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<li><a class="reference internal" href="#">SVM with custom kernel</a></li>
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<section class="sphx-glr-example-title" id="svm-with-custom-kernel">
<span id="sphx-glr-auto-examples-svm-plot-custom-kernel-py"></span><h1>SVM with custom kernel<a class="headerlink" href="#svm-with-custom-kernel" title="Permalink to this heading">¶</a></h1>
<p>Simple usage of Support Vector Machines to classify a sample. It will
plot the decision surface and the support vectors.</p>
<img src="../../_images/sphx_glr_plot_custom_kernel_001.png" srcset="../../_images/sphx_glr_plot_custom_kernel_001.png" alt="3-Class classification using Support Vector Machine with custom kernel" class = "sphx-glr-single-img"/><div class="highlight-default notranslate"><div class="highlight"><pre><span></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="kn">import</span> <span class="n">svm</span><span class="p">,</span> <span class="n">datasets</span>
<span class="kn">from</span> <span class="nn">sklearn.inspection</span> <span class="kn">import</span> <span class="n">DecisionBoundaryDisplay</span>
<span class="c1"># import some data to play with</span>
<span class="n">iris</span> <span class="o">=</span> <span class="n">datasets</span><span class="o">.</span><span class="n">load_iris</span><span class="p">()</span>
<span class="n">X</span> <span class="o">=</span> <span class="n">iris</span><span class="o">.</span><span class="n">data</span><span class="p">[:,</span> <span class="p">:</span><span class="mi">2</span><span class="p">]</span> <span class="c1"># we only take the first two features. We could</span>
<span class="c1"># avoid this ugly slicing by using a two-dim dataset</span>
<span class="n">Y</span> <span class="o">=</span> <span class="n">iris</span><span class="o">.</span><span class="n">target</span>
<span class="k">def</span> <span class="nf">my_kernel</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="w"> </span><span class="sd">"""</span>
<span class="sd"> We create a custom kernel:</span>
<span class="sd"> (2 0)</span>
<span class="sd"> k(X, Y) = X ( ) Y.T</span>
<span class="sd"> (0 1)</span>
<span class="sd"> """</span>
<span class="n">M</span> <span class="o">=</span> <a href="https://numpy.org/doc/stable/reference/generated/numpy.array.html#numpy.array" title="numpy.array" class="sphx-glr-backref-module-numpy sphx-glr-backref-type-py-function"><span class="n">np</span><span class="o">.</span><span class="n">array</span></a><span class="p">([[</span><span class="mi">2</span><span class="p">,</span> <span class="mi">0</span><span class="p">],</span> <span class="p">[</span><span class="mi">0</span><span class="p">,</span> <span class="mf">1.0</span><span class="p">]])</span>
<span class="k">return</span> <a href="https://numpy.org/doc/stable/reference/generated/numpy.dot.html#numpy.dot" title="numpy.dot" class="sphx-glr-backref-module-numpy sphx-glr-backref-type-py-function"><span class="n">np</span><span class="o">.</span><span class="n">dot</span></a><span class="p">(</span><a href="https://numpy.org/doc/stable/reference/generated/numpy.dot.html#numpy.dot" title="numpy.dot" class="sphx-glr-backref-module-numpy sphx-glr-backref-type-py-function"><span class="n">np</span><span class="o">.</span><span class="n">dot</span></a><span class="p">(</span><span class="n">X</span><span class="p">,</span> <span class="n">M</span><span class="p">),</span> <span class="n">Y</span><span class="o">.</span><span class="n">T</span><span class="p">)</span>
<span class="n">h</span> <span class="o">=</span> <span class="mf">0.02</span> <span class="c1"># step size in the mesh</span>
<span class="c1"># we create an instance of SVM and fit out data.</span>
<span class="n">clf</span> <span class="o">=</span> <span class="n">svm</span><span class="o">.</span><span class="n">SVC</span><span class="p">(</span><span class="n">kernel</span><span class="o">=</span><span class="n">my_kernel</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">ax</span> <span class="o">=</span> <a href="https://matplotlib.org/stable/api/_as_gen/matplotlib.pyplot.gca.html#matplotlib.pyplot.gca" title="matplotlib.pyplot.gca" 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">gca</span></a><span class="p">()</span>
<span class="n">DecisionBoundaryDisplay</span><span class="o">.</span><span class="n">from_estimator</span><span class="p">(</span>
<span class="n">clf</span><span class="p">,</span>
<span class="n">X</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">ax</span><span class="o">=</span><span class="n">ax</span><span class="p">,</span>
<span class="n">response_method</span><span class="o">=</span><span class="s2">"predict"</span><span class="p">,</span>
<span class="n">plot_method</span><span class="o">=</span><span class="s2">"pcolormesh"</span><span class="p">,</span>
<span class="n">shading</span><span class="o">=</span><span class="s2">"auto"</span><span class="p">,</span>
<span class="p">)</span>
<span class="c1"># Plot also the training points</span>
<a href="https://matplotlib.org/stable/api/_as_gen/matplotlib.pyplot.scatter.html#matplotlib.pyplot.scatter" title="matplotlib.pyplot.scatter" 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">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="s2">"k"</span><span class="p">)</span>
<a href="https://matplotlib.org/stable/api/_as_gen/matplotlib.pyplot.title.html#matplotlib.pyplot.title" title="matplotlib.pyplot.title" 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">title</span></a><span class="p">(</span><span class="s2">"3-Class classification using Support Vector Machine with custom kernel"</span><span class="p">)</span>
<a href="https://matplotlib.org/stable/api/_as_gen/matplotlib.pyplot.axis.html#matplotlib.pyplot.axis" title="matplotlib.pyplot.axis" 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">axis</span></a><span class="p">(</span><span class="s2">"tight"</span><span class="p">)</span>
<a href="https://matplotlib.org/stable/api/_as_gen/matplotlib.pyplot.show.html#matplotlib.pyplot.show" title="matplotlib.pyplot.show" 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">show</span></a><span class="p">()</span>
</pre></div>
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<p class="sphx-glr-timing"><strong>Total running time of the script:</strong> ( 0 minutes 0.094 seconds)</p>
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<p><a class="reference download internal" download="" href="../../_downloads/31b78d45b09682c72f57e77cf94a939e/plot_custom_kernel.py"><code class="xref download docutils literal notranslate"><span class="pre">Download</span> <span class="pre">Python</span> <span class="pre">source</span> <span class="pre">code:</span> <span class="pre">plot_custom_kernel.py</span></code></a></p>
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