
</dl>
</dd>
<dt class="field-even">Returns</dt>
<dd class="field-even"><dl class="simple">
<dt>self</dt><dd><p>Fitted estimator.</p>
</dd>
</dl>
</dd>
</dl>
</dd></dl>
<dl class="py method">
<dt id="sklearn.cluster.KMeans.fit_predict">
<code class="sig-name descname">fit_predict</code><span class="sig-paren">(</span><em class="sig-param"><span class="n">X</span></em>, <em class="sig-param"><span class="n">y</span><span class="o">=</span><span class="default_value">None</span></em>, <em class="sig-param"><span class="n">sample_weight</span><span class="o">=</span><span class="default_value">None</span></em><span class="sig-paren">)</span><a class="reference external" href="https://github.com/scikit-learn/scikit-learn/blob/23d876161/sklearn/cluster/_kmeans.py#L1055"><span class="viewcode-link">[source]</span></a><a class="headerlink" href="#sklearn.cluster.KMeans.fit_predict" title="Permalink to this definition">¶</a></dt>
<dd><p>Compute cluster centers and predict cluster index for each sample.</p>
<p>Convenience method; equivalent to calling fit(X) followed by
predict(X).</p>
<dl class="field-list simple">
<dt class="field-odd">Parameters</dt>
<dd class="field-odd"><dl class="simple">
<dt><strong>X</strong><span class="classifier">{array-like, sparse matrix} of shape (n_samples, n_features)</span></dt><dd><p>New data to transform.</p>
</dd>
<dt><strong>y</strong><span class="classifier">Ignored</span></dt><dd><p>Not used, present here for API consistency by convention.</p>
</dd>
<dt><strong>sample_weight</strong><span class="classifier">array-like of shape (n_samples,), default=None</span></dt><dd><p>The weights for each observation in X. If None, all observations
are assigned equal weight.</p>
</dd>
</dl>
</dd>
<dt class="field-even">Returns</dt>
<dd class="field-even"><dl class="simple">
<dt><strong>labels</strong><span class="classifier">ndarray of shape (n_samples,)</span></dt><dd><p>Index of the cluster each sample belongs to.</p>
</dd>
</dl>
</dd>
</dl>
</dd></dl>
<dl class="py method">
<dt id="sklearn.cluster.KMeans.fit_transform">
<code class="sig-name descname">fit_transform</code><span class="sig-paren">(</span><em class="sig-param"><span class="n">X</span></em>, <em class="sig-param"><span class="n">y</span><span class="o">=</span><span class="default_value">None</span></em>, <em class="sig-param"><span class="n">sample_weight</span><span class="o">=</span><span class="default_value">None</span></em><span class="sig-paren">)</span><a class="reference external" href="https://github.com/scikit-learn/scikit-learn/blob/23d876161/sklearn/cluster/_kmeans.py#L1080"><span class="viewcode-link">[source]</span></a><a class="headerlink" href="#sklearn.cluster.KMeans.fit_transform" title="Permalink to this definition">¶</a></dt>
<dd><p>Compute clustering and transform X to cluster-distance space.</p>
<p>Equivalent to fit(X).transform(X), but more efficiently implemented.</p>
<dl class="field-list simple">
<dt class="field-odd">Parameters</dt>
<dd class="field-odd"><dl class="simple">
<dt><strong>X</strong><span class="classifier">{array-like, sparse matrix} of shape (n_samples, n_features)</span></dt><dd><p>New data to transform.</p>
</dd>
<dt><strong>y</strong><span class="classifier">Ignored</span></dt><dd><p>Not used, present here for API consistency by convention.</p>
</dd>
<dt><strong>sample_weight</strong><span class="classifier">array-like of shape (n_samples,), default=None</span></dt><dd><p>The weights for each observation in X. If None, all observations
are assigned equal weight.</p>
</dd>
</dl>
</dd>
<dt class="field-even">Returns</dt>
<dd class="field-even"><dl class="simple">
<dt><strong>X_new</strong><span class="classifier">ndarray of shape (n_samples, n_clusters)</span></dt><dd><p>X transformed in the new space.</p>
</dd>
</dl>
</dd>
</dl>
</dd></dl>
<dl class="py method">
<dt id="sklearn.cluster.KMeans.get_params">
<code class="sig-name descname">get_params</code><span class="sig-paren">(</span><em class="sig-param"><span class="n">deep</span><span class="o">=</span><span class="default_value">True</span></em><span class="sig-paren">)</span><a class="reference external" href="https://github.com/scikit-learn/scikit-learn/blob/23d876161/sklearn/base.py#L178"><span class="viewcode-link">[source]</span></a><a class="headerlink" href="#sklearn.cluster.KMeans.get_params" title="Permalink to this definition">¶</a></dt>
<dd><p>Get parameters for this estimator.</p>
<dl class="field-list simple">
<dt class="field-odd">Parameters</dt>
<dd class="field-odd"><dl class="simple">
<dt><strong>deep</strong><span class="classifier">bool, default=True</span></dt><dd><p>If True, will return the parameters for this estimator and
contained subobjects that are estimators.</p>
</dd>
</dl>
</dd>
<dt class="field-even">Returns</dt>
<dd class="field-even"><dl class="simple">
<dt><strong>params</strong><span class="classifier">dict</span></dt><dd><p>Parameter names mapped to their values.</p>
</dd>
</dl>
</dd>
</dl>
</dd></dl>
<dl class="py method">
<dt id="sklearn.cluster.KMeans.predict">
<code class="sig-name descname">predict</code><span class="sig-paren">(</span><em class="sig-param"><span class="n">X</span></em>, <em class="sig-param"><span class="n">sample_weight</span><span class="o">=</span><span class="default_value">None</span></em><span class="sig-paren">)</span><a class="reference external" href="https://github.com/scikit-learn/scikit-learn/blob/23d876161/sklearn/cluster/_kmeans.py#L1134"><span class="viewcode-link">[source]</span></a><a class="headerlink" href="#sklearn.cluster.KMeans.predict" title="Permalink to this definition">¶</a></dt>
<dd><p>Predict the closest cluster each sample in X belongs to.</p>
<p>In the vector quantization literature, <code class="docutils literal notranslate"><span class="pre">cluster_centers_</span></code> is called
the code book and each value returned by <code class="docutils literal notranslate"><span class="pre">predict</span></code> is the index of
the closest code in the code book.</p>
<dl class="field-list simple">
<dt class="field-odd">Parameters</dt>
<dd class="field-odd"><dl class="simple">
<dt><strong>X</strong><span class="classifier">{array-like, sparse matrix} of shape (n_samples, n_features)</span></dt><dd><p>New data to predict.</p>
</dd>
<dt><strong>sample_weight</strong><span class="classifier">array-like of shape (n_samples,), default=None</span></dt><dd><p>The weights for each observation in X. If None, all observations
are assigned equal weight.</p>
</dd>
</dl>
</dd>
<dt class="field-even">Returns</dt>
<dd class="field-even"><dl class="simple">
<dt><strong>labels</strong><span class="classifier">ndarray of shape (n_samples,)</span></dt><dd><p>Index of the cluster each sample belongs to.</p>
</dd>
</dl>
</dd>
</dl>
</dd></dl>
<dl class="py method">
<dt id="sklearn.cluster.KMeans.score">
<code class="sig-name descname">score</code><span class="sig-paren">(</span><em class="sig-param"><span class="n">X</span></em>, <em class="sig-param"><span class="n">y</span><span class="o">=</span><span class="default_value">None</span></em>, <em class="sig-param"><span class="n">sample_weight</span><span class="o">=</span><span class="default_value">None</span></em><span class="sig-paren">)</span><a class="reference external" href="https://github.com/scikit-learn/scikit-learn/blob/23d876161/sklearn/cluster/_kmeans.py#L1164"><span class="viewcode-link">[source]</span></a><a class="headerlink" href="#sklearn.cluster.KMeans.score" title="Permalink to this definition">¶</a></dt>
<dd><p>Opposite of the value of X on the K-means objective.</p>
<dl class="field-list simple">
<dt class="field-odd">Parameters</dt>
<dd class="field-odd"><dl class="simple">
<dt><strong>X</strong><span class="classifier">{array-like, sparse matrix} of shape (n_samples, n_features)</span></dt><dd><p>New data.</p>
</dd>
<dt><strong>y</strong><span class="classifier">Ignored</span></dt><dd><p>Not used, present here for API consistency by convention.</p>
</dd>
<dt><strong>sample_weight</strong><span class="classifier">array-like of shape (n_samples,), default=None</span></dt><dd><p>The weights for each observation in X. If None, all observations
are assigned equal weight.</p>
</dd>
</dl>
</dd>
<dt class="field-even">Returns</dt>
<dd class="field-even"><dl class="simple">
<dt><strong>score</strong><span class="classifier">float</span></dt><dd><p>Opposite of the value of X on the K-means objective.</p>
</dd>
</dl>
</dd>
</dl>
</dd></dl>
<dl class="py method">
<dt id="sklearn.cluster.KMeans.set_params">
<code class="sig-name descname">set_params</code><span class="sig-paren">(</span><em class="sig-param"><span class="o">**</span><span class="n">params</span></em><span class="sig-paren">)</span><a class="reference external" href="https://github.com/scikit-learn/scikit-learn/blob/23d876161/sklearn/base.py#L202"><span class="viewcode-link">[source]</span></a><a class="headerlink" href="#sklearn.cluster.KMeans.set_params" title="Permalink to this definition">¶</a></dt>
<dd><p>Set the parameters of this estimator.</p>
<p>The method works on simple estimators as well as on nested objects
(such as <a class="reference internal" href="sklearn.pipeline.Pipeline.html#sklearn.pipeline.Pipeline" title="sklearn.pipeline.Pipeline"><code class="xref py py-class docutils literal notranslate"><span class="pre">Pipeline</span></code></a>). The latter have
parameters of the form <code class="docutils literal notranslate"><span class="pre"><component>__<parameter></span></code> so that it’s
possible to update each component of a nested object.</p>
<dl class="field-list simple">
<dt class="field-odd">Parameters</dt>
<dd class="field-odd"><dl class="simple">
<dt><strong>**params</strong><span class="classifier">dict</span></dt><dd><p>Estimator parameters.</p>
</dd>
</dl>
</dd>
<dt class="field-even">Returns</dt>
<dd class="field-even"><dl class="simple">
<dt><strong>self</strong><span class="classifier">estimator instance</span></dt><dd><p>Estimator instance.</p>
</dd>
</dl>
</dd>
</dl>
</dd></dl>
<dl class="py method">
<dt id="sklearn.cluster.KMeans.transform">
<code class="sig-name descname">transform</code><span class="sig-paren">(</span><em class="sig-param"><span class="n">X</span></em><span class="sig-paren">)</span><a class="reference external" href="https://github.com/scikit-learn/scikit-learn/blob/23d876161/sklearn/cluster/_kmeans.py#L1108"><span class="viewcode-link">[source]</span></a><a class="headerlink" href="#sklearn.cluster.KMeans.transform" title="Permalink to this definition">¶</a></dt>
<dd><p>Transform X to a cluster-distance space.</p>
<p>In the new space, each dimension is the distance to the cluster
centers. Note that even if X is sparse, the array returned by
<code class="docutils literal notranslate"><span class="pre">transform</span></code> will typically be dense.</p>
<dl class="field-list simple">
<dt class="field-odd">Parameters</dt>
<dd class="field-odd"><dl class="simple">
<dt><strong>X</strong><span class="classifier">{array-like, sparse matrix} of shape (n_samples, n_features)</span></dt><dd><p>New data to transform.</p>
</dd>
</dl>
</dd>
<dt class="field-even">Returns</dt>
<dd class="field-even"><dl class="simple">
<dt><strong>X_new</strong><span class="classifier">ndarray of shape (n_samples, n_clusters)</span></dt><dd><p>X transformed in the new space.</p>
</dd>
</dl>
</dd>
</dl>
</dd></dl>
</dd></dl>
<div class="section" id="examples-using-sklearn-cluster-kmeans">
<h2>Examples using <code class="docutils literal notranslate"><span class="pre">sklearn.cluster.KMeans</span></code><a class="headerlink" href="#examples-using-sklearn-cluster-kmeans" title="Permalink to this headline">¶</a></h2>
<div class="sphx-glr-thumbcontainer" tooltip="We are pleased to announce the release of scikit-learn 0.23! Many bug fixes and improvements we..."><div class="figure align-default" id="id1">
<img alt="Release Highlights for scikit-learn 0.23" src="../../_images/sphx_glr_plot_release_highlights_0_23_0_thumb.png" />
<p class="caption"><span class="caption-text"><a class="reference internal" href="../../auto_examples/release_highlights/plot_release_highlights_0_23_0.html#sphx-glr-auto-examples-release-highlights-plot-release-highlights-0-23-0-py"><span class="std std-ref">Release Highlights for scikit-learn 0.23</span></a></span><a class="headerlink" href="#id1" title="Permalink to this image">¶</a></p>
</div>
</div><div class="sphx-glr-thumbcontainer" tooltip="This example is meant to illustrate situations where k-means will produce unintuitive and possi..."><div class="figure align-default" id="id2">
<img alt="Demonstration of k-means assumptions" src="../../_images/sphx_glr_plot_kmeans_assumptions_thumb.png" />
<p class="caption"><span class="caption-text"><a class="reference internal" href="../../auto_examples/cluster/plot_kmeans_assumptions.html#sphx-glr-auto-examples-cluster-plot-kmeans-assumptions-py"><span class="std std-ref">Demonstration of k-means assumptions</span></a></span><a class="headerlink" href="#id2" title="Permalink to this image">¶</a></p>
</div>
</div><div class="sphx-glr-thumbcontainer" tooltip="Face, a 1024 x 768 size image of a raccoon face, is used here to illustrate how k-means is used..."><div class="figure align-default" id="id3">
<img alt="Vector Quantization Example" src="../../_images/sphx_glr_plot_face_compress_thumb.png" />
<p class="caption"><span class="caption-text"><a class="reference internal" href="../../auto_examples/cluster/plot_face_compress.html#sphx-glr-auto-examples-cluster-plot-face-compress-py"><span class="std std-ref">Vector Quantization Example</span></a></span><a class="headerlink" href="#id3" title="Permalink to this image">¶</a></p>
</div>
</div><div class="sphx-glr-thumbcontainer" tooltip="The plots display firstly what a K-means algorithm would yield using three clusters. It is then..."><div class="figure align-default" id="id4">
<img alt="K-means Clustering" src="../../_images/sphx_glr_plot_cluster_iris_thumb.png" />
<p class="caption"><span class="caption-text"><a class="reference internal" href="../../auto_examples/cluster/plot_cluster_iris.html#sphx-glr-auto-examples-cluster-plot-cluster-iris-py"><span class="std std-ref">K-means Clustering</span></a></span><a class="headerlink" href="#id4" title="Permalink to this image">¶</a></p>
</div>
</div><div class="sphx-glr-thumbcontainer" tooltip="Performs a pixel-wise Vector Quantization (VQ) of an image of the summer palace (China), reduci..."><div class="figure align-default" id="id5">
<img alt="Color Quantization using K-Means" src="../../_images/sphx_glr_plot_color_quantization_thumb.png" />
<p class="caption"><span class="caption-text"><a class="reference internal" href="../../auto_examples/cluster/plot_color_quantization.html#sphx-glr-auto-examples-cluster-plot-color-quantization-py"><span class="std std-ref">Color Quantization using K-Means</span></a></span><a class="headerlink" href="#id5" title="Permalink to this image">¶</a></p>
</div>
</div><div class="sphx-glr-thumbcontainer" tooltip="Evaluate the ability of k-means initializations strategies to make the algorithm convergence ro..."><div class="figure align-default" id="id6">
<img alt="Empirical evaluation of the impact of k-means initialization" src="../../_images/sphx_glr_plot_kmeans_stability_low_dim_dense_thumb.png" />
<p class="caption"><span class="caption-text"><a class="reference internal" href="../../auto_examples/cluster/plot_kmeans_stability_low_dim_dense.html#sphx-glr-auto-examples-cluster-plot-kmeans-stability-low-dim-dense-py"><span class="std std-ref">Empirical evaluation of the impact of k-means initialization</span></a></span><a class="headerlink" href="#id6" title="Permalink to this image">¶</a></p>
</div>
</div><div class="sphx-glr-thumbcontainer" tooltip="We want to compare the performance of the MiniBatchKMeans and KMeans: the MiniBatchKMeans is fa..."><div class="figure align-default" id="id7">
<img alt="Comparison of the K-Means and MiniBatchKMeans clustering algorithms" src="../../_images/sphx_glr_plot_mini_batch_kmeans_thumb.png" />
<p class="caption"><span class="caption-text"><a class="reference internal" href="../../auto_examples/cluster/plot_mini_batch_kmeans.html#sphx-glr-auto-examples-cluster-plot-mini-batch-kmeans-py"><span class="std std-ref">Comparison of the K-Means and MiniBatchKMeans clustering algorithms</span></a></span><a class="headerlink" href="#id7" title="Permalink to this image">¶</a></p>
</div>
</div><div class="sphx-glr-thumbcontainer" tooltip="In this example we compare the various initialization strategies for K-means in terms of runtim..."><div class="figure align-default" id="id8">
<img alt="A demo of K-Means clustering on the handwritten digits data" src="../../_images/sphx_glr_plot_kmeans_digits_thumb.png" />
<p class="caption"><span class="caption-text"><a class="reference internal" href="../../auto_examples/cluster/plot_kmeans_digits.html#sphx-glr-auto-examples-cluster-plot-kmeans-digits-py"><span class="std std-ref">A demo of K-Means clustering on the handwritten digits data</span></a></span><a class="headerlink" href="#id8" title="Permalink to this image">¶</a></p>
</div>
</div><div class="sphx-glr-thumbcontainer" tooltip="Silhouette analysis can be used to study the separation distance between the resulting clusters..."><div class="figure align-default" id="id9">
<img alt="Selecting the number of clusters with silhouette analysis on KMeans clustering" src="../../_images/sphx_glr_plot_kmeans_silhouette_analysis_thumb.png" />
<p class="caption"><span class="caption-text"><a class="reference internal" href="../../auto_examples/cluster/plot_kmeans_silhouette_analysis.html#sphx-glr-auto-examples-cluster-plot-kmeans-silhouette-analysis-py"><span class="std std-ref">Selecting the number of clusters with silhouette analysis on KMeans clustering</span></a></span><a class="headerlink" href="#id9" title="Permalink to this image">¶</a></p>
</div>
</div><div class="sphx-glr-thumbcontainer" tooltip="This is an example showing how the scikit-learn can be used to cluster documents by topics usin..."><div class="figure align-default" id="id10">
<img alt="Clustering text documents using k-means" src="../../_images/sphx_glr_plot_document_clustering_thumb.png" />
<p class="caption"><span class="caption-text"><a class="reference internal" href="../../auto_examples/text/plot_document_clustering.html#sphx-glr-auto-examples-text-plot-document-clustering-py"><span class="std std-ref">Clustering text documents using k-means</span></a></span><a class="headerlink" href="#id10" title="Permalink to this image">¶</a></p>
</div>
</div><div class="clearer"></div></div>
</div>
</div>
<div class="container">
<footer class="sk-content-footer">
© 2007 - 2020, scikit-learn developers (BSD License).
<a href="../../_sources/modules/generated/sklearn.cluster.KMeans.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>
$(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');
var hide_text = 'Hide prompts and outputs';
var show_text = 'Show prompts and outputs';
// create and add the button to all the code blocks that contain >>>
div.each(function(index) {
var jthis = $(this);
if (jthis.find('.gp').length > 0) {
var button = $('<span class="copybutton">>>></span>');
button.attr('title', hide_text);
button.data('hidden', 'false');
jthis.prepend(button);
}
// 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>');
});
// define the behavior of the button when it's clicked
$('.copybutton').click(function(e){
e.preventDefault();
var button = $(this);
if (button.data('hidden') === 'false') {
// hide the code output
button.parent().find('.go, .gp, .gt').hide();
button.next('pre').find('.gt').nextUntil('.gp, .go').css('visibility', 'hidden');
button.css('text-decoration', 'line-through');
button.attr('title', show_text);
button.data('hidden', 'true');
} else {
// show the code output
button.parent().find('.go, .gp, .gt').show();
button.next('pre').find('.gt').nextUntil('.gp, .go').css('visibility', 'visible');
button.css('text-decoration', 'none');
button.attr('title', hide_text);
button.data('hidden', 'false');
}
});
/*** 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>');
});
/*** Hide navbar when scrolling down ***/
// Returns true when headerlink target matches hash in url
(function() {
hashTargetOnTop = function() {
var hash = window.location.hash;
if ( hash.length < 2 ) { return false; }
var target = document.getElementById( hash.slice(1) );
if ( target === null ) { return false; }
var top = target.getBoundingClientRect().top;
return (top < 2) && (top > -2);
};
// Hide navbar on load if hash target is on top
var navBar = document.getElementById("navbar");
var navBarToggler = document.getElementById("sk-navbar-toggler");
var navBarHeightHidden = "-" + navBar.getBoundingClientRect().height + "px";
var $window = $(window);
hideNavBar = function() {
navBar.style.top = navBarHeightHidden;
};
showNavBar = function() {
navBar.style.top = "0";
}
if (hashTargetOnTop()) {
hideNavBar()
}
var prevScrollpos = window.pageYOffset;
hideOnScroll = function(lastScrollTop) {
if (($window.width() < 768) && (navBarToggler.getAttribute("aria-expanded") === 'true')) {
return;
}
if (lastScrollTop > 2 && (prevScrollpos <= lastScrollTop) || hashTargetOnTop()){
hideNavBar()
} else {
showNavBar()
}
prevScrollpos = lastScrollTop;
};
/*** high performance scroll event listener***/
var raf = window.requestAnimationFrame ||
window.webkitRequestAnimationFrame ||
window.mozRequestAnimationFrame ||
window.msRequestAnimationFrame ||
window.oRequestAnimationFrame;
var lastScrollTop = $window.scrollTop();
if (raf) {
loop();
}
function loop() {
var scrollTop = $window.scrollTop();
if (lastScrollTop === scrollTop) {
raf(loop);
return;
} else {
lastScrollTop = scrollTop;
hideOnScroll(lastScrollTop);
raf(loop);
}
}
})();
});
</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>