-
Notifications
You must be signed in to change notification settings - Fork 81
/
Copy pathplot_rbf_parameters.html
497 lines (452 loc) · 54.9 KB
/
plot_rbf_parameters.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
<!DOCTYPE html>
<!-- data-theme below is forced to be "light" but should be changed if we use pydata-theme-sphinx in the future -->
<!--[if IE 8]><html class="no-js lt-ie9" lang="en" data-content_root="../../" data-theme="light"> <![endif]-->
<!--[if gt IE 8]><!--> <html class="no-js" lang="en" data-content_root="../../" data-theme="light"> <!--<![endif]-->
<head>
<meta charset="utf-8">
<meta name="viewport" content="width=device-width, initial-scale=1" />
<meta property="og:title" content="RBF SVM parameters" />
<meta property="og:type" content="website" />
<meta property="og:url" content="https://scikit-learn/stable/auto_examples/svm/plot_rbf_parameters.html" />
<meta property="og:site_name" content="scikit-learn" />
<meta property="og:description" content="This example illustrates the effect of the parameters gamma and C of the Radial Basis Function (RBF) kernel SVM. Intuitively, the gamma parameter defines how far the influence of a single training ..." />
<meta property="og:image" content="https://scikit-learn.org/stable/_static/scikit-learn-logo-small.png" />
<meta property="og:image:alt" content="scikit-learn" />
<meta name="description" content="This example illustrates the effect of the parameters gamma and C of the Radial Basis Function (RBF) kernel SVM. Intuitively, the gamma parameter defines how far the influence of a single training ..." />
<meta name="viewport" content="width=device-width, initial-scale=1.0">
<title>RBF SVM parameters — scikit-learn 1.4.2 documentation</title>
<link rel="canonical" href="https://scikit-learn.org/stable/auto_examples/svm/plot_rbf_parameters.html" />
<link rel="shortcut icon" href="../../_static/favicon.ico"/>
<link rel="stylesheet" href="../../_static/css/vendor/bootstrap.min.css" type="text/css" />
<link rel="stylesheet" href="../../_static/pygments.css" type="text/css" />
<link rel="stylesheet" href="../../_static/css/theme.css" type="text/css" />
<link rel="stylesheet" href="../../_static/copybutton.css" type="text/css" />
<link rel="stylesheet" href="../../_static/plot_directive.css" type="text/css" />
<link rel="stylesheet" href="../../https://fonts.googleapis.com/css?family=Vibur" type="text/css" />
<link rel="stylesheet" href="../../_static/jupyterlite_sphinx.css" type="text/css" />
<link rel="stylesheet" href="../../_static/sg_gallery.css" type="text/css" />
<link rel="stylesheet" href="../../_static/sg_gallery-binder.css" type="text/css" />
<link rel="stylesheet" href="../../_static/sg_gallery-dataframe.css" type="text/css" />
<link rel="stylesheet" href="../../_static/sg_gallery-rendered-html.css" type="text/css" />
<link rel="stylesheet" href="../../_static/css/theme.css" type="text/css" />
<script id="documentation_options" data-url_root="../../" src="../../_static/documentation_options.js"></script>
<script src="../../_static/js/vendor/jquery-3.6.3.slim.min.js"></script>
<script src="../../_static/js/details-permalink.js"></script>
</head>
<body>
<nav id="navbar" class="sk-docs-navbar navbar navbar-expand-md navbar-light bg-light py-0">
<div class="container-fluid sk-docs-container px-0">
<a class="navbar-brand py-0" href="../../index.html">
<img
class="sk-brand-img"
src="../../_static/scikit-learn-logo-small.png"
alt="logo"/>
</a>
<button
id="sk-navbar-toggler"
class="navbar-toggler"
type="button"
data-toggle="collapse"
data-target="#navbarSupportedContent"
aria-controls="navbarSupportedContent"
aria-expanded="false"
aria-label="Toggle navigation"
>
<span class="navbar-toggler-icon"></span>
</button>
<div class="sk-navbar-collapse collapse navbar-collapse" id="navbarSupportedContent">
<ul class="navbar-nav mr-auto">
<li class="nav-item">
<a class="sk-nav-link nav-link" href="../../install.html">Install</a>
</li>
<li class="nav-item">
<a class="sk-nav-link nav-link" href="../../user_guide.html">User Guide</a>
</li>
<li class="nav-item">
<a class="sk-nav-link nav-link" href="../../modules/classes.html">API</a>
</li>
<li class="nav-item">
<a class="sk-nav-link nav-link" href="../index.html">Examples</a>
</li>
<li class="nav-item">
<a class="sk-nav-link nav-link" target="_blank" rel="noopener noreferrer" href="https://blog.scikit-learn.org/">Community</a>
</li>
<li class="nav-item">
<a class="sk-nav-link nav-link nav-more-item-mobile-items" href="../../getting_started.html" >Getting Started</a>
</li>
<li class="nav-item">
<a class="sk-nav-link nav-link nav-more-item-mobile-items" href="../../tutorial/index.html" >Tutorial</a>
</li>
<li class="nav-item">
<a class="sk-nav-link nav-link nav-more-item-mobile-items" href="../../whats_new/v1.4.html" >What's new</a>
</li>
<li class="nav-item">
<a class="sk-nav-link nav-link nav-more-item-mobile-items" href="../../glossary.html" >Glossary</a>
</li>
<li class="nav-item">
<a class="sk-nav-link nav-link nav-more-item-mobile-items" href="https://scikit-learn.org/dev/developers/index.html" target="_blank" rel="noopener noreferrer">Development</a>
</li>
<li class="nav-item">
<a class="sk-nav-link nav-link nav-more-item-mobile-items" href="../../faq.html" >FAQ</a>
</li>
<li class="nav-item">
<a class="sk-nav-link nav-link nav-more-item-mobile-items" href="../../support.html" >Support</a>
</li>
<li class="nav-item">
<a class="sk-nav-link nav-link nav-more-item-mobile-items" href="../../related_projects.html" >Related packages</a>
</li>
<li class="nav-item">
<a class="sk-nav-link nav-link nav-more-item-mobile-items" href="../../roadmap.html" >Roadmap</a>
</li>
<li class="nav-item">
<a class="sk-nav-link nav-link nav-more-item-mobile-items" href="../../governance.html" >Governance</a>
</li>
<li class="nav-item">
<a class="sk-nav-link nav-link nav-more-item-mobile-items" href="../../about.html" >About us</a>
</li>
<li class="nav-item">
<a class="sk-nav-link nav-link nav-more-item-mobile-items" href="https://github.com/scikit-learn/scikit-learn" >GitHub</a>
</li>
<li class="nav-item">
<a class="sk-nav-link nav-link nav-more-item-mobile-items" href="https://scikit-learn.org/dev/versions.html" >Other Versions and Download</a>
</li>
<li class="nav-item dropdown nav-more-item-dropdown">
<a class="sk-nav-link nav-link dropdown-toggle" href="#" id="navbarDropdown" role="button" data-toggle="dropdown" aria-haspopup="true" aria-expanded="false">More</a>
<div class="dropdown-menu" aria-labelledby="navbarDropdown">
<a class="sk-nav-dropdown-item dropdown-item" href="../../getting_started.html" >Getting Started</a>
<a class="sk-nav-dropdown-item dropdown-item" href="../../tutorial/index.html" >Tutorial</a>
<a class="sk-nav-dropdown-item dropdown-item" href="../../whats_new/v1.4.html" >What's new</a>
<a class="sk-nav-dropdown-item dropdown-item" href="../../glossary.html" >Glossary</a>
<a class="sk-nav-dropdown-item dropdown-item" href="https://scikit-learn.org/dev/developers/index.html" target="_blank" rel="noopener noreferrer">Development</a>
<a class="sk-nav-dropdown-item dropdown-item" href="../../faq.html" >FAQ</a>
<a class="sk-nav-dropdown-item dropdown-item" href="../../support.html" >Support</a>
<a class="sk-nav-dropdown-item dropdown-item" href="../../related_projects.html" >Related packages</a>
<a class="sk-nav-dropdown-item dropdown-item" href="../../roadmap.html" >Roadmap</a>
<a class="sk-nav-dropdown-item dropdown-item" href="../../governance.html" >Governance</a>
<a class="sk-nav-dropdown-item dropdown-item" href="../../about.html" >About us</a>
<a class="sk-nav-dropdown-item dropdown-item" href="https://github.com/scikit-learn/scikit-learn" >GitHub</a>
<a class="sk-nav-dropdown-item dropdown-item" href="https://scikit-learn.org/dev/versions.html" >Other Versions and Download</a>
</div>
</li>
</ul>
<div id="searchbox" role="search">
<div class="searchformwrapper">
<form class="search" action="../../search.html" method="get">
<input class="sk-search-text-input" type="text" name="q" aria-labelledby="searchlabel" />
<input class="sk-search-text-btn" type="submit" value="Go" />
</form>
</div>
</div>
</div>
</div>
</nav>
<div class="d-flex" id="sk-doc-wrapper">
<input type="checkbox" name="sk-toggle-checkbox" id="sk-toggle-checkbox">
<label id="sk-sidemenu-toggle" class="sk-btn-toggle-toc btn sk-btn-primary" for="sk-toggle-checkbox">Toggle Menu</label>
<div id="sk-sidebar-wrapper" class="border-right">
<div class="sk-sidebar-toc-wrapper">
<div class="btn-group w-100 mb-2" role="group" aria-label="rellinks">
<a href="plot_linearsvc_support_vectors.html" role="button" class="btn sk-btn-rellink py-1" sk-rellink-tooltip="Plot the support vectors in LinearSVC">Prev</a><a href="index.html" role="button" class="btn sk-btn-rellink py-1" sk-rellink-tooltip="Support Vector Machines">Up</a>
<a href="plot_svm_margin.html" role="button" class="btn sk-btn-rellink py-1" sk-rellink-tooltip="SVM Margins Example">Next</a>
</div>
<div class="alert alert-danger p-1 mb-2" role="alert">
<p class="text-center mb-0">
<strong>scikit-learn 1.4.2</strong><br/>
<a href="https://scikit-learn.org/dev/versions.html">Other versions</a>
</p>
</div>
<div class="alert alert-warning p-1 mb-2" role="alert">
<p class="text-center mb-0">
Please <a class="font-weight-bold" href="../../about.html#citing-scikit-learn"><string>cite us</string></a> if you use the software.
</p>
</div>
<div class="sk-sidebar-toc">
<ul>
<li><a class="reference internal" href="#">RBF SVM parameters</a><ul>
<li><a class="reference internal" href="#load-and-prepare-data-set">Load and prepare data set</a></li>
<li><a class="reference internal" href="#train-classifiers">Train classifiers</a></li>
<li><a class="reference internal" href="#visualization">Visualization</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><a class="reference internal" href="#sphx-glr-download-auto-examples-svm-plot-rbf-parameters-py"><span class="std std-ref">Go to the end</span></a>
to download the full example code or to run this example in your browser via JupyterLite or Binder</p>
</div>
<section class="sphx-glr-example-title" id="rbf-svm-parameters">
<span id="sphx-glr-auto-examples-svm-plot-rbf-parameters-py"></span><h1>RBF SVM parameters<a class="headerlink" href="#rbf-svm-parameters" title="Link to this heading">¶</a></h1>
<p>This example illustrates the effect of the parameters <code class="docutils literal notranslate"><span class="pre">gamma</span></code> and <code class="docutils literal notranslate"><span class="pre">C</span></code> of
the Radial Basis Function (RBF) kernel SVM.</p>
<p>Intuitively, the <code class="docutils literal notranslate"><span class="pre">gamma</span></code> parameter defines how far the influence of a single
training example reaches, with low values meaning ‘far’ and high values meaning
‘close’. The <code class="docutils literal notranslate"><span class="pre">gamma</span></code> parameters can be seen as the inverse of the radius of
influence of samples selected by the model as support vectors.</p>
<p>The <code class="docutils literal notranslate"><span class="pre">C</span></code> parameter trades off correct classification of training examples
against maximization of the decision function’s margin. For larger values of
<code class="docutils literal notranslate"><span class="pre">C</span></code>, a smaller margin will be accepted if the decision function is better at
classifying all training points correctly. A lower <code class="docutils literal notranslate"><span class="pre">C</span></code> will encourage a
larger margin, therefore a simpler decision function, at the cost of training
accuracy. In other words <code class="docutils literal notranslate"><span class="pre">C</span></code> behaves as a regularization parameter in the
SVM.</p>
<p>The first plot is a visualization of the decision function for a variety of
parameter values on a simplified classification problem involving only 2 input
features and 2 possible target classes (binary classification). Note that this
kind of plot is not possible to do for problems with more features or target
classes.</p>
<p>The second plot is a heatmap of the classifier’s cross-validation accuracy as a
function of <code class="docutils literal notranslate"><span class="pre">C</span></code> and <code class="docutils literal notranslate"><span class="pre">gamma</span></code>. For this example we explore a relatively large
grid for illustration purposes. In practice, a logarithmic grid from
<span class="math notranslate nohighlight">\(10^{-3}\)</span> to <span class="math notranslate nohighlight">\(10^3\)</span> is usually sufficient. If the best parameters
lie on the boundaries of the grid, it can be extended in that direction in a
subsequent search.</p>
<p>Note that the heat map plot has a special colorbar with a midpoint value close
to the score values of the best performing models so as to make it easy to tell
them apart in the blink of an eye.</p>
<p>The behavior of the model is very sensitive to the <code class="docutils literal notranslate"><span class="pre">gamma</span></code> parameter. If
<code class="docutils literal notranslate"><span class="pre">gamma</span></code> is too large, the radius of the area of influence of the support
vectors only includes the support vector itself and no amount of
regularization with <code class="docutils literal notranslate"><span class="pre">C</span></code> will be able to prevent overfitting.</p>
<p>When <code class="docutils literal notranslate"><span class="pre">gamma</span></code> is very small, the model is too constrained and cannot capture
the complexity or “shape” of the data. The region of influence of any selected
support vector would include the whole training set. The resulting model will
behave similarly to a linear model with a set of hyperplanes that separate the
centers of high density of any pair of two classes.</p>
<p>For intermediate values, we can see on the second plot that good models can
be found on a diagonal of <code class="docutils literal notranslate"><span class="pre">C</span></code> and <code class="docutils literal notranslate"><span class="pre">gamma</span></code>. Smooth models (lower <code class="docutils literal notranslate"><span class="pre">gamma</span></code>
values) can be made more complex by increasing the importance of classifying
each point correctly (larger <code class="docutils literal notranslate"><span class="pre">C</span></code> values) hence the diagonal of good
performing models.</p>
<p>Finally, one can also observe that for some intermediate values of <code class="docutils literal notranslate"><span class="pre">gamma</span></code> we
get equally performing models when <code class="docutils literal notranslate"><span class="pre">C</span></code> becomes very large. This suggests that
the set of support vectors does not change anymore. The radius of the RBF
kernel alone acts as a good structural regularizer. Increasing <code class="docutils literal notranslate"><span class="pre">C</span></code> further
doesn’t help, likely because there are no more training points in violation
(inside the margin or wrongly classified), or at least no better solution can
be found. Scores being equal, it may make sense to use the smaller <code class="docutils literal notranslate"><span class="pre">C</span></code>
values, since very high <code class="docutils literal notranslate"><span class="pre">C</span></code> values typically increase fitting time.</p>
<p>On the other hand, lower <code class="docutils literal notranslate"><span class="pre">C</span></code> values generally lead to more support vectors,
which may increase prediction time. Therefore, lowering the value of <code class="docutils literal notranslate"><span class="pre">C</span></code>
involves a trade-off between fitting time and prediction time.</p>
<p>We should also note that small differences in scores results from the random
splits of the cross-validation procedure. Those spurious variations can be
smoothed out by increasing the number of CV iterations <code class="docutils literal notranslate"><span class="pre">n_splits</span></code> at the
expense of compute time. Increasing the value number of <code class="docutils literal notranslate"><span class="pre">C_range</span></code> and
<code class="docutils literal notranslate"><span class="pre">gamma_range</span></code> steps will increase the resolution of the hyper-parameter heat
map.</p>
<p>Utility class to move the midpoint of a colormap to be around
the values of interest.</p>
<div class="highlight-Python notranslate"><div class="highlight"><pre><span></span><span class="kn">import</span> <span class="nn">numpy</span> <span class="k">as</span> <span class="nn">np</span>
<span class="kn">from</span> <span class="nn">matplotlib.colors</span> <span class="kn">import</span> <a href="https://matplotlib.org/stable/api/_as_gen/matplotlib.colors.Normalize.html#matplotlib.colors.Normalize" title="matplotlib.colors.Normalize" class="sphx-glr-backref-module-matplotlib-colors sphx-glr-backref-type-py-class sphx-glr-backref-instance"><span class="n">Normalize</span></a>
<span class="k">class</span> <span class="nc">MidpointNormalize</span><span class="p">(</span><a href="https://matplotlib.org/stable/api/_as_gen/matplotlib.colors.Normalize.html#matplotlib.colors.Normalize" title="matplotlib.colors.Normalize" class="sphx-glr-backref-module-matplotlib-colors sphx-glr-backref-type-py-class sphx-glr-backref-instance"><span class="n">Normalize</span></a><span class="p">):</span>
<span class="k">def</span> <span class="fm">__init__</span><span class="p">(</span><span class="bp">self</span><span class="p">,</span> <span class="n">vmin</span><span class="o">=</span><span class="kc">None</span><span class="p">,</span> <span class="n">vmax</span><span class="o">=</span><span class="kc">None</span><span class="p">,</span> <span class="n">midpoint</span><span class="o">=</span><span class="kc">None</span><span class="p">,</span> <span class="n">clip</span><span class="o">=</span><span class="kc">False</span><span class="p">):</span>
<span class="bp">self</span><span class="o">.</span><span class="n">midpoint</span> <span class="o">=</span> <span class="n">midpoint</span>
<a href="https://matplotlib.org/stable/api/_as_gen/matplotlib.colors.Normalize.html#matplotlib.colors.Normalize" title="matplotlib.colors.Normalize" class="sphx-glr-backref-module-matplotlib-colors sphx-glr-backref-type-py-class sphx-glr-backref-instance"><span class="n">Normalize</span></a><span class="o">.</span><span class="fm">__init__</span><span class="p">(</span><span class="bp">self</span><span class="p">,</span> <span class="n">vmin</span><span class="p">,</span> <span class="n">vmax</span><span class="p">,</span> <span class="n">clip</span><span class="p">)</span>
<span class="k">def</span> <span class="fm">__call__</span><span class="p">(</span><span class="bp">self</span><span class="p">,</span> <span class="n">value</span><span class="p">,</span> <span class="n">clip</span><span class="o">=</span><span class="kc">None</span><span class="p">):</span>
<span class="n">x</span><span class="p">,</span> <span class="n">y</span> <span class="o">=</span> <span class="p">[</span><span class="bp">self</span><span class="o">.</span><span class="n">vmin</span><span class="p">,</span> <span class="bp">self</span><span class="o">.</span><span class="n">midpoint</span><span class="p">,</span> <span class="bp">self</span><span class="o">.</span><span class="n">vmax</span><span class="p">],</span> <span class="p">[</span><span class="mi">0</span><span class="p">,</span> <span class="mf">0.5</span><span class="p">,</span> <span class="mi">1</span><span class="p">]</span>
<span class="k">return</span> <a href="https://numpy.org/doc/stable/reference/generated/numpy.ma.masked_array.html#numpy.ma.masked_array" title="numpy.ma.masked_array" class="sphx-glr-backref-module-numpy-ma sphx-glr-backref-type-py-attribute"><span class="n">np</span><span class="o">.</span><span class="n">ma</span><span class="o">.</span><span class="n">masked_array</span></a><span class="p">(</span><a href="https://numpy.org/doc/stable/reference/generated/numpy.interp.html#numpy.interp" title="numpy.interp" class="sphx-glr-backref-module-numpy sphx-glr-backref-type-py-function"><span class="n">np</span><span class="o">.</span><span class="n">interp</span></a><span class="p">(</span><span class="n">value</span><span class="p">,</span> <span class="n">x</span><span class="p">,</span> <span class="n">y</span><span class="p">))</span>
</pre></div>
</div>
<section id="load-and-prepare-data-set">
<h2>Load and prepare data set<a class="headerlink" href="#load-and-prepare-data-set" title="Link to this heading">¶</a></h2>
<p>dataset for grid search</p>
<div class="highlight-Python notranslate"><div class="highlight"><pre><span></span><span class="kn">from</span> <span class="nn">sklearn.datasets</span> <span class="kn">import</span> <a href="../../modules/generated/sklearn.datasets.load_iris.html#sklearn.datasets.load_iris" title="sklearn.datasets.load_iris" class="sphx-glr-backref-module-sklearn-datasets sphx-glr-backref-type-py-function"><span class="n">load_iris</span></a>
<span class="n">iris</span> <span class="o">=</span> <a href="../../modules/generated/sklearn.datasets.load_iris.html#sklearn.datasets.load_iris" title="sklearn.datasets.load_iris" class="sphx-glr-backref-module-sklearn-datasets sphx-glr-backref-type-py-function"><span class="n">load_iris</span></a><span class="p">()</span>
<span class="n">X</span> <span class="o">=</span> <span class="n">iris</span><span class="o">.</span><span class="n">data</span>
<span class="n">y</span> <span class="o">=</span> <span class="n">iris</span><span class="o">.</span><span class="n">target</span>
</pre></div>
</div>
<p>Dataset for decision function visualization: we only keep the first two
features in X and sub-sample the dataset to keep only 2 classes and
make it a binary classification problem.</p>
<div class="highlight-Python notranslate"><div class="highlight"><pre><span></span><span class="n">X_2d</span> <span class="o">=</span> <span class="n">X</span><span class="p">[:,</span> <span class="p">:</span><span class="mi">2</span><span class="p">]</span>
<span class="n">X_2d</span> <span class="o">=</span> <span class="n">X_2d</span><span class="p">[</span><span class="n">y</span> <span class="o">></span> <span class="mi">0</span><span class="p">]</span>
<span class="n">y_2d</span> <span class="o">=</span> <span class="n">y</span><span class="p">[</span><span class="n">y</span> <span class="o">></span> <span class="mi">0</span><span class="p">]</span>
<span class="n">y_2d</span> <span class="o">-=</span> <span class="mi">1</span>
</pre></div>
</div>
<p>It is usually a good idea to scale the data for SVM training.
We are cheating a bit in this example in scaling all of the data,
instead of fitting the transformation on the training set and
just applying it on the test set.</p>
<div class="highlight-Python notranslate"><div class="highlight"><pre><span></span><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="sklearn.preprocessing.StandardScaler" class="sphx-glr-backref-module-sklearn-preprocessing sphx-glr-backref-type-py-class sphx-glr-backref-instance"><span class="n">StandardScaler</span></a>
<span class="n">scaler</span> <span class="o">=</span> <a href="../../modules/generated/sklearn.preprocessing.StandardScaler.html#sklearn.preprocessing.StandardScaler" title="sklearn.preprocessing.StandardScaler" class="sphx-glr-backref-module-sklearn-preprocessing sphx-glr-backref-type-py-class sphx-glr-backref-instance"><span class="n">StandardScaler</span></a><span class="p">()</span>
<span class="n">X</span> <span class="o">=</span> <span class="n">scaler</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="n">X_2d</span> <span class="o">=</span> <span class="n">scaler</span><span class="o">.</span><span class="n">fit_transform</span><span class="p">(</span><span class="n">X_2d</span><span class="p">)</span>
</pre></div>
</div>
</section>
<section id="train-classifiers">
<h2>Train classifiers<a class="headerlink" href="#train-classifiers" title="Link to this heading">¶</a></h2>
<p>For an initial search, a logarithmic grid with basis
10 is often helpful. Using a basis of 2, a finer
tuning can be achieved but at a much higher cost.</p>
<div class="highlight-Python notranslate"><div class="highlight"><pre><span></span><span class="kn">from</span> <span class="nn">sklearn.model_selection</span> <span class="kn">import</span> <a href="../../modules/generated/sklearn.model_selection.GridSearchCV.html#sklearn.model_selection.GridSearchCV" title="sklearn.model_selection.GridSearchCV" class="sphx-glr-backref-module-sklearn-model_selection sphx-glr-backref-type-py-class sphx-glr-backref-instance"><span class="n">GridSearchCV</span></a><span class="p">,</span> <a href="../../modules/generated/sklearn.model_selection.StratifiedShuffleSplit.html#sklearn.model_selection.StratifiedShuffleSplit" title="sklearn.model_selection.StratifiedShuffleSplit" class="sphx-glr-backref-module-sklearn-model_selection sphx-glr-backref-type-py-class sphx-glr-backref-instance"><span class="n">StratifiedShuffleSplit</span></a>
<span class="kn">from</span> <span class="nn">sklearn.svm</span> <span class="kn">import</span> <a href="../../modules/generated/sklearn.svm.SVC.html#sklearn.svm.SVC" title="sklearn.svm.SVC" class="sphx-glr-backref-module-sklearn-svm sphx-glr-backref-type-py-class sphx-glr-backref-instance"><span class="n">SVC</span></a>
<span class="n">C_range</span> <span class="o">=</span> <a href="https://numpy.org/doc/stable/reference/generated/numpy.logspace.html#numpy.logspace" title="numpy.logspace" class="sphx-glr-backref-module-numpy sphx-glr-backref-type-py-function"><span class="n">np</span><span class="o">.</span><span class="n">logspace</span></a><span class="p">(</span><span class="o">-</span><span class="mi">2</span><span class="p">,</span> <span class="mi">10</span><span class="p">,</span> <span class="mi">13</span><span class="p">)</span>
<span class="n">gamma_range</span> <span class="o">=</span> <a href="https://numpy.org/doc/stable/reference/generated/numpy.logspace.html#numpy.logspace" title="numpy.logspace" class="sphx-glr-backref-module-numpy sphx-glr-backref-type-py-function"><span class="n">np</span><span class="o">.</span><span class="n">logspace</span></a><span class="p">(</span><span class="o">-</span><span class="mi">9</span><span class="p">,</span> <span class="mi">3</span><span class="p">,</span> <span class="mi">13</span><span class="p">)</span>
<span class="n">param_grid</span> <span class="o">=</span> <span class="nb">dict</span><span class="p">(</span><span class="n">gamma</span><span class="o">=</span><span class="n">gamma_range</span><span class="p">,</span> <span class="n">C</span><span class="o">=</span><span class="n">C_range</span><span class="p">)</span>
<span class="n">cv</span> <span class="o">=</span> <a href="../../modules/generated/sklearn.model_selection.StratifiedShuffleSplit.html#sklearn.model_selection.StratifiedShuffleSplit" title="sklearn.model_selection.StratifiedShuffleSplit" class="sphx-glr-backref-module-sklearn-model_selection sphx-glr-backref-type-py-class sphx-glr-backref-instance"><span class="n">StratifiedShuffleSplit</span></a><span class="p">(</span><span class="n">n_splits</span><span class="o">=</span><span class="mi">5</span><span class="p">,</span> <span class="n">test_size</span><span class="o">=</span><span class="mf">0.2</span><span class="p">,</span> <span class="n">random_state</span><span class="o">=</span><span class="mi">42</span><span class="p">)</span>
<span class="n">grid</span> <span class="o">=</span> <a href="../../modules/generated/sklearn.model_selection.GridSearchCV.html#sklearn.model_selection.GridSearchCV" title="sklearn.model_selection.GridSearchCV" class="sphx-glr-backref-module-sklearn-model_selection sphx-glr-backref-type-py-class sphx-glr-backref-instance"><span class="n">GridSearchCV</span></a><span class="p">(</span><a href="../../modules/generated/sklearn.svm.SVC.html#sklearn.svm.SVC" title="sklearn.svm.SVC" class="sphx-glr-backref-module-sklearn-svm sphx-glr-backref-type-py-class sphx-glr-backref-instance"><span class="n">SVC</span></a><span class="p">(),</span> <span class="n">param_grid</span><span class="o">=</span><span class="n">param_grid</span><span class="p">,</span> <span class="n">cv</span><span class="o">=</span><span class="n">cv</span><span class="p">)</span>
<span class="n">grid</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="n">y</span><span class="p">)</span>
<span class="nb">print</span><span class="p">(</span>
<span class="s2">"The best parameters are </span><span class="si">%s</span><span class="s2"> with a score of </span><span class="si">%0.2f</span><span class="s2">"</span>
<span class="o">%</span> <span class="p">(</span><span class="n">grid</span><span class="o">.</span><span class="n">best_params_</span><span class="p">,</span> <span class="n">grid</span><span class="o">.</span><span class="n">best_score_</span><span class="p">)</span>
<span class="p">)</span>
</pre></div>
</div>
<div class="sphx-glr-script-out highlight-none notranslate"><div class="highlight"><pre><span></span>The best parameters are {'C': 1.0, 'gamma': 0.09999999999999999} with a score of 0.97
</pre></div>
</div>
<p>Now we need to fit a classifier for all parameters in the 2d version
(we use a smaller set of parameters here because it takes a while to train)</p>
<div class="highlight-Python notranslate"><div class="highlight"><pre><span></span><span class="n">C_2d_range</span> <span class="o">=</span> <span class="p">[</span><span class="mf">1e-2</span><span class="p">,</span> <span class="mi">1</span><span class="p">,</span> <span class="mf">1e2</span><span class="p">]</span>
<span class="n">gamma_2d_range</span> <span class="o">=</span> <span class="p">[</span><span class="mf">1e-1</span><span class="p">,</span> <span class="mi">1</span><span class="p">,</span> <span class="mf">1e1</span><span class="p">]</span>
<span class="n">classifiers</span> <span class="o">=</span> <span class="p">[]</span>
<span class="k">for</span> <span class="n">C</span> <span class="ow">in</span> <span class="n">C_2d_range</span><span class="p">:</span>
<span class="k">for</span> <span class="n">gamma</span> <span class="ow">in</span> <span class="n">gamma_2d_range</span><span class="p">:</span>
<span class="n">clf</span> <span class="o">=</span> <a href="../../modules/generated/sklearn.svm.SVC.html#sklearn.svm.SVC" title="sklearn.svm.SVC" class="sphx-glr-backref-module-sklearn-svm sphx-glr-backref-type-py-class sphx-glr-backref-instance"><span class="n">SVC</span></a><span class="p">(</span><span class="n">C</span><span class="o">=</span><span class="n">C</span><span class="p">,</span> <span class="n">gamma</span><span class="o">=</span><span class="n">gamma</span><span class="p">)</span>
<span class="n">clf</span><span class="o">.</span><span class="n">fit</span><span class="p">(</span><span class="n">X_2d</span><span class="p">,</span> <span class="n">y_2d</span><span class="p">)</span>
<span class="n">classifiers</span><span class="o">.</span><span class="n">append</span><span class="p">((</span><span class="n">C</span><span class="p">,</span> <span class="n">gamma</span><span class="p">,</span> <span class="n">clf</span><span class="p">))</span>
</pre></div>
</div>
</section>
<section id="visualization">
<h2>Visualization<a class="headerlink" href="#visualization" title="Link to this heading">¶</a></h2>
<p>draw visualization of parameter effects</p>
<div class="highlight-Python notranslate"><div class="highlight"><pre><span></span><span class="kn">import</span> <span class="nn">matplotlib.pyplot</span> <span class="k">as</span> <span class="nn">plt</span>
<a href="https://matplotlib.org/stable/api/_as_gen/matplotlib.pyplot.figure.html#matplotlib.pyplot.figure" title="matplotlib.pyplot.figure" class="sphx-glr-backref-module-matplotlib-pyplot sphx-glr-backref-type-py-function"><span class="n">plt</span><span class="o">.</span><span class="n">figure</span></a><span class="p">(</span><span class="n">figsize</span><span class="o">=</span><span class="p">(</span><span class="mi">8</span><span class="p">,</span> <span class="mi">6</span><span class="p">))</span>
<span class="n">xx</span><span class="p">,</span> <span class="n">yy</span> <span class="o">=</span> <a href="https://numpy.org/doc/stable/reference/generated/numpy.meshgrid.html#numpy.meshgrid" title="numpy.meshgrid" class="sphx-glr-backref-module-numpy sphx-glr-backref-type-py-function"><span class="n">np</span><span class="o">.</span><span class="n">meshgrid</span></a><span class="p">(</span><a href="https://numpy.org/doc/stable/reference/generated/numpy.linspace.html#numpy.linspace" title="numpy.linspace" class="sphx-glr-backref-module-numpy sphx-glr-backref-type-py-function"><span class="n">np</span><span class="o">.</span><span class="n">linspace</span></a><span class="p">(</span><span class="o">-</span><span class="mi">3</span><span class="p">,</span> <span class="mi">3</span><span class="p">,</span> <span class="mi">200</span><span class="p">),</span> <a href="https://numpy.org/doc/stable/reference/generated/numpy.linspace.html#numpy.linspace" title="numpy.linspace" class="sphx-glr-backref-module-numpy sphx-glr-backref-type-py-function"><span class="n">np</span><span class="o">.</span><span class="n">linspace</span></a><span class="p">(</span><span class="o">-</span><span class="mi">3</span><span class="p">,</span> <span class="mi">3</span><span class="p">,</span> <span class="mi">200</span><span class="p">))</span>
<span class="k">for</span> <span class="n">k</span><span class="p">,</span> <span class="p">(</span><span class="n">C</span><span class="p">,</span> <span class="n">gamma</span><span class="p">,</span> <span class="n">clf</span><span class="p">)</span> <span class="ow">in</span> <span class="nb">enumerate</span><span class="p">(</span><span class="n">classifiers</span><span class="p">):</span>
<span class="c1"># evaluate decision function in a grid</span>
<span class="n">Z</span> <span class="o">=</span> <span class="n">clf</span><span class="o">.</span><span class="n">decision_function</span><span class="p">(</span><a href="https://numpy.org/doc/stable/reference/generated/numpy.c_.html#numpy.c_" title="numpy.c_" class="sphx-glr-backref-module-numpy sphx-glr-backref-type-py-data"><span class="n">np</span><span class="o">.</span><span class="n">c_</span></a><span class="p">[</span><span class="n">xx</span><span class="o">.</span><span class="n">ravel</span><span class="p">(),</span> <span class="n">yy</span><span class="o">.</span><span class="n">ravel</span><span class="p">()])</span>
<span class="n">Z</span> <span class="o">=</span> <span class="n">Z</span><span class="o">.</span><span class="n">reshape</span><span class="p">(</span><span class="n">xx</span><span class="o">.</span><span class="n">shape</span><span class="p">)</span>
<span class="c1"># visualize decision function for these parameters</span>
<a href="https://matplotlib.org/stable/api/_as_gen/matplotlib.pyplot.subplot.html#matplotlib.pyplot.subplot" title="matplotlib.pyplot.subplot" class="sphx-glr-backref-module-matplotlib-pyplot sphx-glr-backref-type-py-function"><span class="n">plt</span><span class="o">.</span><span class="n">subplot</span></a><span class="p">(</span><span class="nb">len</span><span class="p">(</span><span class="n">C_2d_range</span><span class="p">),</span> <span class="nb">len</span><span class="p">(</span><span class="n">gamma_2d_range</span><span class="p">),</span> <span class="n">k</span> <span class="o">+</span> <span class="mi">1</span><span class="p">)</span>
<a href="https://matplotlib.org/stable/api/_as_gen/matplotlib.pyplot.title.html#matplotlib.pyplot.title" title="matplotlib.pyplot.title" class="sphx-glr-backref-module-matplotlib-pyplot sphx-glr-backref-type-py-function"><span class="n">plt</span><span class="o">.</span><span class="n">title</span></a><span class="p">(</span><span class="s2">"gamma=10^</span><span class="si">%d</span><span class="s2">, C=10^</span><span class="si">%d</span><span class="s2">"</span> <span class="o">%</span> <span class="p">(</span><a href="https://numpy.org/doc/stable/reference/generated/numpy.log10.html#numpy.log10" title="numpy.log10" class="sphx-glr-backref-module-numpy sphx-glr-backref-type-py-data"><span class="n">np</span><span class="o">.</span><span class="n">log10</span></a><span class="p">(</span><span class="n">gamma</span><span class="p">),</span> <a href="https://numpy.org/doc/stable/reference/generated/numpy.log10.html#numpy.log10" title="numpy.log10" class="sphx-glr-backref-module-numpy sphx-glr-backref-type-py-data"><span class="n">np</span><span class="o">.</span><span class="n">log10</span></a><span class="p">(</span><span class="n">C</span><span class="p">)),</span> <span class="n">size</span><span class="o">=</span><span class="s2">"medium"</span><span class="p">)</span>
<span class="c1"># visualize parameter's effect on decision function</span>
<a href="https://matplotlib.org/stable/api/_as_gen/matplotlib.pyplot.pcolormesh.html#matplotlib.pyplot.pcolormesh" title="matplotlib.pyplot.pcolormesh" class="sphx-glr-backref-module-matplotlib-pyplot sphx-glr-backref-type-py-function"><span class="n">plt</span><span class="o">.</span><span class="n">pcolormesh</span></a><span class="p">(</span><span class="n">xx</span><span class="p">,</span> <span class="n">yy</span><span class="p">,</span> <span class="o">-</span><span class="n">Z</span><span class="p">,</span> <span class="n">cmap</span><span class="o">=</span><span class="n">plt</span><span class="o">.</span><span class="n">cm</span><span class="o">.</span><span class="n">RdBu</span><span class="p">)</span>
<a href="https://matplotlib.org/stable/api/_as_gen/matplotlib.pyplot.scatter.html#matplotlib.pyplot.scatter" title="matplotlib.pyplot.scatter" class="sphx-glr-backref-module-matplotlib-pyplot sphx-glr-backref-type-py-function"><span class="n">plt</span><span class="o">.</span><span class="n">scatter</span></a><span class="p">(</span><span class="n">X_2d</span><span class="p">[:,</span> <span class="mi">0</span><span class="p">],</span> <span class="n">X_2d</span><span class="p">[:,</span> <span class="mi">1</span><span class="p">],</span> <span class="n">c</span><span class="o">=</span><span class="n">y_2d</span><span class="p">,</span> <span class="n">cmap</span><span class="o">=</span><span class="n">plt</span><span class="o">.</span><span class="n">cm</span><span class="o">.</span><span class="n">RdBu_r</span><span class="p">,</span> <span class="n">edgecolors</span><span class="o">=</span><span class="s2">"k"</span><span class="p">)</span>
<a href="https://matplotlib.org/stable/api/_as_gen/matplotlib.pyplot.xticks.html#matplotlib.pyplot.xticks" title="matplotlib.pyplot.xticks" class="sphx-glr-backref-module-matplotlib-pyplot sphx-glr-backref-type-py-function"><span class="n">plt</span><span class="o">.</span><span class="n">xticks</span></a><span class="p">(())</span>
<a href="https://matplotlib.org/stable/api/_as_gen/matplotlib.pyplot.yticks.html#matplotlib.pyplot.yticks" title="matplotlib.pyplot.yticks" class="sphx-glr-backref-module-matplotlib-pyplot sphx-glr-backref-type-py-function"><span class="n">plt</span><span class="o">.</span><span class="n">yticks</span></a><span class="p">(())</span>
<a href="https://matplotlib.org/stable/api/_as_gen/matplotlib.pyplot.axis.html#matplotlib.pyplot.axis" title="matplotlib.pyplot.axis" class="sphx-glr-backref-module-matplotlib-pyplot sphx-glr-backref-type-py-function"><span class="n">plt</span><span class="o">.</span><span class="n">axis</span></a><span class="p">(</span><span class="s2">"tight"</span><span class="p">)</span>
<span class="n">scores</span> <span class="o">=</span> <span class="n">grid</span><span class="o">.</span><span class="n">cv_results_</span><span class="p">[</span><span class="s2">"mean_test_score"</span><span class="p">]</span><span class="o">.</span><span class="n">reshape</span><span class="p">(</span><span class="nb">len</span><span class="p">(</span><span class="n">C_range</span><span class="p">),</span> <span class="nb">len</span><span class="p">(</span><span class="n">gamma_range</span><span class="p">))</span>
</pre></div>
</div>
<img src="../../_images/sphx_glr_plot_rbf_parameters_001.png" srcset="../../_images/sphx_glr_plot_rbf_parameters_001.png" alt="gamma=10^-1, C=10^-2, gamma=10^0, C=10^-2, gamma=10^1, C=10^-2, gamma=10^-1, C=10^0, gamma=10^0, C=10^0, gamma=10^1, C=10^0, gamma=10^-1, C=10^2, gamma=10^0, C=10^2, gamma=10^1, C=10^2" class = "sphx-glr-single-img"/><p>Draw heatmap of the validation accuracy as a function of gamma and C</p>
<p>The score are encoded as colors with the hot colormap which varies from dark
red to bright yellow. As the most interesting scores are all located in the
0.92 to 0.97 range we use a custom normalizer to set the mid-point to 0.92 so
as to make it easier to visualize the small variations of score values in the
interesting range while not brutally collapsing all the low score values to
the same color.</p>
<div class="highlight-Python notranslate"><div class="highlight"><pre><span></span><a href="https://matplotlib.org/stable/api/_as_gen/matplotlib.pyplot.figure.html#matplotlib.pyplot.figure" title="matplotlib.pyplot.figure" class="sphx-glr-backref-module-matplotlib-pyplot sphx-glr-backref-type-py-function"><span class="n">plt</span><span class="o">.</span><span class="n">figure</span></a><span class="p">(</span><span class="n">figsize</span><span class="o">=</span><span class="p">(</span><span class="mi">8</span><span class="p">,</span> <span class="mi">6</span><span class="p">))</span>
<a href="https://matplotlib.org/stable/api/_as_gen/matplotlib.pyplot.subplots_adjust.html#matplotlib.pyplot.subplots_adjust" title="matplotlib.pyplot.subplots_adjust" class="sphx-glr-backref-module-matplotlib-pyplot sphx-glr-backref-type-py-function"><span class="n">plt</span><span class="o">.</span><span class="n">subplots_adjust</span></a><span class="p">(</span><span class="n">left</span><span class="o">=</span><span class="mf">0.2</span><span class="p">,</span> <span class="n">right</span><span class="o">=</span><span class="mf">0.95</span><span class="p">,</span> <span class="n">bottom</span><span class="o">=</span><span class="mf">0.15</span><span class="p">,</span> <span class="n">top</span><span class="o">=</span><span class="mf">0.95</span><span class="p">)</span>
<a href="https://matplotlib.org/stable/api/_as_gen/matplotlib.pyplot.imshow.html#matplotlib.pyplot.imshow" title="matplotlib.pyplot.imshow" class="sphx-glr-backref-module-matplotlib-pyplot sphx-glr-backref-type-py-function"><span class="n">plt</span><span class="o">.</span><span class="n">imshow</span></a><span class="p">(</span>
<span class="n">scores</span><span class="p">,</span>
<span class="n">interpolation</span><span class="o">=</span><span class="s2">"nearest"</span><span class="p">,</span>
<span class="n">cmap</span><span class="o">=</span><span class="n">plt</span><span class="o">.</span><span class="n">cm</span><span class="o">.</span><span class="n">hot</span><span class="p">,</span>
<span class="n">norm</span><span class="o">=</span><span class="n">MidpointNormalize</span><span class="p">(</span><span class="n">vmin</span><span class="o">=</span><span class="mf">0.2</span><span class="p">,</span> <span class="n">midpoint</span><span class="o">=</span><span class="mf">0.92</span><span class="p">),</span>
<span class="p">)</span>
<a href="https://matplotlib.org/stable/api/_as_gen/matplotlib.pyplot.xlabel.html#matplotlib.pyplot.xlabel" title="matplotlib.pyplot.xlabel" class="sphx-glr-backref-module-matplotlib-pyplot sphx-glr-backref-type-py-function"><span class="n">plt</span><span class="o">.</span><span class="n">xlabel</span></a><span class="p">(</span><span class="s2">"gamma"</span><span class="p">)</span>
<a href="https://matplotlib.org/stable/api/_as_gen/matplotlib.pyplot.ylabel.html#matplotlib.pyplot.ylabel" title="matplotlib.pyplot.ylabel" class="sphx-glr-backref-module-matplotlib-pyplot sphx-glr-backref-type-py-function"><span class="n">plt</span><span class="o">.</span><span class="n">ylabel</span></a><span class="p">(</span><span class="s2">"C"</span><span class="p">)</span>
<a href="https://matplotlib.org/stable/api/_as_gen/matplotlib.pyplot.colorbar.html#matplotlib.pyplot.colorbar" title="matplotlib.pyplot.colorbar" class="sphx-glr-backref-module-matplotlib-pyplot sphx-glr-backref-type-py-function"><span class="n">plt</span><span class="o">.</span><span class="n">colorbar</span></a><span class="p">()</span>
<a href="https://matplotlib.org/stable/api/_as_gen/matplotlib.pyplot.xticks.html#matplotlib.pyplot.xticks" title="matplotlib.pyplot.xticks" class="sphx-glr-backref-module-matplotlib-pyplot sphx-glr-backref-type-py-function"><span class="n">plt</span><span class="o">.</span><span class="n">xticks</span></a><span class="p">(</span><a href="https://numpy.org/doc/stable/reference/generated/numpy.arange.html#numpy.arange" title="numpy.arange" class="sphx-glr-backref-module-numpy sphx-glr-backref-type-py-function"><span class="n">np</span><span class="o">.</span><span class="n">arange</span></a><span class="p">(</span><span class="nb">len</span><span class="p">(</span><span class="n">gamma_range</span><span class="p">)),</span> <span class="n">gamma_range</span><span class="p">,</span> <span class="n">rotation</span><span class="o">=</span><span class="mi">45</span><span class="p">)</span>
<a href="https://matplotlib.org/stable/api/_as_gen/matplotlib.pyplot.yticks.html#matplotlib.pyplot.yticks" title="matplotlib.pyplot.yticks" class="sphx-glr-backref-module-matplotlib-pyplot sphx-glr-backref-type-py-function"><span class="n">plt</span><span class="o">.</span><span class="n">yticks</span></a><span class="p">(</span><a href="https://numpy.org/doc/stable/reference/generated/numpy.arange.html#numpy.arange" title="numpy.arange" class="sphx-glr-backref-module-numpy sphx-glr-backref-type-py-function"><span class="n">np</span><span class="o">.</span><span class="n">arange</span></a><span class="p">(</span><span class="nb">len</span><span class="p">(</span><span class="n">C_range</span><span class="p">)),</span> <span class="n">C_range</span><span class="p">)</span>
<a href="https://matplotlib.org/stable/api/_as_gen/matplotlib.pyplot.title.html#matplotlib.pyplot.title" title="matplotlib.pyplot.title" class="sphx-glr-backref-module-matplotlib-pyplot sphx-glr-backref-type-py-function"><span class="n">plt</span><span class="o">.</span><span class="n">title</span></a><span class="p">(</span><span class="s2">"Validation accuracy"</span><span class="p">)</span>
<a href="https://matplotlib.org/stable/api/_as_gen/matplotlib.pyplot.show.html#matplotlib.pyplot.show" title="matplotlib.pyplot.show" class="sphx-glr-backref-module-matplotlib-pyplot sphx-glr-backref-type-py-function"><span class="n">plt</span><span class="o">.</span><span class="n">show</span></a><span class="p">()</span>
</pre></div>
</div>
<img src="../../_images/sphx_glr_plot_rbf_parameters_002.png" srcset="../../_images/sphx_glr_plot_rbf_parameters_002.png" alt="Validation accuracy" class = "sphx-glr-single-img"/><p class="sphx-glr-timing"><strong>Total running time of the script:</strong> (0 minutes 4.827 seconds)</p>
<div class="sphx-glr-footer sphx-glr-footer-example docutils container" id="sphx-glr-download-auto-examples-svm-plot-rbf-parameters-py">
<div class="binder-badge docutils container">
<a class="reference external image-reference" href="https://mybinder.org/v2/gh/scikit-learn/scikit-learn/1.4.X?urlpath=lab/tree/notebooks/auto_examples/svm/plot_rbf_parameters.ipynb"><img alt="Launch binder" src="../../_images/binder_badge_logo30.svg" width="150px" /></a>
</div>
<div class="lite-badge docutils container">
<a class="reference external image-reference" href="../../lite/lab/?path=auto_examples/svm/plot_rbf_parameters.ipynb"><img alt="Launch JupyterLite" src="../../_images/jupyterlite_badge_logo30.svg" width="150px" /></a>
</div>
<div class="sphx-glr-download sphx-glr-download-jupyter docutils container">
<p><a class="reference download internal" download="" href="../../_downloads/d55388904f5399e98ed36e971c4da3cf/plot_rbf_parameters.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_rbf_parameters.ipynb</span></code></a></p>
</div>
<div class="sphx-glr-download sphx-glr-download-python docutils container">
<p><a class="reference download internal" download="" href="../../_downloads/ea8b449d4699d078ef9cc5cded54cc67/plot_rbf_parameters.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_rbf_parameters.py</span></code></a></p>
</div>
</div>
<p class="rubric">Related examples</p>
<div class="sphx-glr-thumbnails"><div class="sphx-glr-thumbcontainer" tooltip="In this plot you can see the training scores and validation scores of an SVM for different valu..."><img alt="" src="../../_images/sphx_glr_plot_validation_curve_thumb.png" />
<p><a class="reference internal" href="../model_selection/plot_validation_curve.html#sphx-glr-auto-examples-model-selection-plot-validation-curve-py"><span class="std std-ref">Plotting Validation Curves</span></a></p>
<div class="sphx-glr-thumbnail-title">Plotting Validation Curves</div>
</div><div class="sphx-glr-thumbcontainer" tooltip="Perform binary classification using non-linear SVC with RBF kernel. The target to predict is a ..."><img alt="" src="../../_images/sphx_glr_plot_svm_nonlinear_thumb.png" />
<p><a class="reference internal" href="plot_svm_nonlinear.html#sphx-glr-auto-examples-svm-plot-svm-nonlinear-py"><span class="std std-ref">Non-linear SVM</span></a></p>
<div class="sphx-glr-thumbnail-title">Non-linear SVM</div>
</div><div class="sphx-glr-thumbcontainer" tooltip="SVCs aim to find a hyperplane that effectively separates the classes in their training data by ..."><img alt="" src="../../_images/sphx_glr_plot_svm_kernels_thumb.png" />
<p><a class="reference internal" href="plot_svm_kernels.html#sphx-glr-auto-examples-svm-plot-svm-kernels-py"><span class="std std-ref">Plot classification boundaries with different SVM Kernels</span></a></p>
<div class="sphx-glr-thumbnail-title">Plot classification boundaries with different SVM Kernels</div>
</div><div class="sphx-glr-thumbcontainer" tooltip="Plot decision function of a weighted dataset, where the size of points is proportional to its w..."><img alt="" src="../../_images/sphx_glr_plot_weighted_samples_thumb.png" />
<p><a class="reference internal" href="plot_weighted_samples.html#sphx-glr-auto-examples-svm-plot-weighted-samples-py"><span class="std std-ref">SVM: Weighted samples</span></a></p>
<div class="sphx-glr-thumbnail-title">SVM: Weighted samples</div>
</div><div class="sphx-glr-thumbcontainer" tooltip="Comparison of different linear SVM classifiers on a 2D projection of the iris dataset. We only ..."><img alt="" src="../../_images/sphx_glr_plot_iris_svc_thumb.png" />
<p><a class="reference internal" href="plot_iris_svc.html#sphx-glr-auto-examples-svm-plot-iris-svc-py"><span class="std std-ref">Plot different SVM classifiers in the iris dataset</span></a></p>
<div class="sphx-glr-thumbnail-title">Plot different SVM classifiers in the iris dataset</div>
</div></div><p class="sphx-glr-signature"><a class="reference external" href="https://sphinx-gallery.github.io">Gallery generated by Sphinx-Gallery</a></p>
</section>
</section>
</div>
<div class="container">
<footer class="sk-content-footer">
© 2007 - 2024, scikit-learn developers (BSD License).
<a href="../../_sources/auto_examples/svm/plot_rbf_parameters.rst.txt" rel="nofollow">Show this page source</a>
</footer>
</div>
</div>
</div>
<script src="../../_static/js/vendor/bootstrap.min.js"></script>
<script>
window.ga=window.ga||function(){(ga.q=ga.q||[]).push(arguments)};ga.l=+new Date;
ga('create', 'UA-22606712-2', 'auto');
ga('set', 'anonymizeIp', true);
ga('send', 'pageview');
</script>
<script async src='https://www.google-analytics.com/analytics.js'></script>
<script defer data-domain="scikit-learn.org" src="https://views.scientific-python.org/js/script.js">
</script>
<script src="../../_static/clipboard.min.js"></script>
<script src="../../_static/copybutton.js"></script>
<script>
$(document).ready(function() {
/* Add a [>>>] button on the top-right corner of code samples to hide
* the >>> and ... prompts and the output and thus make the code
* copyable. */
var div = $('.highlight-python .highlight,' +
'.highlight-python3 .highlight,' +
'.highlight-pycon .highlight,' +
'.highlight-default .highlight')
var pre = div.find('pre');
// get the styles from the current theme
pre.parent().parent().css('position', 'relative');
// create and add the button to all the code blocks that contain >>>
div.each(function(index) {
var jthis = $(this);
// tracebacks (.gt) contain bare text elements that need to be
// wrapped in a span to work with .nextUntil() (see later)
jthis.find('pre:has(.gt)').contents().filter(function() {
return ((this.nodeType == 3) && (this.data.trim().length > 0));
}).wrap('<span>');
});
/*** Add permalink buttons next to glossary terms ***/
$('dl.glossary > dt[id]').append(function() {
return ('<a class="headerlink" href="#' +
this.getAttribute('id') +
'" title="Permalink to this term">¶</a>');
});
});
</script>
<script id="MathJax-script" async src="https://cdn.jsdelivr.net/npm/mathjax@3/es5/tex-chtml.js"></script>
<script src="https://scikit-learn.org/versionwarning.js"></script>
</body>
</html>