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<div class="section" id="svm-kernels">
<span id="sphx-glr-auto-examples-svm-plot-svm-kernels-py"></span><h1>SVM-Kernels<a class="headerlink" href="#svm-kernels" title="Permalink to this headline">¶</a></h1>
<p>Three different types of SVM-Kernels are displayed below.
The polynomial and RBF are especially useful when the
data-points are not linearly separable.</p>
<ul class="sphx-glr-horizontal">
<li><a class="first reference internal image-reference" href="../../_images/sphx_glr_plot_svm_kernels_001.png"><img alt="../../_images/sphx_glr_plot_svm_kernels_001.png" src="../../_images/sphx_glr_plot_svm_kernels_001.png" style="width: 188.0px; height: 141.0px;" /></a>
</li>
<li><a class="first reference internal image-reference" href="../../_images/sphx_glr_plot_svm_kernels_002.png"><img alt="../../_images/sphx_glr_plot_svm_kernels_002.png" src="../../_images/sphx_glr_plot_svm_kernels_002.png" style="width: 188.0px; height: 141.0px;" /></a>
</li>
<li><a class="first reference internal image-reference" href="../../_images/sphx_glr_plot_svm_kernels_003.png"><img alt="../../_images/sphx_glr_plot_svm_kernels_003.png" src="../../_images/sphx_glr_plot_svm_kernels_003.png" style="width: 188.0px; height: 141.0px;" /></a>
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<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="c1"># Code source: Gaël Varoquaux</span>
<span class="c1"># License: BSD 3 clause</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"># Our dataset and targets</span>
<span class="n">X</span> <span class="o">=</span> <a href="http://docs.scipy.org/doc/numpy-1.8.1/reference/generated/numpy.c_.html#numpy.c_" title="View documentation for numpy.c_"><span class="n">np</span><span class="o">.</span><span class="n">c_</span></a><span class="p">[(</span><span class="o">.</span><span class="mi">4</span><span class="p">,</span> <span class="o">-.</span><span class="mi">7</span><span class="p">),</span>
<span class="p">(</span><span class="o">-</span><span class="mf">1.5</span><span class="p">,</span> <span class="o">-</span><span class="mi">1</span><span class="p">),</span>
<span class="p">(</span><span class="o">-</span><span class="mf">1.4</span><span class="p">,</span> <span class="o">-.</span><span class="mi">9</span><span class="p">),</span>
<span class="p">(</span><span class="o">-</span><span class="mf">1.3</span><span class="p">,</span> <span class="o">-</span><span class="mf">1.2</span><span class="p">),</span>
<span class="p">(</span><span class="o">-</span><span class="mf">1.1</span><span class="p">,</span> <span class="o">-.</span><span class="mi">2</span><span class="p">),</span>
<span class="p">(</span><span class="o">-</span><span class="mf">1.2</span><span class="p">,</span> <span class="o">-.</span><span class="mi">4</span><span class="p">),</span>
<span class="p">(</span><span class="o">-.</span><span class="mi">5</span><span class="p">,</span> <span class="mf">1.2</span><span class="p">),</span>
<span class="p">(</span><span class="o">-</span><span class="mf">1.5</span><span class="p">,</span> <span class="mf">2.1</span><span class="p">),</span>
<span class="p">(</span><span class="mi">1</span><span class="p">,</span> <span class="mi">1</span><span class="p">),</span>
<span class="c1"># --</span>
<span class="p">(</span><span class="mf">1.3</span><span class="p">,</span> <span class="o">.</span><span class="mi">8</span><span class="p">),</span>
<span class="p">(</span><span class="mf">1.2</span><span class="p">,</span> <span class="o">.</span><span class="mi">5</span><span class="p">),</span>
<span class="p">(</span><span class="o">.</span><span class="mi">2</span><span class="p">,</span> <span class="o">-</span><span class="mi">2</span><span class="p">),</span>
<span class="p">(</span><span class="o">.</span><span class="mi">5</span><span class="p">,</span> <span class="o">-</span><span class="mf">2.4</span><span class="p">),</span>
<span class="p">(</span><span class="o">.</span><span class="mi">2</span><span class="p">,</span> <span class="o">-</span><span class="mf">2.3</span><span class="p">),</span>
<span class="p">(</span><span class="mi">0</span><span class="p">,</span> <span class="o">-</span><span class="mf">2.7</span><span class="p">),</span>
<span class="p">(</span><span class="mf">1.3</span><span class="p">,</span> <span class="mf">2.1</span><span class="p">)]</span><span class="o">.</span><span class="n">T</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="mi">8</span> <span class="o">+</span> <span class="p">[</span><span class="mi">1</span><span class="p">]</span> <span class="o">*</span> <span class="mi">8</span>
<span class="c1"># figure number</span>
<span class="n">fignum</span> <span class="o">=</span> <span class="mi">1</span>
<span class="c1"># fit the model</span>
<span class="k">for</span> <span class="n">kernel</span> <span class="ow">in</span> <span class="p">(</span><span class="s1">'linear'</span><span class="p">,</span> <span class="s1">'poly'</span><span class="p">,</span> <span class="s1">'rbf'</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="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="n">kernel</span><span class="p">,</span> <span class="n">gamma</span><span class="o">=</span><span class="mi">2</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"># plot the line, the points, and the nearest vectors to the plane</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="n">fignum</span><span class="p">,</span> <span class="n">figsize</span><span class="o">=</span><span class="p">(</span><span class="mi">4</span><span class="p">,</span> <span class="mi">3</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>
<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">clf</span><span class="o">.</span><span class="n">support_vectors_</span><span class="p">[:,</span> <span class="mi">0</span><span class="p">],</span> <span class="n">clf</span><span class="o">.</span><span class="n">support_vectors_</span><span class="p">[:,</span> <span class="mi">1</span><span class="p">],</span> <span class="n">s</span><span class="o">=</span><span class="mi">80</span><span class="p">,</span>
<span class="n">facecolors</span><span class="o">=</span><span class="s1">'none'</span><span class="p">,</span> <span class="n">zorder</span><span class="o">=</span><span class="mi">10</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/_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">zorder</span><span class="o">=</span><span class="mi">10</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/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>
<span class="n">x_min</span> <span class="o">=</span> <span class="o">-</span><span class="mi">3</span>
<span class="n">x_max</span> <span class="o">=</span> <span class="mi">3</span>
<span class="n">y_min</span> <span class="o">=</span> <span class="o">-</span><span class="mi">3</span>
<span class="n">y_max</span> <span class="o">=</span> <span class="mi">3</span>
<span class="n">XX</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.mgrid.html#numpy.mgrid" title="View documentation for numpy.mgrid"><span class="n">np</span><span class="o">.</span><span class="n">mgrid</span></a><span class="p">[</span><span class="n">x_min</span><span class="p">:</span><span class="n">x_max</span><span class="p">:</span><span class="mi">200j</span><span class="p">,</span> <span class="n">y_min</span><span class="p">:</span><span class="n">y_max</span><span class="p">:</span><span class="mi">200j</span><span class="p">]</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="http://docs.scipy.org/doc/numpy-1.8.1/reference/generated/numpy.c_.html#numpy.c_" title="View documentation for numpy.c_"><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="c1"># Put the result into a color plot</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>
<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="n">fignum</span><span class="p">,</span> <span class="n">figsize</span><span class="o">=</span><span class="p">(</span><span class="mi">4</span><span class="p">,</span> <span class="mi">3</span><span class="p">))</span>
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<span class="n">levels</span><span class="o">=</span><span class="p">[</span><span class="o">-.</span><span class="mi">5</span><span class="p">,</span> <span class="mi">0</span><span class="p">,</span> <span class="o">.</span><span class="mi">5</span><span class="p">])</span>
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<span class="n">fignum</span> <span class="o">=</span> <span class="n">fignum</span> <span class="o">+</span> <span class="mi">1</span>
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