-
Notifications
You must be signed in to change notification settings - Fork 81
/
Copy pathplot_feature_selection.html
342 lines (288 loc) · 24.6 KB
/
plot_feature_selection.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
<!DOCTYPE html PUBLIC "-//W3C//DTD XHTML 1.0 Transitional//EN"
"http://www.w3.org/TR/xhtml1/DTD/xhtml1-transitional.dtd">
<html xmlns="http://www.w3.org/1999/xhtml">
<head>
<meta http-equiv="Content-Type" content="text/html; charset=utf-8" />
<title>Univariate Feature Selection — scikit-learn 0.19.2 documentation</title>
<!-- htmltitle is before nature.css - we use this hack to load bootstrap first -->
<meta name="viewport" content="width=device-width, initial-scale=1.0" />
<link rel="stylesheet" href="../../_static/css/bootstrap.min.css" media="screen" />
<link rel="stylesheet" href="../../_static/css/bootstrap-responsive.css"/>
<link rel="stylesheet" href="../../_static/nature.css" type="text/css" />
<link rel="stylesheet" href="../../_static/pygments.css" type="text/css" />
<link rel="stylesheet" href="../../_static/gallery.css" type="text/css" />
<script type="text/javascript">
var DOCUMENTATION_OPTIONS = {
URL_ROOT: '../../',
VERSION: '0.19.2',
COLLAPSE_INDEX: false,
FILE_SUFFIX: '.html',
HAS_SOURCE: true,
SOURCELINK_SUFFIX: '.txt'
};
</script>
<script type="text/javascript" src="../../_static/jquery.js"></script>
<script type="text/javascript" src="../../_static/underscore.js"></script>
<script type="text/javascript" src="../../_static/doctools.js"></script>
<script type="text/javascript" src="../../_static/js/copybutton.js"></script>
<link rel="shortcut icon" href="../../_static/favicon.ico"/>
<link rel="author" title="About these documents" href="../../about.html" />
<link rel="search" title="Search" href="../../search.html" />
<link rel="next" title="Illustration of Gaussian process classification (GPC) on the XOR dataset" href="../gaussian_process/plot_gpc_xor.html" />
<link rel="prev" title="Test with permutations the significance of a classification score" href="plot_permutation_test_for_classification.html" />
<meta name="viewport" content="width=device-width, initial-scale=1.0" />
<script src="../../_static/js/bootstrap.min.js" type="text/javascript"></script>
<script>
VERSION_SUBDIR = (function(groups) {
return groups ? groups[1] : null;
})(location.href.match(/^https?:\/\/scikit-learn.org\/([^\/]+)/));
</script>
<link rel="canonical" href="https://scikit-learn.org/stable/auto_examples/feature_selection/plot_feature_selection.html" />
<script type="text/javascript">
$("div.buttonNext, div.buttonPrevious").hover(
function () {
$(this).css('background-color', '#FF9C34');
},
function () {
$(this).css('background-color', '#A7D6E2');
}
);
function showMenu() {
var topNav = document.getElementById("scikit-navbar");
if (topNav.className === "navbar") {
topNav.className += " responsive";
} else {
topNav.className = "navbar";
}
};
</script>
</head>
<body>
<div class="header-wrapper">
<div class="header">
<p class="logo"><a href="../../index.html">
<img src="../../_static/scikit-learn-logo-small.png" alt="Logo"/>
</a>
</p><div class="navbar" id="scikit-navbar">
<ul>
<li><a href="../../index.html">Home</a></li>
<li><a href="../../install.html">Installation</a></li>
<li class="btn-li"><div class="btn-group">
<a href="../../documentation.html">Documentation</a>
<a class="btn dropdown-toggle" data-toggle="dropdown">
<span class="caret"></span>
</a>
<ul class="dropdown-menu">
<li class="link-title">Scikit-learn <script>document.write(DOCUMENTATION_OPTIONS.VERSION + (VERSION_SUBDIR ? " (" + VERSION_SUBDIR + ")" : ""));</script></li>
<li><a href="../../tutorial/index.html">Tutorials</a></li>
<li><a href="../../user_guide.html">User guide</a></li>
<li><a href="../../modules/classes.html">API</a></li>
<li><a href="../../faq.html">FAQ</a></li>
<li><a href="../../developers/contributing.html">Contributing</a></li>
<li class="divider"></li>
<script>if (VERSION_SUBDIR != "stable") document.write('<li><a href="http://scikit-learn.org/stable/documentation.html">Stable version</a></li>')</script>
<script>if (VERSION_SUBDIR != "dev") document.write('<li><a href="http://scikit-learn.org/dev/documentation.html">Development version</a></li>')</script>
<li><a href="http://scikit-learn.org/dev/versions.html">All available versions</a></li>
<li><a href="../../_downloads/scikit-learn-docs.pdf">PDF documentation</a></li>
</ul>
</div>
</li>
<li><a href="../index.html">Examples</a></li>
</ul>
<a href="javascript:void(0);" onclick="showMenu()">
<div class="nav-icon">
<div class="hamburger-line"></div>
<div class="hamburger-line"></div>
<div class="hamburger-line"></div>
</div>
</a>
<div class="search_form">
<div class="gcse-search" id="cse" style="width: 100%;"></div>
</div>
</div> <!-- end navbar --></div>
</div>
<!-- GitHub "fork me" ribbon -->
<a href="https://github.com/scikit-learn/scikit-learn">
<img class="fork-me"
style="position: absolute; top: 0; right: 0; border: 0;"
src="../../_static/img/forkme.png"
alt="Fork me on GitHub" />
</a>
<div class="content-wrapper">
<div class="sphinxsidebar">
<div class="sphinxsidebarwrapper">
<div class="rel">
<div class="rellink">
<a href="plot_permutation_test_for_classification.html"
accesskey="P">Previous
<br/>
<span class="smallrellink">
Test with per...
</span>
<span class="hiddenrellink">
Test with permutations the significance of a classification score
</span>
</a>
</div>
<div class="spacer">
</div>
<div class="rellink">
<a href="../gaussian_process/plot_gpc_xor.html"
accesskey="N">Next
<br/>
<span class="smallrellink">
Illustration ...
</span>
<span class="hiddenrellink">
Illustration of Gaussian process classification (GPC) on the XOR dataset
</span>
</a>
</div>
<!-- Ad a link to the 'up' page -->
<div class="spacer">
</div>
<div class="rellink">
<a href="../index.html">
Up
<br/>
<span class="smallrellink">
Examples
</span>
<span class="hiddenrellink">
Examples
</span>
</a>
</div>
</div>
<p class="doc-version"><b>scikit-learn v0.19.2</b><br/>
<a href="http://scikit-learn.org/stable/support.html#documentation-resources">Other versions</a></p>
<p class="citing">Please <b><a href="../../about.html#citing-scikit-learn" style="font-size: 110%;">cite us </a></b>if you use the software.</p>
<ul>
<li><a class="reference internal" href="#">Univariate Feature Selection</a></li>
</ul>
</div>
</div>
<input type="checkbox" id="nav-trigger" class="nav-trigger" checked />
<label for="nav-trigger"></label>
<div class="content">
<div class="documentwrapper">
<div class="bodywrapper">
<div class="body" role="main">
<div class="section" id="univariate-feature-selection">
<span id="sphx-glr-auto-examples-feature-selection-plot-feature-selection-py"></span><h1>Univariate Feature Selection<a class="headerlink" href="#univariate-feature-selection" title="Permalink to this headline">¶</a></h1>
<p>An example showing univariate feature selection.</p>
<p>Noisy (non informative) features are added to the iris data and
univariate feature selection is applied. For each feature, we plot the
p-values for the univariate feature selection and the corresponding
weights of an SVM. We can see that univariate feature selection
selects the informative features and that these have larger SVM weights.</p>
<p>In the total set of features, only the 4 first ones are significant. We
can see that they have the highest score with univariate feature
selection. The SVM assigns a large weight to one of these features, but also
Selects many of the non-informative features.
Applying univariate feature selection before the SVM
increases the SVM weight attributed to the significant features, and will
thus improve classification.</p>
<img alt="../../_images/sphx_glr_plot_feature_selection_001.png" class="align-center" src="../../_images/sphx_glr_plot_feature_selection_001.png" />
<div class="highlight-python"><div class="highlight"><pre><span></span><span class="k">print</span><span class="p">(</span><span class="vm">__doc__</span><span class="p">)</span>
<span class="kn">import</span> <span class="nn">numpy</span> <span class="kn">as</span> <span class="nn">np</span>
<span class="kn">import</span> <span class="nn">matplotlib.pyplot</span> <span class="kn">as</span> <span class="nn">plt</span>
<span class="kn">from</span> <span class="nn">sklearn</span> <span class="kn">import</span> <span class="n">datasets</span><span class="p">,</span> <span class="n">svm</span>
<span class="kn">from</span> <span class="nn">sklearn.feature_selection</span> <span class="kn">import</span> <a href="../../modules/generated/sklearn.feature_selection.SelectPercentile.html#sklearn.feature_selection.SelectPercentile" title="View documentation for sklearn.feature_selection.SelectPercentile"><span class="n">SelectPercentile</span></a><span class="p">,</span> <a href="../../modules/generated/sklearn.feature_selection.f_classif.html#sklearn.feature_selection.f_classif" title="View documentation for sklearn.feature_selection.f_classif"><span class="n">f_classif</span></a>
<span class="c1"># #############################################################################</span>
<span class="c1"># Import some data to play with</span>
<span class="c1"># The iris dataset</span>
<span class="n">iris</span> <span class="o">=</span> <a href="../../modules/generated/sklearn.datasets.load_iris.html#sklearn.datasets.load_iris" title="View documentation for sklearn.datasets.load_iris"><span class="n">datasets</span><span class="o">.</span><span class="n">load_iris</span></a><span class="p">()</span>
<span class="c1"># Some noisy data not correlated</span>
<span class="n">E</span> <span class="o">=</span> <a href="http://docs.scipy.org/doc/numpy-1.8.1/reference/generated/numpy.random.uniform.html#numpy.random.uniform" title="View documentation for numpy.random.uniform"><span class="n">np</span><span class="o">.</span><span class="n">random</span><span class="o">.</span><span class="n">uniform</span></a><span class="p">(</span><span class="mi">0</span><span class="p">,</span> <span class="mf">0.1</span><span class="p">,</span> <span class="n">size</span><span class="o">=</span><span class="p">(</span><span class="nb">len</span><span class="p">(</span><span class="n">iris</span><span class="o">.</span><span class="n">data</span><span class="p">),</span> <span class="mi">20</span><span class="p">))</span>
<span class="c1"># Add the noisy data to the informative features</span>
<span class="n">X</span> <span class="o">=</span> <a href="http://docs.scipy.org/doc/numpy-1.8.1/reference/generated/numpy.hstack.html#numpy.hstack" title="View documentation for numpy.hstack"><span class="n">np</span><span class="o">.</span><span class="n">hstack</span></a><span class="p">((</span><span class="n">iris</span><span class="o">.</span><span class="n">data</span><span class="p">,</span> <span class="n">E</span><span class="p">))</span>
<span class="n">y</span> <span class="o">=</span> <span class="n">iris</span><span class="o">.</span><span class="n">target</span>
<a href="http://matplotlib.org/api/_as_gen/matplotlib.figure.AxesStack.html#matplotlib.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="mi">1</span><span class="p">)</span>
<a href="http://matplotlib.org/api/_as_gen/matplotlib.pyplot.clf.html#matplotlib.pyplot.clf" title="View documentation for matplotlib.pyplot.clf"><span class="n">plt</span><span class="o">.</span><span class="n">clf</span></a><span class="p">()</span>
<span class="n">X_indices</span> <span class="o">=</span> <a href="http://docs.scipy.org/doc/numpy-1.8.1/reference/generated/numpy.arange.html#numpy.arange" title="View documentation for numpy.arange"><span class="n">np</span><span class="o">.</span><span class="n">arange</span></a><span class="p">(</span><span class="n">X</span><span class="o">.</span><span class="n">shape</span><span class="p">[</span><span class="o">-</span><span class="mi">1</span><span class="p">])</span>
<span class="c1"># #############################################################################</span>
<span class="c1"># Univariate feature selection with F-test for feature scoring</span>
<span class="c1"># We use the default selection function: the 10% most significant features</span>
<span class="n">selector</span> <span class="o">=</span> <a href="../../modules/generated/sklearn.feature_selection.SelectPercentile.html#sklearn.feature_selection.SelectPercentile" title="View documentation for sklearn.feature_selection.SelectPercentile"><span class="n">SelectPercentile</span></a><span class="p">(</span><a href="../../modules/generated/sklearn.feature_selection.f_classif.html#sklearn.feature_selection.f_classif" title="View documentation for sklearn.feature_selection.f_classif"><span class="n">f_classif</span></a><span class="p">,</span> <span class="n">percentile</span><span class="o">=</span><span class="mi">10</span><span class="p">)</span>
<span class="n">selector</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="n">scores</span> <span class="o">=</span> <span class="o">-</span><a href="http://docs.scipy.org/doc/numpy-1.8.1/reference/generated/numpy.log10.html#numpy.log10" title="View documentation for numpy.log10"><span class="n">np</span><span class="o">.</span><span class="n">log10</span></a><span class="p">(</span><span class="n">selector</span><span class="o">.</span><span class="n">pvalues_</span><span class="p">)</span>
<span class="n">scores</span> <span class="o">/=</span> <span class="n">scores</span><span class="o">.</span><span class="n">max</span><span class="p">()</span>
<a href="http://matplotlib.org/api/_as_gen/matplotlib.pyplot.bar.html#matplotlib.pyplot.bar" title="View documentation for matplotlib.pyplot.bar"><span class="n">plt</span><span class="o">.</span><span class="n">bar</span></a><span class="p">(</span><span class="n">X_indices</span> <span class="o">-</span> <span class="o">.</span><span class="mi">45</span><span class="p">,</span> <span class="n">scores</span><span class="p">,</span> <span class="n">width</span><span class="o">=.</span><span class="mi">2</span><span class="p">,</span>
<span class="n">label</span><span class="o">=</span><span class="sa">r</span><span class="s1">'Univariate score ($-Log(p_{value})$)'</span><span class="p">,</span> <span class="n">color</span><span class="o">=</span><span class="s1">'darkorange'</span><span class="p">,</span>
<span class="n">edgecolor</span><span class="o">=</span><span class="s1">'black'</span><span class="p">)</span>
<span class="c1"># #############################################################################</span>
<span class="c1"># Compare to the weights of an SVM</span>
<span class="n">clf</span> <span class="o">=</span> <a href="../../modules/generated/sklearn.svm.SVC.html#sklearn.svm.SVC" title="View documentation for sklearn.svm.SVC"><span class="n">svm</span><span class="o">.</span><span class="n">SVC</span></a><span class="p">(</span><span class="n">kernel</span><span class="o">=</span><span class="s1">'linear'</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</span><span class="p">,</span> <span class="n">y</span><span class="p">)</span>
<span class="n">svm_weights</span> <span class="o">=</span> <span class="p">(</span><span class="n">clf</span><span class="o">.</span><span class="n">coef_</span> <span class="o">**</span> <span class="mi">2</span><span class="p">)</span><span class="o">.</span><span class="n">sum</span><span class="p">(</span><span class="n">axis</span><span class="o">=</span><span class="mi">0</span><span class="p">)</span>
<span class="n">svm_weights</span> <span class="o">/=</span> <span class="n">svm_weights</span><span class="o">.</span><span class="n">max</span><span class="p">()</span>
<a href="http://matplotlib.org/api/_as_gen/matplotlib.pyplot.bar.html#matplotlib.pyplot.bar" title="View documentation for matplotlib.pyplot.bar"><span class="n">plt</span><span class="o">.</span><span class="n">bar</span></a><span class="p">(</span><span class="n">X_indices</span> <span class="o">-</span> <span class="o">.</span><span class="mi">25</span><span class="p">,</span> <span class="n">svm_weights</span><span class="p">,</span> <span class="n">width</span><span class="o">=.</span><span class="mi">2</span><span class="p">,</span> <span class="n">label</span><span class="o">=</span><span class="s1">'SVM weight'</span><span class="p">,</span>
<span class="n">color</span><span class="o">=</span><span class="s1">'navy'</span><span class="p">,</span> <span class="n">edgecolor</span><span class="o">=</span><span class="s1">'black'</span><span class="p">)</span>
<span class="n">clf_selected</span> <span class="o">=</span> <a href="../../modules/generated/sklearn.svm.SVC.html#sklearn.svm.SVC" title="View documentation for sklearn.svm.SVC"><span class="n">svm</span><span class="o">.</span><span class="n">SVC</span></a><span class="p">(</span><span class="n">kernel</span><span class="o">=</span><span class="s1">'linear'</span><span class="p">)</span>
<span class="n">clf_selected</span><span class="o">.</span><span class="n">fit</span><span class="p">(</span><span class="n">selector</span><span class="o">.</span><span class="n">transform</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">svm_weights_selected</span> <span class="o">=</span> <span class="p">(</span><span class="n">clf_selected</span><span class="o">.</span><span class="n">coef_</span> <span class="o">**</span> <span class="mi">2</span><span class="p">)</span><span class="o">.</span><span class="n">sum</span><span class="p">(</span><span class="n">axis</span><span class="o">=</span><span class="mi">0</span><span class="p">)</span>
<span class="n">svm_weights_selected</span> <span class="o">/=</span> <span class="n">svm_weights_selected</span><span class="o">.</span><span class="n">max</span><span class="p">()</span>
<a href="http://matplotlib.org/api/_as_gen/matplotlib.pyplot.bar.html#matplotlib.pyplot.bar" title="View documentation for matplotlib.pyplot.bar"><span class="n">plt</span><span class="o">.</span><span class="n">bar</span></a><span class="p">(</span><span class="n">X_indices</span><span class="p">[</span><span class="n">selector</span><span class="o">.</span><span class="n">get_support</span><span class="p">()]</span> <span class="o">-</span> <span class="o">.</span><span class="mo">05</span><span class="p">,</span> <span class="n">svm_weights_selected</span><span class="p">,</span>
<span class="n">width</span><span class="o">=.</span><span class="mi">2</span><span class="p">,</span> <span class="n">label</span><span class="o">=</span><span class="s1">'SVM weights after selection'</span><span class="p">,</span> <span class="n">color</span><span class="o">=</span><span class="s1">'c'</span><span class="p">,</span>
<span class="n">edgecolor</span><span class="o">=</span><span class="s1">'black'</span><span class="p">)</span>
<a href="http://matplotlib.org/api/_as_gen/matplotlib.pyplot.title.html#matplotlib.pyplot.title" title="View documentation for matplotlib.pyplot.title"><span class="n">plt</span><span class="o">.</span><span class="n">title</span></a><span class="p">(</span><span class="s2">"Comparing feature selection"</span><span class="p">)</span>
<a href="http://matplotlib.org/api/_as_gen/matplotlib.pyplot.xlabel.html#matplotlib.pyplot.xlabel" title="View documentation for matplotlib.pyplot.xlabel"><span class="n">plt</span><span class="o">.</span><span class="n">xlabel</span></a><span class="p">(</span><span class="s1">'Feature number'</span><span class="p">)</span>
<a href="http://matplotlib.org/api/_as_gen/matplotlib.pyplot.yticks.html#matplotlib.pyplot.yticks" title="View documentation for matplotlib.pyplot.yticks"><span class="n">plt</span><span class="o">.</span><span class="n">yticks</span></a><span class="p">(())</span>
<a href="http://matplotlib.org/api/axis_api.html#matplotlib.axis" title="View documentation for matplotlib.pyplot.axis"><span class="n">plt</span><span class="o">.</span><span class="n">axis</span></a><span class="p">(</span><span class="s1">'tight'</span><span class="p">)</span>
<a href="http://matplotlib.org/api/legend_api.html#matplotlib.legend" title="View documentation for matplotlib.pyplot.legend"><span class="n">plt</span><span class="o">.</span><span class="n">legend</span></a><span class="p">(</span><span class="n">loc</span><span class="o">=</span><span class="s1">'upper right'</span><span class="p">)</span>
<a href="http://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>
<p><strong>Total running time of the script:</strong> ( 0 minutes 0.066 seconds)</p>
<div class="sphx-glr-footer docutils container">
<div class="sphx-glr-download docutils container">
<a class="reference download internal" href="../../_downloads/plot_feature_selection.py" download=""><code class="xref download docutils literal"><span class="pre">Download</span> <span class="pre">Python</span> <span class="pre">source</span> <span class="pre">code:</span> <span class="pre">plot_feature_selection.py</span></code></a></div>
<div class="sphx-glr-download docutils container">
<a class="reference download internal" href="../../_downloads/plot_feature_selection.ipynb" download=""><code class="xref download docutils literal"><span class="pre">Download</span> <span class="pre">Jupyter</span> <span class="pre">notebook:</span> <span class="pre">plot_feature_selection.ipynb</span></code></a></div>
</div>
<p class="sphx-glr-signature"><a class="reference external" href="https://sphinx-gallery.readthedocs.io">Generated by Sphinx-Gallery</a></p>
</div>
</div>
</div>
</div>
<div class="clearer"></div>
</div>
</div>
<div class="footer">
© 2007 - 2017, scikit-learn developers (BSD License).
<a href="../../_sources/auto_examples/feature_selection/plot_feature_selection.rst.txt" rel="nofollow">Show this page source</a>
</div>
<div class="rel">
<div class="buttonPrevious">
<a href="plot_permutation_test_for_classification.html">Previous
</a>
</div>
<div class="buttonNext">
<a href="../gaussian_process/plot_gpc_xor.html">Next
</a>
</div>
</div>
<script type="text/javascript">
var _gaq = _gaq || [];
_gaq.push(['_setAccount', 'UA-22606712-2']);
_gaq.push(['_trackPageview']);
(function() {
var ga = document.createElement('script'); ga.type = 'text/javascript'; ga.async = true;
ga.src = ('https:' == document.location.protocol ? 'https://ssl' : 'http://www') + '.google-analytics.com/ga.js';
var s = document.getElementsByTagName('script')[0]; s.parentNode.insertBefore(ga, s);
})();
</script>
<script>
(function() {
var cx = '016639176250731907682:tjtqbvtvij0';
var gcse = document.createElement('script'); gcse.type = 'text/javascript'; gcse.async = true;
gcse.src = 'https://cse.google.com/cse.js?cx=' + cx;
var s = document.getElementsByTagName('script')[0]; s.parentNode.insertBefore(gcse, s);
})();
</script>
<script src="https://scikit-learn.org/versionwarning.js"></script>
</body>
</html>