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<li><a class="reference internal" href="#">Univariate Feature Selection</a></li>
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<div class="sphx-glr-download-link-note admonition note">
<p class="first admonition-title">Note</p>
<p class="last">Click <a class="reference internal" href="#sphx-glr-download-auto-examples-feature-selection-plot-feature-selection-py"><span class="std std-ref">here</span></a> to download the full example code</p>
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<div class="sphx-glr-example-title 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="sphx-glr-single-img" src="../../_images/sphx_glr_plot_feature_selection_001.png" />
<p class="sphx-glr-script-out">Out:</p>
<div class="sphx-glr-script-out highlight-none"><div class="highlight"><pre><span></span>
</pre></div>
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</div>
<div class="highlight-default"><div class="highlight"><pre><span></span><span class="nb">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="k">as</span> <span class="nn">np</span>
<span class="kn">import</span> <span class="nn">matplotlib.pyplot</span> <span class="k">as</span> <span class="nn">plt</span>
<span class="kn">from</span> <span class="nn">sklearn</span> <span class="k">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="k">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> <span class="n">np</span><span class="o">.</span><span class="n">random</span><span class="o">.</span><span class="n">uniform</span><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="https://docs.scipy.org/doc/numpy/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="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="mi">1</span><span class="p">)</span>
<a href="https://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="https://docs.scipy.org/doc/numpy/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="https://docs.scipy.org/doc/numpy/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="https://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 ($-Log(p_</span><span class="si">{value}</span><span class="s1">)$)'</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="https://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="https://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="mi">05</span><span class="p">,</span> <span class="n">svm_weights_selected</span><span class="p">,</span>
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