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<div class="section" id="svm-separating-hyperplane-for-unbalanced-classes">
<span id="sphx-glr-auto-examples-svm-plot-separating-hyperplane-unbalanced-py"></span><h1>SVM: Separating hyperplane for unbalanced classes<a class="headerlink" href="#svm-separating-hyperplane-for-unbalanced-classes" title="Permalink to this headline">¶</a></h1>
<p>Find the optimal separating hyperplane using an SVC for classes that
are unbalanced.</p>
<p>We first find the separating plane with a plain SVC and then plot
(dashed) the separating hyperplane with automatically correction for
unbalanced classes.</p>
<div class="admonition note">
<p class="first admonition-title">Note</p>
<p>This example will also work by replacing <code class="docutils literal"><span class="pre">SVC(kernel="linear")</span></code>
with <code class="docutils literal"><span class="pre">SGDClassifier(loss="hinge")</span></code>. Setting the <code class="docutils literal"><span class="pre">loss</span></code> parameter
of the <a class="reference internal" href="../../modules/generated/sklearn.linear_model.SGDClassifier.html#sklearn.linear_model.SGDClassifier" title="sklearn.linear_model.SGDClassifier"><code class="xref py py-class docutils literal"><span class="pre">SGDClassifier</span></code></a> equal to <code class="docutils literal"><span class="pre">hinge</span></code> will yield behaviour
such as that of a SVC with a linear kernel.</p>
<p>For example try instead of the <code class="docutils literal"><span class="pre">SVC</span></code>:</p>
<div class="last highlight-default"><div class="highlight"><pre><span></span><span class="n">clf</span> <span class="o">=</span> <span class="n">SGDClassifier</span><span class="p">(</span><span class="n">n_iter</span><span class="o">=</span><span class="mi">100</span><span class="p">,</span> <span class="n">alpha</span><span class="o">=</span><span class="mf">0.01</span><span class="p">)</span>
</pre></div>
</div>
</div>
<img alt="../../_images/sphx_glr_plot_separating_hyperplane_unbalanced_001.png" class="align-center" src="../../_images/sphx_glr_plot_separating_hyperplane_unbalanced_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">svm</span>
<span class="c1"># we create clusters with 1000 and 100 points</span>
<span class="n">rng</span> <span class="o">=</span> <a href="http://docs.scipy.org/doc/numpy-1.8.1/reference/generated/numpy.random.RandomState.wald.html#numpy.random.RandomState" title="View documentation for numpy.random.RandomState"><span class="n">np</span><span class="o">.</span><span class="n">random</span><span class="o">.</span><span class="n">RandomState</span></a><span class="p">(</span><span class="mi">0</span><span class="p">)</span>
<span class="n">n_samples_1</span> <span class="o">=</span> <span class="mi">1000</span>
<span class="n">n_samples_2</span> <span class="o">=</span> <span class="mi">100</span>
<span class="n">X</span> <span class="o">=</span> <a href="http://docs.scipy.org/doc/numpy-1.8.1/reference/generated/numpy.r_.html#numpy.r_" title="View documentation for numpy.r_"><span class="n">np</span><span class="o">.</span><span class="n">r_</span></a><span class="p">[</span><span class="mf">1.5</span> <span class="o">*</span> <span class="n">rng</span><span class="o">.</span><span class="n">randn</span><span class="p">(</span><span class="n">n_samples_1</span><span class="p">,</span> <span class="mi">2</span><span class="p">),</span>
<span class="mf">0.5</span> <span class="o">*</span> <span class="n">rng</span><span class="o">.</span><span class="n">randn</span><span class="p">(</span><span class="n">n_samples_2</span><span class="p">,</span> <span class="mi">2</span><span class="p">)</span> <span class="o">+</span> <span class="p">[</span><span class="mi">2</span><span class="p">,</span> <span class="mi">2</span><span class="p">]]</span>
<span class="n">y</span> <span class="o">=</span> <span class="p">[</span><span class="mi">0</span><span class="p">]</span> <span class="o">*</span> <span class="p">(</span><span class="n">n_samples_1</span><span class="p">)</span> <span class="o">+</span> <span class="p">[</span><span class="mi">1</span><span class="p">]</span> <span class="o">*</span> <span class="p">(</span><span class="n">n_samples_2</span><span class="p">)</span>
<span class="c1"># fit the model and get the separating hyperplane</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">C</span><span class="o">=</span><span class="mf">1.0</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="c1"># fit the model and get the separating hyperplane using weighted classes</span>
<span class="n">wclf</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">class_weight</span><span class="o">=</span><span class="p">{</span><span class="mi">1</span><span class="p">:</span> <span class="mi">10</span><span class="p">})</span>
<span class="n">wclf</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="c1"># plot separating hyperplanes and samples</span>
<a href="http://matplotlib.org/api/_as_gen/matplotlib.pyplot.scatter.html#matplotlib.pyplot.scatter" title="View documentation for matplotlib.pyplot.scatter"><span class="n">plt</span><span class="o">.</span><span class="n">scatter</span></a><span class="p">(</span><span class="n">X</span><span class="p">[:,</span> <span class="mi">0</span><span class="p">],</span> <span class="n">X</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</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">Paired</span><span class="p">,</span> <span class="n">edgecolors</span><span class="o">=</span><span class="s1">'k'</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="c1"># plot the decision functions for both classifiers</span>
<span class="n">ax</span> <span class="o">=</span> <a href="http://matplotlib.org/api/_as_gen/matplotlib.pyplot.gca.html#matplotlib.pyplot.gca" title="View documentation for matplotlib.pyplot.gca"><span class="n">plt</span><span class="o">.</span><span class="n">gca</span></a><span class="p">()</span>
<span class="n">xlim</span> <span class="o">=</span> <span class="n">ax</span><span class="o">.</span><span class="n">get_xlim</span><span class="p">()</span>
<span class="n">ylim</span> <span class="o">=</span> <span class="n">ax</span><span class="o">.</span><span class="n">get_ylim</span><span class="p">()</span>
<span class="c1"># create grid to evaluate model</span>
<span class="n">xx</span> <span class="o">=</span> <a href="http://docs.scipy.org/doc/numpy-1.8.1/reference/generated/numpy.linspace.html#numpy.linspace" title="View documentation for numpy.linspace"><span class="n">np</span><span class="o">.</span><span class="n">linspace</span></a><span class="p">(</span><span class="n">xlim</span><span class="p">[</span><span class="mi">0</span><span class="p">],</span> <span class="n">xlim</span><span class="p">[</span><span class="mi">1</span><span class="p">],</span> <span class="mi">30</span><span class="p">)</span>
<span class="n">yy</span> <span class="o">=</span> <a href="http://docs.scipy.org/doc/numpy-1.8.1/reference/generated/numpy.linspace.html#numpy.linspace" title="View documentation for numpy.linspace"><span class="n">np</span><span class="o">.</span><span class="n">linspace</span></a><span class="p">(</span><span class="n">ylim</span><span class="p">[</span><span class="mi">0</span><span class="p">],</span> <span class="n">ylim</span><span class="p">[</span><span class="mi">1</span><span class="p">],</span> <span class="mi">30</span><span class="p">)</span>
<span class="n">YY</span><span class="p">,</span> <span class="n">XX</span> <span class="o">=</span> <a href="http://docs.scipy.org/doc/numpy-1.8.1/reference/generated/numpy.meshgrid.html#numpy.meshgrid" title="View documentation for numpy.meshgrid"><span class="n">np</span><span class="o">.</span><span class="n">meshgrid</span></a><span class="p">(</span><span class="n">yy</span><span class="p">,</span> <span class="n">xx</span><span class="p">)</span>
<span class="n">xy</span> <span class="o">=</span> <a href="http://docs.scipy.org/doc/numpy-1.8.1/reference/generated/numpy.vstack.html#numpy.vstack" title="View documentation for numpy.vstack"><span class="n">np</span><span class="o">.</span><span class="n">vstack</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="o">.</span><span class="n">T</span>
<span class="c1"># get the separating hyperplane</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><span class="n">xy</span><span class="p">)</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"># plot decision boundary and margins</span>
<span class="n">a</span> <span class="o">=</span> <span class="n">ax</span><span class="o">.</span><span class="n">contour</span><span class="p">(</span><span class="n">XX</span><span class="p">,</span> <span class="n">YY</span><span class="p">,</span> <span class="n">Z</span><span class="p">,</span> <span class="n">colors</span><span class="o">=</span><span class="s1">'k'</span><span class="p">,</span> <span class="n">levels</span><span class="o">=</span><span class="p">[</span><span class="mi">0</span><span class="p">],</span> <span class="n">alpha</span><span class="o">=</span><span class="mf">0.5</span><span class="p">,</span> <span class="n">linestyles</span><span class="o">=</span><span class="p">[</span><span class="s1">'-'</span><span class="p">])</span>
<span class="c1"># get the separating hyperplane for weighted classes</span>
<span class="n">Z</span> <span class="o">=</span> <span class="n">wclf</span><span class="o">.</span><span class="n">decision_function</span><span class="p">(</span><span class="n">xy</span><span class="p">)</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"># plot decision boundary and margins for weighted classes</span>
<span class="n">b</span> <span class="o">=</span> <span class="n">ax</span><span class="o">.</span><span class="n">contour</span><span class="p">(</span><span class="n">XX</span><span class="p">,</span> <span class="n">YY</span><span class="p">,</span> <span class="n">Z</span><span class="p">,</span> <span class="n">colors</span><span class="o">=</span><span class="s1">'r'</span><span class="p">,</span> <span class="n">levels</span><span class="o">=</span><span class="p">[</span><span class="mi">0</span><span class="p">],</span> <span class="n">alpha</span><span class="o">=</span><span class="mf">0.5</span><span class="p">,</span> <span class="n">linestyles</span><span class="o">=</span><span class="p">[</span><span class="s1">'-'</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">a</span><span class="o">.</span><span class="n">collections</span><span class="p">[</span><span class="mi">0</span><span class="p">],</span> <span class="n">b</span><span class="o">.</span><span class="n">collections</span><span class="p">[</span><span class="mi">0</span><span class="p">]],</span> <span class="p">[</span><span class="s2">"non weighted"</span><span class="p">,</span> <span class="s2">"weighted"</span><span class="p">],</span>
<span class="n">loc</span><span class="o">=</span><span class="s2">"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>
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