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<section class="sphx-glr-example-title" 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="Link to this heading">¶</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 src="../../_images/sphx_glr_plot_svm_nonlinear_001.png" srcset="../../_images/sphx_glr_plot_svm_nonlinear_001.png" alt="plot svm nonlinear" class = "sphx-glr-single-img"/><div class="highlight-Python notranslate"><div class="highlight"><pre><span></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">import</span> <span class="nn">numpy</span> <span class="k">as</span> <span class="nn">np</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="https://numpy.org/doc/stable/reference/generated/numpy.meshgrid.html#numpy.meshgrid" title="numpy.meshgrid" class="sphx-glr-backref-module-numpy sphx-glr-backref-type-py-function"><span class="n">np</span><span class="o">.</span><span class="n">meshgrid</span></a><span class="p">(</span><a href="https://numpy.org/doc/stable/reference/generated/numpy.linspace.html#numpy.linspace" title="numpy.linspace" class="sphx-glr-backref-module-numpy sphx-glr-backref-type-py-function"><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="https://numpy.org/doc/stable/reference/generated/numpy.linspace.html#numpy.linspace" title="numpy.linspace" class="sphx-glr-backref-module-numpy sphx-glr-backref-type-py-function"><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="https://numpy.org/doc/stable/reference/random/generated/numpy.random.seed.html#numpy.random.seed" title="numpy.random.seed" class="sphx-glr-backref-module-numpy-random sphx-glr-backref-type-py-function"><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="https://numpy.org/doc/stable/reference/random/generated/numpy.random.randn.html#numpy.random.randn" title="numpy.random.randn" class="sphx-glr-backref-module-numpy-random sphx-glr-backref-type-py-function"><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="https://numpy.org/doc/stable/reference/generated/numpy.logical_xor.html#numpy.logical_xor" title="numpy.logical_xor" class="sphx-glr-backref-module-numpy sphx-glr-backref-type-py-data"><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="sklearn.svm.NuSVC" class="sphx-glr-backref-module-sklearn-svm sphx-glr-backref-type-py-class sphx-glr-backref-instance"><span class="n">svm</span><span class="o">.</span><span class="n">NuSVC</span></a><span class="p">(</span><span class="n">gamma</span><span class="o">=</span><span class="s2">"auto"</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 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="https://numpy.org/doc/stable/reference/generated/numpy.c_.html#numpy.c_" title="numpy.c_" class="sphx-glr-backref-module-numpy sphx-glr-backref-type-py-data"><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="https://matplotlib.org/stable/api/_as_gen/matplotlib.pyplot.imshow.html#matplotlib.pyplot.imshow" title="matplotlib.pyplot.imshow" class="sphx-glr-backref-module-matplotlib-pyplot sphx-glr-backref-type-py-function"><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="s2">"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="s2">"auto"</span><span class="p">,</span>
<span class="n">origin</span><span class="o">=</span><span class="s2">"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="p">)</span>
<span class="n">contours</span> <span class="o">=</span> <a href="https://matplotlib.org/stable/api/_as_gen/matplotlib.pyplot.contour.html#matplotlib.pyplot.contour" title="matplotlib.pyplot.contour" class="sphx-glr-backref-module-matplotlib-pyplot sphx-glr-backref-type-py-function"><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">linestyles</span><span class="o">=</span><span class="s2">"dashed"</span><span class="p">)</span>
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