-
Notifications
You must be signed in to change notification settings - Fork 81
/
Copy pathplot_all_scaling.html
685 lines (618 loc) · 61.7 KB
/
plot_all_scaling.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
<!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">
<meta name="Description" content="scikit-learn: machine learning in Python">
<title>Compare the effect of different scalers on data with outliers — scikit-learn 0.22.2 documentation</title>
<link rel="canonical" href="https://scikit-learn.org/stable/auto_examples/preprocessing/plot_all_scaling.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/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="../../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 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="../../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="../../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</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="../../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="../../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</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="plot_discretization_classification.html" role="button" class="btn sk-btn-rellink py-1" sk-rellink-tooltip="Feature discretization">Prev</a><a href="../index.html" role="button" class="btn sk-btn-rellink py-1" sk-rellink-tooltip="Examples">Up</a>
<a href="../release_highlights/plot_release_highlights_0_22_0.html" role="button" class="btn sk-btn-rellink py-1" sk-rellink-tooltip="Release Highlights for scikit-learn 0.22">Next</a>
</div>
<div class="alert alert-danger p-1 mb-2" role="alert">
<p class="text-center mb-0">
<strong>scikit-learn 0.22.2</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="#">Compare the effect of different scalers on data with outliers</a><ul>
<li><a class="reference internal" href="#original-data">Original data</a></li>
<li><a class="reference internal" href="#standardscaler">StandardScaler</a></li>
<li><a class="reference internal" href="#minmaxscaler">MinMaxScaler</a></li>
<li><a class="reference internal" href="#maxabsscaler">MaxAbsScaler</a></li>
<li><a class="reference internal" href="#robustscaler">RobustScaler</a></li>
<li><a class="reference internal" href="#powertransformer">PowerTransformer</a></li>
<li><a class="reference internal" href="#quantiletransformer-gaussian-output">QuantileTransformer (Gaussian output)</a></li>
<li><a class="reference internal" href="#quantiletransformer-uniform-output">QuantileTransformer (uniform output)</a></li>
<li><a class="reference internal" href="#normalizer">Normalizer</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="sphx-glr-download-link-note admonition note">
<p class="admonition-title">Note</p>
<p>Click <a class="reference internal" href="#sphx-glr-download-auto-examples-preprocessing-plot-all-scaling-py"><span class="std std-ref">here</span></a> to download the full example code or to run this example in your browser via Binder</p>
</div>
<div class="sphx-glr-example-title section" id="compare-the-effect-of-different-scalers-on-data-with-outliers">
<span id="sphx-glr-auto-examples-preprocessing-plot-all-scaling-py"></span><h1>Compare the effect of different scalers on data with outliers<a class="headerlink" href="#compare-the-effect-of-different-scalers-on-data-with-outliers" title="Permalink to this headline">¶</a></h1>
<p>Feature 0 (median income in a block) and feature 5 (number of households) of
the <a class="reference external" href="https://www.dcc.fc.up.pt/~ltorgo/Regression/cal_housing.html">California housing dataset</a> have very
different scales and contain some very large outliers. These two
characteristics lead to difficulties to visualize the data and, more
importantly, they can degrade the predictive performance of many machine
learning algorithms. Unscaled data can also slow down or even prevent the
convergence of many gradient-based estimators.</p>
<p>Indeed many estimators are designed with the assumption that each feature takes
values close to zero or more importantly that all features vary on comparable
scales. In particular, metric-based and gradient-based estimators often assume
approximately standardized data (centered features with unit variances). A
notable exception are decision tree-based estimators that are robust to
arbitrary scaling of the data.</p>
<p>This example uses different scalers, transformers, and normalizers to bring the
data within a pre-defined range.</p>
<p>Scalers are linear (or more precisely affine) transformers and differ from each
other in the way to estimate the parameters used to shift and scale each
feature.</p>
<p><code class="docutils literal notranslate"><span class="pre">QuantileTransformer</span></code> provides non-linear transformations in which distances
between marginal outliers and inliers are shrunk. <code class="docutils literal notranslate"><span class="pre">PowerTransformer</span></code> provides
non-linear transformations in which data is mapped to a normal distribution to
stabilize variance and minimize skewness.</p>
<p>Unlike the previous transformations, normalization refers to a per sample
transformation instead of a per feature transformation.</p>
<p>The following code is a bit verbose, feel free to jump directly to the analysis
of the <a class="reference internal" href="#results">results</a>.</p>
<div class="highlight-default notranslate"><div class="highlight"><pre><span></span><span class="c1"># Author: Raghav RV <[email protected]></span>
<span class="c1"># Guillaume Lemaitre <[email protected]></span>
<span class="c1"># Thomas Unterthiner</span>
<span class="c1"># License: BSD 3 clause</span>
<span class="kn">import</span> <span class="nn">numpy</span> <span class="k">as</span> <span class="nn">np</span>
<span class="kn">import</span> <span class="nn">matplotlib</span> <span class="k">as</span> <span class="nn">mpl</span>
<span class="kn">from</span> <span class="nn">matplotlib</span> <span class="kn">import</span> <span class="n">pyplot</span> <span class="k">as</span> <span class="n">plt</span>
<span class="kn">from</span> <span class="nn">matplotlib</span> <span class="kn">import</span> <a href="https://matplotlib.org/api/cm_api.html#module-matplotlib.cm" title="View documentation for matplotlib.cm"><span class="n">cm</span></a>
<span class="kn">from</span> <span class="nn">sklearn.preprocessing</span> <span class="kn">import</span> <a href="../../modules/generated/sklearn.preprocessing.MinMaxScaler.html#sklearn.preprocessing.MinMaxScaler" title="View documentation for sklearn.preprocessing.MinMaxScaler"><span class="n">MinMaxScaler</span></a>
<span class="kn">from</span> <span class="nn">sklearn.preprocessing</span> <span class="kn">import</span> <a href="../../modules/generated/sklearn.preprocessing.minmax_scale.html#sklearn.preprocessing.minmax_scale" title="View documentation for sklearn.preprocessing.minmax_scale"><span class="n">minmax_scale</span></a>
<span class="kn">from</span> <span class="nn">sklearn.preprocessing</span> <span class="kn">import</span> <a href="../../modules/generated/sklearn.preprocessing.MaxAbsScaler.html#sklearn.preprocessing.MaxAbsScaler" title="View documentation for sklearn.preprocessing.MaxAbsScaler"><span class="n">MaxAbsScaler</span></a>
<span class="kn">from</span> <span class="nn">sklearn.preprocessing</span> <span class="kn">import</span> <a href="../../modules/generated/sklearn.preprocessing.StandardScaler.html#sklearn.preprocessing.StandardScaler" title="View documentation for sklearn.preprocessing.StandardScaler"><span class="n">StandardScaler</span></a>
<span class="kn">from</span> <span class="nn">sklearn.preprocessing</span> <span class="kn">import</span> <a href="../../modules/generated/sklearn.preprocessing.RobustScaler.html#sklearn.preprocessing.RobustScaler" title="View documentation for sklearn.preprocessing.RobustScaler"><span class="n">RobustScaler</span></a>
<span class="kn">from</span> <span class="nn">sklearn.preprocessing</span> <span class="kn">import</span> <a href="../../modules/generated/sklearn.preprocessing.Normalizer.html#sklearn.preprocessing.Normalizer" title="View documentation for sklearn.preprocessing.Normalizer"><span class="n">Normalizer</span></a>
<span class="kn">from</span> <span class="nn">sklearn.preprocessing</span> <span class="kn">import</span> <a href="../../modules/generated/sklearn.preprocessing.QuantileTransformer.html#sklearn.preprocessing.QuantileTransformer" title="View documentation for sklearn.preprocessing.QuantileTransformer"><span class="n">QuantileTransformer</span></a>
<span class="kn">from</span> <span class="nn">sklearn.preprocessing</span> <span class="kn">import</span> <a href="../../modules/generated/sklearn.preprocessing.PowerTransformer.html#sklearn.preprocessing.PowerTransformer" title="View documentation for sklearn.preprocessing.PowerTransformer"><span class="n">PowerTransformer</span></a>
<span class="kn">from</span> <span class="nn">sklearn.datasets</span> <span class="kn">import</span> <a href="../../modules/generated/sklearn.datasets.fetch_california_housing.html#sklearn.datasets.fetch_california_housing" title="View documentation for sklearn.datasets.fetch_california_housing"><span class="n">fetch_california_housing</span></a>
<span class="nb">print</span><span class="p">(</span><span class="vm">__doc__</span><span class="p">)</span>
<span class="n">dataset</span> <span class="o">=</span> <a href="../../modules/generated/sklearn.datasets.fetch_california_housing.html#sklearn.datasets.fetch_california_housing" title="View documentation for sklearn.datasets.fetch_california_housing"><span class="n">fetch_california_housing</span></a><span class="p">()</span>
<span class="n">X_full</span><span class="p">,</span> <span class="n">y_full</span> <span class="o">=</span> <span class="n">dataset</span><span class="o">.</span><span class="n">data</span><span class="p">,</span> <span class="n">dataset</span><span class="o">.</span><span class="n">target</span>
<span class="c1"># Take only 2 features to make visualization easier</span>
<span class="c1"># Feature of 0 has a long tail distribution.</span>
<span class="c1"># Feature 5 has a few but very large outliers.</span>
<span class="n">X</span> <span class="o">=</span> <span class="n">X_full</span><span class="p">[:,</span> <span class="p">[</span><span class="mi">0</span><span class="p">,</span> <span class="mi">5</span><span class="p">]]</span>
<span class="n">distributions</span> <span class="o">=</span> <span class="p">[</span>
<span class="p">(</span><span class="s1">'Unscaled data'</span><span class="p">,</span> <span class="n">X</span><span class="p">),</span>
<span class="p">(</span><span class="s1">'Data after standard scaling'</span><span class="p">,</span>
<a href="../../modules/generated/sklearn.preprocessing.StandardScaler.html#sklearn.preprocessing.StandardScaler" title="View documentation for sklearn.preprocessing.StandardScaler"><span class="n">StandardScaler</span></a><span class="p">()</span><span class="o">.</span><span class="n">fit_transform</span><span class="p">(</span><span class="n">X</span><span class="p">)),</span>
<span class="p">(</span><span class="s1">'Data after min-max scaling'</span><span class="p">,</span>
<a href="../../modules/generated/sklearn.preprocessing.MinMaxScaler.html#sklearn.preprocessing.MinMaxScaler" title="View documentation for sklearn.preprocessing.MinMaxScaler"><span class="n">MinMaxScaler</span></a><span class="p">()</span><span class="o">.</span><span class="n">fit_transform</span><span class="p">(</span><span class="n">X</span><span class="p">)),</span>
<span class="p">(</span><span class="s1">'Data after max-abs scaling'</span><span class="p">,</span>
<a href="../../modules/generated/sklearn.preprocessing.MaxAbsScaler.html#sklearn.preprocessing.MaxAbsScaler" title="View documentation for sklearn.preprocessing.MaxAbsScaler"><span class="n">MaxAbsScaler</span></a><span class="p">()</span><span class="o">.</span><span class="n">fit_transform</span><span class="p">(</span><span class="n">X</span><span class="p">)),</span>
<span class="p">(</span><span class="s1">'Data after robust scaling'</span><span class="p">,</span>
<a href="../../modules/generated/sklearn.preprocessing.RobustScaler.html#sklearn.preprocessing.RobustScaler" title="View documentation for sklearn.preprocessing.RobustScaler"><span class="n">RobustScaler</span></a><span class="p">(</span><span class="n">quantile_range</span><span class="o">=</span><span class="p">(</span><span class="mi">25</span><span class="p">,</span> <span class="mi">75</span><span class="p">))</span><span class="o">.</span><span class="n">fit_transform</span><span class="p">(</span><span class="n">X</span><span class="p">)),</span>
<span class="p">(</span><span class="s1">'Data after power transformation (Yeo-Johnson)'</span><span class="p">,</span>
<a href="../../modules/generated/sklearn.preprocessing.PowerTransformer.html#sklearn.preprocessing.PowerTransformer" title="View documentation for sklearn.preprocessing.PowerTransformer"><span class="n">PowerTransformer</span></a><span class="p">(</span><span class="n">method</span><span class="o">=</span><span class="s1">'yeo-johnson'</span><span class="p">)</span><span class="o">.</span><span class="n">fit_transform</span><span class="p">(</span><span class="n">X</span><span class="p">)),</span>
<span class="p">(</span><span class="s1">'Data after power transformation (Box-Cox)'</span><span class="p">,</span>
<a href="../../modules/generated/sklearn.preprocessing.PowerTransformer.html#sklearn.preprocessing.PowerTransformer" title="View documentation for sklearn.preprocessing.PowerTransformer"><span class="n">PowerTransformer</span></a><span class="p">(</span><span class="n">method</span><span class="o">=</span><span class="s1">'box-cox'</span><span class="p">)</span><span class="o">.</span><span class="n">fit_transform</span><span class="p">(</span><span class="n">X</span><span class="p">)),</span>
<span class="p">(</span><span class="s1">'Data after quantile transformation (gaussian pdf)'</span><span class="p">,</span>
<a href="../../modules/generated/sklearn.preprocessing.QuantileTransformer.html#sklearn.preprocessing.QuantileTransformer" title="View documentation for sklearn.preprocessing.QuantileTransformer"><span class="n">QuantileTransformer</span></a><span class="p">(</span><span class="n">output_distribution</span><span class="o">=</span><span class="s1">'normal'</span><span class="p">)</span>
<span class="o">.</span><span class="n">fit_transform</span><span class="p">(</span><span class="n">X</span><span class="p">)),</span>
<span class="p">(</span><span class="s1">'Data after quantile transformation (uniform pdf)'</span><span class="p">,</span>
<a href="../../modules/generated/sklearn.preprocessing.QuantileTransformer.html#sklearn.preprocessing.QuantileTransformer" title="View documentation for sklearn.preprocessing.QuantileTransformer"><span class="n">QuantileTransformer</span></a><span class="p">(</span><span class="n">output_distribution</span><span class="o">=</span><span class="s1">'uniform'</span><span class="p">)</span>
<span class="o">.</span><span class="n">fit_transform</span><span class="p">(</span><span class="n">X</span><span class="p">)),</span>
<span class="p">(</span><span class="s1">'Data after sample-wise L2 normalizing'</span><span class="p">,</span>
<a href="../../modules/generated/sklearn.preprocessing.Normalizer.html#sklearn.preprocessing.Normalizer" title="View documentation for sklearn.preprocessing.Normalizer"><span class="n">Normalizer</span></a><span class="p">()</span><span class="o">.</span><span class="n">fit_transform</span><span class="p">(</span><span class="n">X</span><span class="p">)),</span>
<span class="p">]</span>
<span class="c1"># scale the output between 0 and 1 for the colorbar</span>
<span class="n">y</span> <span class="o">=</span> <a href="../../modules/generated/sklearn.preprocessing.minmax_scale.html#sklearn.preprocessing.minmax_scale" title="View documentation for sklearn.preprocessing.minmax_scale"><span class="n">minmax_scale</span></a><span class="p">(</span><span class="n">y_full</span><span class="p">)</span>
<span class="c1"># plasma does not exist in matplotlib < 1.5</span>
<span class="n">cmap</span> <span class="o">=</span> <span class="nb">getattr</span><span class="p">(</span><a href="https://matplotlib.org/api/cm_api.html#module-matplotlib.cm" title="View documentation for matplotlib.cm"><span class="n">cm</span></a><span class="p">,</span> <span class="s1">'plasma_r'</span><span class="p">,</span> <a href="https://matplotlib.org/api/cm_api.html#module-matplotlib.cm" title="View documentation for matplotlib.cm"><span class="n">cm</span></a><span class="o">.</span><span class="n">hot_r</span><span class="p">)</span>
<span class="k">def</span> <span class="nf">create_axes</span><span class="p">(</span><span class="n">title</span><span class="p">,</span> <span class="n">figsize</span><span class="o">=</span><span class="p">(</span><span class="mi">16</span><span class="p">,</span> <span class="mi">6</span><span class="p">)):</span>
<span class="n">fig</span> <span class="o">=</span> <a href="https://matplotlib.org/api/_as_gen/matplotlib.pyplot.figure.html#matplotlib.pyplot.figure" title="View documentation for matplotlib.pyplot.figure"><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="n">figsize</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="c1"># define the axis for the first plot</span>
<span class="n">left</span><span class="p">,</span> <span class="n">width</span> <span class="o">=</span> <span class="mf">0.1</span><span class="p">,</span> <span class="mf">0.22</span>
<span class="n">bottom</span><span class="p">,</span> <span class="n">height</span> <span class="o">=</span> <span class="mf">0.1</span><span class="p">,</span> <span class="mf">0.7</span>
<span class="n">bottom_h</span> <span class="o">=</span> <span class="n">height</span> <span class="o">+</span> <span class="mf">0.15</span>
<span class="n">left_h</span> <span class="o">=</span> <span class="n">left</span> <span class="o">+</span> <span class="n">width</span> <span class="o">+</span> <span class="mf">0.02</span>
<span class="n">rect_scatter</span> <span class="o">=</span> <span class="p">[</span><span class="n">left</span><span class="p">,</span> <span class="n">bottom</span><span class="p">,</span> <span class="n">width</span><span class="p">,</span> <span class="n">height</span><span class="p">]</span>
<span class="n">rect_histx</span> <span class="o">=</span> <span class="p">[</span><span class="n">left</span><span class="p">,</span> <span class="n">bottom_h</span><span class="p">,</span> <span class="n">width</span><span class="p">,</span> <span class="mf">0.1</span><span class="p">]</span>
<span class="n">rect_histy</span> <span class="o">=</span> <span class="p">[</span><span class="n">left_h</span><span class="p">,</span> <span class="n">bottom</span><span class="p">,</span> <span class="mf">0.05</span><span class="p">,</span> <span class="n">height</span><span class="p">]</span>
<span class="n">ax_scatter</span> <span class="o">=</span> <a href="https://matplotlib.org/api/_as_gen/matplotlib.pyplot.axes.html#matplotlib.pyplot.axes" title="View documentation for matplotlib.pyplot.axes"><span class="n">plt</span><span class="o">.</span><span class="n">axes</span></a><span class="p">(</span><span class="n">rect_scatter</span><span class="p">)</span>
<span class="n">ax_histx</span> <span class="o">=</span> <a href="https://matplotlib.org/api/_as_gen/matplotlib.pyplot.axes.html#matplotlib.pyplot.axes" title="View documentation for matplotlib.pyplot.axes"><span class="n">plt</span><span class="o">.</span><span class="n">axes</span></a><span class="p">(</span><span class="n">rect_histx</span><span class="p">)</span>
<span class="n">ax_histy</span> <span class="o">=</span> <a href="https://matplotlib.org/api/_as_gen/matplotlib.pyplot.axes.html#matplotlib.pyplot.axes" title="View documentation for matplotlib.pyplot.axes"><span class="n">plt</span><span class="o">.</span><span class="n">axes</span></a><span class="p">(</span><span class="n">rect_histy</span><span class="p">)</span>
<span class="c1"># define the axis for the zoomed-in plot</span>
<span class="n">left</span> <span class="o">=</span> <span class="n">width</span> <span class="o">+</span> <span class="n">left</span> <span class="o">+</span> <span class="mf">0.2</span>
<span class="n">left_h</span> <span class="o">=</span> <span class="n">left</span> <span class="o">+</span> <span class="n">width</span> <span class="o">+</span> <span class="mf">0.02</span>
<span class="n">rect_scatter</span> <span class="o">=</span> <span class="p">[</span><span class="n">left</span><span class="p">,</span> <span class="n">bottom</span><span class="p">,</span> <span class="n">width</span><span class="p">,</span> <span class="n">height</span><span class="p">]</span>
<span class="n">rect_histx</span> <span class="o">=</span> <span class="p">[</span><span class="n">left</span><span class="p">,</span> <span class="n">bottom_h</span><span class="p">,</span> <span class="n">width</span><span class="p">,</span> <span class="mf">0.1</span><span class="p">]</span>
<span class="n">rect_histy</span> <span class="o">=</span> <span class="p">[</span><span class="n">left_h</span><span class="p">,</span> <span class="n">bottom</span><span class="p">,</span> <span class="mf">0.05</span><span class="p">,</span> <span class="n">height</span><span class="p">]</span>
<span class="n">ax_scatter_zoom</span> <span class="o">=</span> <a href="https://matplotlib.org/api/_as_gen/matplotlib.pyplot.axes.html#matplotlib.pyplot.axes" title="View documentation for matplotlib.pyplot.axes"><span class="n">plt</span><span class="o">.</span><span class="n">axes</span></a><span class="p">(</span><span class="n">rect_scatter</span><span class="p">)</span>
<span class="n">ax_histx_zoom</span> <span class="o">=</span> <a href="https://matplotlib.org/api/_as_gen/matplotlib.pyplot.axes.html#matplotlib.pyplot.axes" title="View documentation for matplotlib.pyplot.axes"><span class="n">plt</span><span class="o">.</span><span class="n">axes</span></a><span class="p">(</span><span class="n">rect_histx</span><span class="p">)</span>
<span class="n">ax_histy_zoom</span> <span class="o">=</span> <a href="https://matplotlib.org/api/_as_gen/matplotlib.pyplot.axes.html#matplotlib.pyplot.axes" title="View documentation for matplotlib.pyplot.axes"><span class="n">plt</span><span class="o">.</span><span class="n">axes</span></a><span class="p">(</span><span class="n">rect_histy</span><span class="p">)</span>
<span class="c1"># define the axis for the colorbar</span>
<span class="n">left</span><span class="p">,</span> <span class="n">width</span> <span class="o">=</span> <span class="n">width</span> <span class="o">+</span> <span class="n">left</span> <span class="o">+</span> <span class="mf">0.13</span><span class="p">,</span> <span class="mf">0.01</span>
<span class="n">rect_colorbar</span> <span class="o">=</span> <span class="p">[</span><span class="n">left</span><span class="p">,</span> <span class="n">bottom</span><span class="p">,</span> <span class="n">width</span><span class="p">,</span> <span class="n">height</span><span class="p">]</span>
<span class="n">ax_colorbar</span> <span class="o">=</span> <a href="https://matplotlib.org/api/_as_gen/matplotlib.pyplot.axes.html#matplotlib.pyplot.axes" title="View documentation for matplotlib.pyplot.axes"><span class="n">plt</span><span class="o">.</span><span class="n">axes</span></a><span class="p">(</span><span class="n">rect_colorbar</span><span class="p">)</span>
<span class="k">return</span> <span class="p">((</span><span class="n">ax_scatter</span><span class="p">,</span> <span class="n">ax_histy</span><span class="p">,</span> <span class="n">ax_histx</span><span class="p">),</span>
<span class="p">(</span><span class="n">ax_scatter_zoom</span><span class="p">,</span> <span class="n">ax_histy_zoom</span><span class="p">,</span> <span class="n">ax_histx_zoom</span><span class="p">),</span>
<span class="n">ax_colorbar</span><span class="p">)</span>
<span class="k">def</span> <span class="nf">plot_distribution</span><span class="p">(</span><span class="n">axes</span><span class="p">,</span> <span class="n">X</span><span class="p">,</span> <span class="n">y</span><span class="p">,</span> <span class="n">hist_nbins</span><span class="o">=</span><span class="mi">50</span><span class="p">,</span> <span class="n">title</span><span class="o">=</span><span class="s2">""</span><span class="p">,</span>
<span class="n">x0_label</span><span class="o">=</span><span class="s2">""</span><span class="p">,</span> <span class="n">x1_label</span><span class="o">=</span><span class="s2">""</span><span class="p">):</span>
<span class="n">ax</span><span class="p">,</span> <span class="n">hist_X1</span><span class="p">,</span> <span class="n">hist_X0</span> <span class="o">=</span> <span class="n">axes</span>
<span class="n">ax</span><span class="o">.</span><span class="n">set_title</span><span class="p">(</span><span class="n">title</span><span class="p">)</span>
<span class="n">ax</span><span class="o">.</span><span class="n">set_xlabel</span><span class="p">(</span><span class="n">x0_label</span><span class="p">)</span>
<span class="n">ax</span><span class="o">.</span><span class="n">set_ylabel</span><span class="p">(</span><span class="n">x1_label</span><span class="p">)</span>
<span class="c1"># The scatter plot</span>
<span class="n">colors</span> <span class="o">=</span> <span class="n">cmap</span><span class="p">(</span><span class="n">y</span><span class="p">)</span>
<span class="n">ax</span><span class="o">.</span><span class="n">scatter</span><span class="p">(</span><span class="n">X</span><span class="p">[:,</span> <span class="mi">0</span><span class="p">],</span> <span class="n">X</span><span class="p">[:,</span> <span class="mi">1</span><span class="p">],</span> <span class="n">alpha</span><span class="o">=</span><span class="mf">0.5</span><span class="p">,</span> <span class="n">marker</span><span class="o">=</span><span class="s1">'o'</span><span class="p">,</span> <span class="n">s</span><span class="o">=</span><span class="mi">5</span><span class="p">,</span> <span class="n">lw</span><span class="o">=</span><span class="mi">0</span><span class="p">,</span> <span class="n">c</span><span class="o">=</span><span class="n">colors</span><span class="p">)</span>
<span class="c1"># Removing the top and the right spine for aesthetics</span>
<span class="c1"># make nice axis layout</span>
<span class="n">ax</span><span class="o">.</span><span class="n">spines</span><span class="p">[</span><span class="s1">'top'</span><span class="p">]</span><span class="o">.</span><span class="n">set_visible</span><span class="p">(</span><span class="kc">False</span><span class="p">)</span>
<span class="n">ax</span><span class="o">.</span><span class="n">spines</span><span class="p">[</span><span class="s1">'right'</span><span class="p">]</span><span class="o">.</span><span class="n">set_visible</span><span class="p">(</span><span class="kc">False</span><span class="p">)</span>
<span class="n">ax</span><span class="o">.</span><span class="n">get_xaxis</span><span class="p">()</span><span class="o">.</span><span class="n">tick_bottom</span><span class="p">()</span>
<span class="n">ax</span><span class="o">.</span><span class="n">get_yaxis</span><span class="p">()</span><span class="o">.</span><span class="n">tick_left</span><span class="p">()</span>
<span class="n">ax</span><span class="o">.</span><span class="n">spines</span><span class="p">[</span><span class="s1">'left'</span><span class="p">]</span><span class="o">.</span><span class="n">set_position</span><span class="p">((</span><span class="s1">'outward'</span><span class="p">,</span> <span class="mi">10</span><span class="p">))</span>
<span class="n">ax</span><span class="o">.</span><span class="n">spines</span><span class="p">[</span><span class="s1">'bottom'</span><span class="p">]</span><span class="o">.</span><span class="n">set_position</span><span class="p">((</span><span class="s1">'outward'</span><span class="p">,</span> <span class="mi">10</span><span class="p">))</span>
<span class="c1"># Histogram for axis X1 (feature 5)</span>
<span class="n">hist_X1</span><span class="o">.</span><span class="n">set_ylim</span><span class="p">(</span><span class="n">ax</span><span class="o">.</span><span class="n">get_ylim</span><span class="p">())</span>
<span class="n">hist_X1</span><span class="o">.</span><span class="n">hist</span><span class="p">(</span><span class="n">X</span><span class="p">[:,</span> <span class="mi">1</span><span class="p">],</span> <span class="n">bins</span><span class="o">=</span><span class="n">hist_nbins</span><span class="p">,</span> <span class="n">orientation</span><span class="o">=</span><span class="s1">'horizontal'</span><span class="p">,</span>
<span class="n">color</span><span class="o">=</span><span class="s1">'grey'</span><span class="p">,</span> <span class="n">ec</span><span class="o">=</span><span class="s1">'grey'</span><span class="p">)</span>
<span class="n">hist_X1</span><span class="o">.</span><span class="n">axis</span><span class="p">(</span><span class="s1">'off'</span><span class="p">)</span>
<span class="c1"># Histogram for axis X0 (feature 0)</span>
<span class="n">hist_X0</span><span class="o">.</span><span class="n">set_xlim</span><span class="p">(</span><span class="n">ax</span><span class="o">.</span><span class="n">get_xlim</span><span class="p">())</span>
<span class="n">hist_X0</span><span class="o">.</span><span class="n">hist</span><span class="p">(</span><span class="n">X</span><span class="p">[:,</span> <span class="mi">0</span><span class="p">],</span> <span class="n">bins</span><span class="o">=</span><span class="n">hist_nbins</span><span class="p">,</span> <span class="n">orientation</span><span class="o">=</span><span class="s1">'vertical'</span><span class="p">,</span>
<span class="n">color</span><span class="o">=</span><span class="s1">'grey'</span><span class="p">,</span> <span class="n">ec</span><span class="o">=</span><span class="s1">'grey'</span><span class="p">)</span>
<span class="n">hist_X0</span><span class="o">.</span><span class="n">axis</span><span class="p">(</span><span class="s1">'off'</span><span class="p">)</span>
</pre></div>
</div>
<p>Two plots will be shown for each scaler/normalizer/transformer. The left
figure will show a scatter plot of the full data set while the right figure
will exclude the extreme values considering only 99 % of the data set,
excluding marginal outliers. In addition, the marginal distributions for each
feature will be shown on the side of the scatter plot.</p>
<div class="highlight-default notranslate"><div class="highlight"><pre><span></span><span class="k">def</span> <span class="nf">make_plot</span><span class="p">(</span><span class="n">item_idx</span><span class="p">):</span>
<span class="n">title</span><span class="p">,</span> <span class="n">X</span> <span class="o">=</span> <span class="n">distributions</span><span class="p">[</span><span class="n">item_idx</span><span class="p">]</span>
<span class="n">ax_zoom_out</span><span class="p">,</span> <span class="n">ax_zoom_in</span><span class="p">,</span> <span class="n">ax_colorbar</span> <span class="o">=</span> <span class="n">create_axes</span><span class="p">(</span><span class="n">title</span><span class="p">)</span>
<span class="n">axarr</span> <span class="o">=</span> <span class="p">(</span><span class="n">ax_zoom_out</span><span class="p">,</span> <span class="n">ax_zoom_in</span><span class="p">)</span>
<span class="n">plot_distribution</span><span class="p">(</span><span class="n">axarr</span><span class="p">[</span><span class="mi">0</span><span class="p">],</span> <span class="n">X</span><span class="p">,</span> <span class="n">y</span><span class="p">,</span> <span class="n">hist_nbins</span><span class="o">=</span><span class="mi">200</span><span class="p">,</span>
<span class="n">x0_label</span><span class="o">=</span><span class="s2">"Median Income"</span><span class="p">,</span>
<span class="n">x1_label</span><span class="o">=</span><span class="s2">"Number of households"</span><span class="p">,</span>
<span class="n">title</span><span class="o">=</span><span class="s2">"Full data"</span><span class="p">)</span>
<span class="c1"># zoom-in</span>
<span class="n">zoom_in_percentile_range</span> <span class="o">=</span> <span class="p">(</span><span class="mi">0</span><span class="p">,</span> <span class="mi">99</span><span class="p">)</span>
<span class="n">cutoffs_X0</span> <span class="o">=</span> <a href="https://docs.scipy.org/doc/numpy/reference/generated/numpy.percentile.html#numpy.percentile" title="View documentation for numpy.percentile"><span class="n">np</span><span class="o">.</span><span class="n">percentile</span></a><span class="p">(</span><span class="n">X</span><span class="p">[:,</span> <span class="mi">0</span><span class="p">],</span> <span class="n">zoom_in_percentile_range</span><span class="p">)</span>
<span class="n">cutoffs_X1</span> <span class="o">=</span> <a href="https://docs.scipy.org/doc/numpy/reference/generated/numpy.percentile.html#numpy.percentile" title="View documentation for numpy.percentile"><span class="n">np</span><span class="o">.</span><span class="n">percentile</span></a><span class="p">(</span><span class="n">X</span><span class="p">[:,</span> <span class="mi">1</span><span class="p">],</span> <span class="n">zoom_in_percentile_range</span><span class="p">)</span>
<span class="n">non_outliers_mask</span> <span class="o">=</span> <span class="p">(</span>
<a href="https://docs.scipy.org/doc/numpy/reference/generated/numpy.all.html#numpy.all" title="View documentation for numpy.all"><span class="n">np</span><span class="o">.</span><span class="n">all</span></a><span class="p">(</span><span class="n">X</span> <span class="o">></span> <span class="p">[</span><span class="n">cutoffs_X0</span><span class="p">[</span><span class="mi">0</span><span class="p">],</span> <span class="n">cutoffs_X1</span><span class="p">[</span><span class="mi">0</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>
<a href="https://docs.scipy.org/doc/numpy/reference/generated/numpy.all.html#numpy.all" title="View documentation for numpy.all"><span class="n">np</span><span class="o">.</span><span class="n">all</span></a><span class="p">(</span><span class="n">X</span> <span class="o"><</span> <span class="p">[</span><span class="n">cutoffs_X0</span><span class="p">[</span><span class="mi">1</span><span class="p">],</span> <span class="n">cutoffs_X1</span><span class="p">[</span><span class="mi">1</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="n">plot_distribution</span><span class="p">(</span><span class="n">axarr</span><span class="p">[</span><span class="mi">1</span><span class="p">],</span> <span class="n">X</span><span class="p">[</span><span class="n">non_outliers_mask</span><span class="p">],</span> <span class="n">y</span><span class="p">[</span><span class="n">non_outliers_mask</span><span class="p">],</span>
<span class="n">hist_nbins</span><span class="o">=</span><span class="mi">50</span><span class="p">,</span>
<span class="n">x0_label</span><span class="o">=</span><span class="s2">"Median Income"</span><span class="p">,</span>
<span class="n">x1_label</span><span class="o">=</span><span class="s2">"Number of households"</span><span class="p">,</span>
<span class="n">title</span><span class="o">=</span><span class="s2">"Zoom-in"</span><span class="p">)</span>
<span class="n">norm</span> <span class="o">=</span> <a href="https://matplotlib.org/api/_as_gen/matplotlib.colors.Normalize.html#matplotlib.colors.Normalize" title="View documentation for matplotlib.colors.Normalize"><span class="n">mpl</span><span class="o">.</span><span class="n">colors</span><span class="o">.</span><span class="n">Normalize</span></a><span class="p">(</span><span class="n">y_full</span><span class="o">.</span><span class="n">min</span><span class="p">(),</span> <span class="n">y_full</span><span class="o">.</span><span class="n">max</span><span class="p">())</span>
<a href="https://matplotlib.org/api/colorbar_api.html#matplotlib.colorbar.ColorbarBase" title="View documentation for matplotlib.colorbar.ColorbarBase"><span class="n">mpl</span><span class="o">.</span><span class="n">colorbar</span><span class="o">.</span><span class="n">ColorbarBase</span></a><span class="p">(</span><span class="n">ax_colorbar</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">norm</span><span class="o">=</span><span class="n">norm</span><span class="p">,</span> <span class="n">orientation</span><span class="o">=</span><span class="s1">'vertical'</span><span class="p">,</span>
<span class="n">label</span><span class="o">=</span><span class="s1">'Color mapping for values of y'</span><span class="p">)</span>
</pre></div>
</div>
<div class="section" id="original-data">
<span id="results"></span><h2>Original data<a class="headerlink" href="#original-data" title="Permalink to this headline">¶</a></h2>
<p>Each transformation is plotted showing two transformed features, with the
left plot showing the entire dataset, and the right zoomed-in to show the
dataset without the marginal outliers. A large majority of the samples are
compacted to a specific range, [0, 10] for the median income and [0, 6] for
the number of households. Note that there are some marginal outliers (some
blocks have more than 1200 households). Therefore, a specific pre-processing
can be very beneficial depending of the application. In the following, we
present some insights and behaviors of those pre-processing methods in the
presence of marginal outliers.</p>
<div class="highlight-default notranslate"><div class="highlight"><pre><span></span><span class="n">make_plot</span><span class="p">(</span><span class="mi">0</span><span class="p">)</span>
</pre></div>
</div>
<img alt="../../_images/sphx_glr_plot_all_scaling_001.png" class="sphx-glr-single-img" src="../../_images/sphx_glr_plot_all_scaling_001.png" />
</div>
<div class="section" id="standardscaler">
<h2>StandardScaler<a class="headerlink" href="#standardscaler" title="Permalink to this headline">¶</a></h2>
<p><code class="docutils literal notranslate"><span class="pre">StandardScaler</span></code> removes the mean and scales the data to unit variance.
However, the outliers have an influence when computing the empirical mean and
standard deviation which shrink the range of the feature values as shown in
the left figure below. Note in particular that because the outliers on each
feature have different magnitudes, the spread of the transformed data on
each feature is very different: most of the data lie in the [-2, 4] range for
the transformed median income feature while the same data is squeezed in the
smaller [-0.2, 0.2] range for the transformed number of households.</p>
<p><code class="docutils literal notranslate"><span class="pre">StandardScaler</span></code> therefore cannot guarantee balanced feature scales in the
presence of outliers.</p>
<div class="highlight-default notranslate"><div class="highlight"><pre><span></span><span class="n">make_plot</span><span class="p">(</span><span class="mi">1</span><span class="p">)</span>
</pre></div>
</div>
<img alt="../../_images/sphx_glr_plot_all_scaling_002.png" class="sphx-glr-single-img" src="../../_images/sphx_glr_plot_all_scaling_002.png" />
</div>
<div class="section" id="minmaxscaler">
<h2>MinMaxScaler<a class="headerlink" href="#minmaxscaler" title="Permalink to this headline">¶</a></h2>
<p><code class="docutils literal notranslate"><span class="pre">MinMaxScaler</span></code> rescales the data set such that all feature values are in
the range [0, 1] as shown in the right panel below. However, this scaling
compress all inliers in the narrow range [0, 0.005] for the transformed
number of households.</p>
<p>As <code class="docutils literal notranslate"><span class="pre">StandardScaler</span></code>, <code class="docutils literal notranslate"><span class="pre">MinMaxScaler</span></code> is very sensitive to the presence of
outliers.</p>
<div class="highlight-default notranslate"><div class="highlight"><pre><span></span><span class="n">make_plot</span><span class="p">(</span><span class="mi">2</span><span class="p">)</span>
</pre></div>
</div>
<img alt="../../_images/sphx_glr_plot_all_scaling_003.png" class="sphx-glr-single-img" src="../../_images/sphx_glr_plot_all_scaling_003.png" />
</div>
<div class="section" id="maxabsscaler">
<h2>MaxAbsScaler<a class="headerlink" href="#maxabsscaler" title="Permalink to this headline">¶</a></h2>
<p><code class="docutils literal notranslate"><span class="pre">MaxAbsScaler</span></code> differs from the previous scaler such that the absolute
values are mapped in the range [0, 1]. On positive only data, this scaler
behaves similarly to <code class="docutils literal notranslate"><span class="pre">MinMaxScaler</span></code> and therefore also suffers from the
presence of large outliers.</p>
<div class="highlight-default notranslate"><div class="highlight"><pre><span></span><span class="n">make_plot</span><span class="p">(</span><span class="mi">3</span><span class="p">)</span>
</pre></div>
</div>
<img alt="../../_images/sphx_glr_plot_all_scaling_004.png" class="sphx-glr-single-img" src="../../_images/sphx_glr_plot_all_scaling_004.png" />
</div>
<div class="section" id="robustscaler">
<h2>RobustScaler<a class="headerlink" href="#robustscaler" title="Permalink to this headline">¶</a></h2>
<p>Unlike the previous scalers, the centering and scaling statistics of this
scaler are based on percentiles and are therefore not influenced by a few
number of very large marginal outliers. Consequently, the resulting range of
the transformed feature values is larger than for the previous scalers and,
more importantly, are approximately similar: for both features most of the
transformed values lie in a [-2, 3] range as seen in the zoomed-in figure.
Note that the outliers themselves are still present in the transformed data.
If a separate outlier clipping is desirable, a non-linear transformation is
required (see below).</p>
<div class="highlight-default notranslate"><div class="highlight"><pre><span></span><span class="n">make_plot</span><span class="p">(</span><span class="mi">4</span><span class="p">)</span>
</pre></div>
</div>
<img alt="../../_images/sphx_glr_plot_all_scaling_005.png" class="sphx-glr-single-img" src="../../_images/sphx_glr_plot_all_scaling_005.png" />
</div>
<div class="section" id="powertransformer">
<h2>PowerTransformer<a class="headerlink" href="#powertransformer" title="Permalink to this headline">¶</a></h2>
<p><code class="docutils literal notranslate"><span class="pre">PowerTransformer</span></code> applies a power transformation to each feature to make
the data more Gaussian-like. Currently, <code class="docutils literal notranslate"><span class="pre">PowerTransformer</span></code> implements the
Yeo-Johnson and Box-Cox transforms. The power transform finds the optimal
scaling factor to stabilize variance and mimimize skewness through maximum
likelihood estimation. By default, <code class="docutils literal notranslate"><span class="pre">PowerTransformer</span></code> also applies
zero-mean, unit variance normalization to the transformed output. Note that
Box-Cox can only be applied to strictly positive data. Income and number of
households happen to be strictly positive, but if negative values are present
the Yeo-Johnson transformed is to be preferred.</p>
<div class="highlight-default notranslate"><div class="highlight"><pre><span></span><span class="n">make_plot</span><span class="p">(</span><span class="mi">5</span><span class="p">)</span>
<span class="n">make_plot</span><span class="p">(</span><span class="mi">6</span><span class="p">)</span>
</pre></div>
</div>
<ul class="sphx-glr-horizontal">
<li><img alt="../../_images/sphx_glr_plot_all_scaling_006.png" class="sphx-glr-multi-img" src="../../_images/sphx_glr_plot_all_scaling_006.png" />
</li>
<li><img alt="../../_images/sphx_glr_plot_all_scaling_007.png" class="sphx-glr-multi-img" src="../../_images/sphx_glr_plot_all_scaling_007.png" />
</li>
</ul>
</div>
<div class="section" id="quantiletransformer-gaussian-output">
<h2>QuantileTransformer (Gaussian output)<a class="headerlink" href="#quantiletransformer-gaussian-output" title="Permalink to this headline">¶</a></h2>
<p><code class="docutils literal notranslate"><span class="pre">QuantileTransformer</span></code> has an additional <code class="docutils literal notranslate"><span class="pre">output_distribution</span></code> parameter
allowing to match a Gaussian distribution instead of a uniform distribution.
Note that this non-parametetric transformer introduces saturation artifacts
for extreme values.</p>
<div class="highlight-default notranslate"><div class="highlight"><pre><span></span><span class="n">make_plot</span><span class="p">(</span><span class="mi">7</span><span class="p">)</span>
</pre></div>
</div>
<img alt="../../_images/sphx_glr_plot_all_scaling_008.png" class="sphx-glr-single-img" src="../../_images/sphx_glr_plot_all_scaling_008.png" />
</div>
<div class="section" id="quantiletransformer-uniform-output">
<h2>QuantileTransformer (uniform output)<a class="headerlink" href="#quantiletransformer-uniform-output" title="Permalink to this headline">¶</a></h2>
<p><code class="docutils literal notranslate"><span class="pre">QuantileTransformer</span></code> applies a non-linear transformation such that the
probability density function of each feature will be mapped to a uniform
distribution. In this case, all the data will be mapped in the range [0, 1],
even the outliers which cannot be distinguished anymore from the inliers.</p>
<p>As <code class="docutils literal notranslate"><span class="pre">RobustScaler</span></code>, <code class="docutils literal notranslate"><span class="pre">QuantileTransformer</span></code> is robust to outliers in the
sense that adding or removing outliers in the training set will yield
approximately the same transformation on held out data. But contrary to
<code class="docutils literal notranslate"><span class="pre">RobustScaler</span></code>, <code class="docutils literal notranslate"><span class="pre">QuantileTransformer</span></code> will also automatically collapse
any outlier by setting them to the a priori defined range boundaries (0 and
1).</p>
<div class="highlight-default notranslate"><div class="highlight"><pre><span></span><span class="n">make_plot</span><span class="p">(</span><span class="mi">8</span><span class="p">)</span>
</pre></div>
</div>
<img alt="../../_images/sphx_glr_plot_all_scaling_009.png" class="sphx-glr-single-img" src="../../_images/sphx_glr_plot_all_scaling_009.png" />
</div>
<div class="section" id="normalizer">
<h2>Normalizer<a class="headerlink" href="#normalizer" title="Permalink to this headline">¶</a></h2>
<p>The <code class="docutils literal notranslate"><span class="pre">Normalizer</span></code> rescales the vector for each sample to have unit norm,
independently of the distribution of the samples. It can be seen on both
figures below where all samples are mapped onto the unit circle. In our
example the two selected features have only positive values; therefore the
transformed data only lie in the positive quadrant. This would not be the
case if some original features had a mix of positive and negative values.</p>
<div class="highlight-default notranslate"><div class="highlight"><pre><span></span><span class="n">make_plot</span><span class="p">(</span><span class="mi">9</span><span class="p">)</span>
<a href="https://matplotlib.org/api/_as_gen/matplotlib.pyplot.show.html#matplotlib.pyplot.show" title="View documentation for matplotlib.pyplot.show"><span class="n">plt</span><span class="o">.</span><span class="n">show</span></a><span class="p">()</span>
</pre></div>
</div>
<img alt="../../_images/sphx_glr_plot_all_scaling_010.png" class="sphx-glr-single-img" src="../../_images/sphx_glr_plot_all_scaling_010.png" />
<p class="sphx-glr-timing"><strong>Total running time of the script:</strong> ( 0 minutes 11.455 seconds)</p>
<p><strong>Estimated memory usage:</strong> 8 MB</p>
<div class="sphx-glr-footer class sphx-glr-footer-example docutils container" id="sphx-glr-download-auto-examples-preprocessing-plot-all-scaling-py">
<div class="binder-badge docutils container">
<a class="reference external image-reference" href="https://mybinder.org/v2/gh/scikit-learn/scikit-learn/0.22.X?urlpath=lab/tree/notebooks/auto_examples/preprocessing/plot_all_scaling.ipynb"><img alt="https://mybinder.org/badge_logo.svg" src="https://mybinder.org/badge_logo.svg" width="150px" /></a>
</div>
<div class="sphx-glr-download docutils container">
<p><a class="reference download internal" download="" href="../../_downloads/7699944fcd7908d5390bc6e94695487b/plot_all_scaling.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_all_scaling.py</span></code></a></p>
</div>
<div class="sphx-glr-download docutils container">
<p><a class="reference download internal" download="" href="../../_downloads/72cc9063542e8d12ba1a5d7ceb8c3473/plot_all_scaling.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_all_scaling.ipynb</span></code></a></p>
</div>
</div>
<p class="sphx-glr-signature"><a class="reference external" href="https://sphinx-gallery.github.io">Gallery generated by Sphinx-Gallery</a></p>
</div>
</div>
</div>
<div class="container">
<footer class="sk-content-footer">
© 2007 - 2019, scikit-learn developers (BSD License).
<a href="../../_sources/auto_examples/preprocessing/plot_all_scaling.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>