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<div class="section" id="non-linear-svm">
<span id="sphx-glr-auto-examples-svm-plot-svm-nonlinear-py"></span><h1>Non-linear SVM<a class="headerlink" href="#non-linear-svm" title="Permalink to this headline">¶</a></h1>
<p>Perform binary classification using non-linear SVC
with RBF kernel. The target to predict is a XOR of the
inputs.</p>
<p>The color map illustrates the decision function learned by the SVC.</p>
<img alt="../../_images/sphx_glr_plot_svm_nonlinear_001.png" class="align-center" src="../../_images/sphx_glr_plot_svm_nonlinear_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="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.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><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="o">-</span><span class="mi">3</span><span class="p">,</span> <span class="mi">3</span><span class="p">,</span> <span class="mi">500</span><span class="p">),</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="o">-</span><span class="mi">3</span><span class="p">,</span> <span class="mi">3</span><span class="p">,</span> <span class="mi">500</span><span class="p">))</span>
<a href="http://docs.scipy.org/doc/numpy-1.8.1/reference/generated/numpy.random.seed.html#numpy.random.seed" title="View documentation for numpy.random.seed"><span class="n">np</span><span class="o">.</span><span class="n">random</span><span class="o">.</span><span class="n">seed</span></a><span class="p">(</span><span class="mi">0</span><span class="p">)</span>
<span class="n">X</span> <span class="o">=</span> <a href="http://docs.scipy.org/doc/numpy-1.8.1/reference/generated/numpy.random.randn.html#numpy.random.randn" title="View documentation for numpy.random.randn"><span class="n">np</span><span class="o">.</span><span class="n">random</span><span class="o">.</span><span class="n">randn</span></a><span class="p">(</span><span class="mi">300</span><span class="p">,</span> <span class="mi">2</span><span class="p">)</span>
<span class="n">Y</span> <span class="o">=</span> <a href="http://docs.scipy.org/doc/numpy-1.8.1/reference/generated/numpy.logical_xor.html#numpy.logical_xor" title="View documentation for numpy.logical_xor"><span class="n">np</span><span class="o">.</span><span class="n">logical_xor</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="o">></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="o">></span> <span class="mi">0</span><span class="p">)</span>
<span class="c1"># fit the model</span>
<span class="n">clf</span> <span class="o">=</span> <a href="../../modules/generated/sklearn.svm.NuSVC.html#sklearn.svm.NuSVC" title="View documentation for sklearn.svm.NuSVC"><span class="n">svm</span><span class="o">.</span><span class="n">NuSVC</span></a><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 decision function for each datapoint on the 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="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="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.pyplot.imshow.html#matplotlib.pyplot.imshow" title="View documentation for matplotlib.pyplot.imshow"><span class="n">plt</span><span class="o">.</span><span class="n">imshow</span></a><span class="p">(</span><span class="n">Z</span><span class="p">,</span> <span class="n">interpolation</span><span class="o">=</span><span class="s1">'nearest'</span><span class="p">,</span>
<span class="n">extent</span><span class="o">=</span><span class="p">(</span><span class="n">xx</span><span class="o">.</span><span class="n">min</span><span class="p">(),</span> <span class="n">xx</span><span class="o">.</span><span class="n">max</span><span class="p">(),</span> <span class="n">yy</span><span class="o">.</span><span class="n">min</span><span class="p">(),</span> <span class="n">yy</span><span class="o">.</span><span class="n">max</span><span class="p">()),</span> <span class="n">aspect</span><span class="o">=</span><span class="s1">'auto'</span><span class="p">,</span>
<span class="n">origin</span><span class="o">=</span><span class="s1">'lower'</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">PuOr_r</span><span class="p">)</span>
<span class="n">contours</span> <span class="o">=</span> <a href="http://matplotlib.org/api/contour_api.html#matplotlib.contour" title="View documentation for matplotlib.pyplot.contour"><span class="n">plt</span><span class="o">.</span><span class="n">contour</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="n">Z</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">linewidths</span><span class="o">=</span><span class="mi">2</span><span class="p">,</span>
<span class="n">linetypes</span><span class="o">=</span><span class="s1">'--'</span><span class="p">)</span>
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<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.xticks.html#matplotlib.pyplot.xticks" title="View documentation for matplotlib.pyplot.xticks"><span class="n">plt</span><span class="o">.</span><span class="n">xticks</span></a><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="o">-</span><span class="mi">3</span><span class="p">,</span> <span class="mi">3</span><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>
<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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