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<li><a class="reference internal" href="#">One-class SVM with non-linear kernel (RBF)</a></li>
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<section class="sphx-glr-example-title" id="one-class-svm-with-non-linear-kernel-rbf">
<span id="sphx-glr-auto-examples-svm-plot-oneclass-py"></span><h1>One-class SVM with non-linear kernel (RBF)<a class="headerlink" href="#one-class-svm-with-non-linear-kernel-rbf" title="Permalink to this heading">¶</a></h1>
<p>An example using a one-class SVM for novelty detection.</p>
<p><a class="reference internal" href="../../modules/svm.html#svm-outlier-detection"><span class="std std-ref">One-class SVM</span></a> is an unsupervised
algorithm that learns a decision function for novelty detection:
classifying new data as similar or different to the training set.</p>
<img src="../../_images/sphx_glr_plot_oneclass_001.png" srcset="../../_images/sphx_glr_plot_oneclass_001.png" alt="Novelty Detection" 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">import</span> <span class="nn">matplotlib.font_manager</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">5</span><span class="p">,</span> <span class="mi">5</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">5</span><span class="p">,</span> <span class="mi">5</span><span class="p">,</span> <span class="mi">500</span><span class="p">))</span>
<span class="c1"># Generate train data</span>
<span class="n">X</span> <span class="o">=</span> <span class="mf">0.3</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">100</span><span class="p">,</span> <span class="mi">2</span><span class="p">)</span>
<span class="n">X_train</span> <span class="o">=</span> <a href="https://numpy.org/doc/stable/reference/generated/numpy.r_.html#numpy.r_" title="numpy.r_" class="sphx-glr-backref-module-numpy sphx-glr-backref-type-py-data"><span class="n">np</span><span class="o">.</span><span class="n">r_</span></a><span class="p">[</span><span class="n">X</span> <span class="o">+</span> <span class="mi">2</span><span class="p">,</span> <span class="n">X</span> <span class="o">-</span> <span class="mi">2</span><span class="p">]</span>
<span class="c1"># Generate some regular novel observations</span>
<span class="n">X</span> <span class="o">=</span> <span class="mf">0.3</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">20</span><span class="p">,</span> <span class="mi">2</span><span class="p">)</span>
<span class="n">X_test</span> <span class="o">=</span> <a href="https://numpy.org/doc/stable/reference/generated/numpy.r_.html#numpy.r_" title="numpy.r_" class="sphx-glr-backref-module-numpy sphx-glr-backref-type-py-data"><span class="n">np</span><span class="o">.</span><span class="n">r_</span></a><span class="p">[</span><span class="n">X</span> <span class="o">+</span> <span class="mi">2</span><span class="p">,</span> <span class="n">X</span> <span class="o">-</span> <span class="mi">2</span><span class="p">]</span>
<span class="c1"># Generate some abnormal novel observations</span>
<span class="n">X_outliers</span> <span class="o">=</span> <a href="https://numpy.org/doc/stable/reference/random/generated/numpy.random.uniform.html#numpy.random.uniform" title="numpy.random.uniform" 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">uniform</span></a><span class="p">(</span><span class="n">low</span><span class="o">=-</span><span class="mi">4</span><span class="p">,</span> <span class="n">high</span><span class="o">=</span><span class="mi">4</span><span class="p">,</span> <span class="n">size</span><span class="o">=</span><span class="p">(</span><span class="mi">20</span><span class="p">,</span> <span class="mi">2</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.OneClassSVM.html#sklearn.svm.OneClassSVM" title="sklearn.svm.OneClassSVM" 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">OneClassSVM</span></a><span class="p">(</span><span class="n">nu</span><span class="o">=</span><span class="mf">0.1</span><span class="p">,</span> <span class="n">kernel</span><span class="o">=</span><span class="s2">"rbf"</span><span class="p">,</span> <span class="n">gamma</span><span class="o">=</span><span class="mf">0.1</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_train</span><span class="p">)</span>
<span class="n">y_pred_train</span> <span class="o">=</span> <span class="n">clf</span><span class="o">.</span><span class="n">predict</span><span class="p">(</span><span class="n">X_train</span><span class="p">)</span>
<span class="n">y_pred_test</span> <span class="o">=</span> <span class="n">clf</span><span class="o">.</span><span class="n">predict</span><span class="p">(</span><span class="n">X_test</span><span class="p">)</span>
<span class="n">y_pred_outliers</span> <span class="o">=</span> <span class="n">clf</span><span class="o">.</span><span class="n">predict</span><span class="p">(</span><span class="n">X_outliers</span><span class="p">)</span>
<span class="n">n_error_train</span> <span class="o">=</span> <span class="n">y_pred_train</span><span class="p">[</span><span class="n">y_pred_train</span> <span class="o">==</span> <span class="o">-</span><span class="mi">1</span><span class="p">]</span><span class="o">.</span><span class="n">size</span>
<span class="n">n_error_test</span> <span class="o">=</span> <span class="n">y_pred_test</span><span class="p">[</span><span class="n">y_pred_test</span> <span class="o">==</span> <span class="o">-</span><span class="mi">1</span><span class="p">]</span><span class="o">.</span><span class="n">size</span>
<span class="n">n_error_outliers</span> <span class="o">=</span> <span class="n">y_pred_outliers</span><span class="p">[</span><span class="n">y_pred_outliers</span> <span class="o">==</span> <span class="mi">1</span><span class="p">]</span><span class="o">.</span><span class="n">size</span>
<span class="c1"># plot the line, the points, and the nearest vectors to the plane</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.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">"Novelty Detection"</span><span class="p">)</span>
<a href="https://matplotlib.org/stable/api/_as_gen/matplotlib.pyplot.contourf.html#matplotlib.pyplot.contourf" title="matplotlib.pyplot.contourf" 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">contourf</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><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="n">Z</span><span class="o">.</span><span class="n">min</span><span class="p">(),</span> <span class="mi">0</span><span class="p">,</span> <span class="mi">7</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">PuBu</span><span class="p">)</span>
<span class="n">a</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">colors</span><span class="o">=</span><span class="s2">"darkred"</span><span class="p">)</span>
<a href="https://matplotlib.org/stable/api/_as_gen/matplotlib.pyplot.contourf.html#matplotlib.pyplot.contourf" title="matplotlib.pyplot.contourf" 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">contourf</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">Z</span><span class="o">.</span><span class="n">max</span><span class="p">()],</span> <span class="n">colors</span><span class="o">=</span><span class="s2">"palevioletred"</span><span class="p">)</span>
<span class="n">s</span> <span class="o">=</span> <span class="mi">40</span>
<span class="n">b1</span> <span class="o">=</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_train</span><span class="p">[:,</span> <span class="mi">0</span><span class="p">],</span> <span class="n">X_train</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="s2">"white"</span><span class="p">,</span> <span class="n">s</span><span class="o">=</span><span class="n">s</span><span class="p">,</span> <span class="n">edgecolors</span><span class="o">=</span><span class="s2">"k"</span><span class="p">)</span>
<span class="n">b2</span> <span class="o">=</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_test</span><span class="p">[:,</span> <span class="mi">0</span><span class="p">],</span> <span class="n">X_test</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="s2">"blueviolet"</span><span class="p">,</span> <span class="n">s</span><span class="o">=</span><span class="n">s</span><span class="p">,</span> <span class="n">edgecolors</span><span class="o">=</span><span class="s2">"k"</span><span class="p">)</span>
<span class="n">c</span> <span class="o">=</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_outliers</span><span class="p">[:,</span> <span class="mi">0</span><span class="p">],</span> <span class="n">X_outliers</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="s2">"gold"</span><span class="p">,</span> <span class="n">s</span><span class="o">=</span><span class="n">s</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.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.xlim.html#matplotlib.pyplot.xlim" title="matplotlib.pyplot.xlim" 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">xlim</span></a><span class="p">((</span><span class="o">-</span><span class="mi">5</span><span class="p">,</span> <span class="mi">5</span><span class="p">))</span>
<a href="https://matplotlib.org/stable/api/_as_gen/matplotlib.pyplot.ylim.html#matplotlib.pyplot.ylim" title="matplotlib.pyplot.ylim" 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">ylim</span></a><span class="p">((</span><span class="o">-</span><span class="mi">5</span><span class="p">,</span> <span class="mi">5</span><span class="p">))</span>
<a href="https://matplotlib.org/stable/api/_as_gen/matplotlib.pyplot.legend.html#matplotlib.pyplot.legend" title="matplotlib.pyplot.legend" 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">legend</span></a><span class="p">(</span>
<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">b1</span><span class="p">,</span> <span class="n">b2</span><span class="p">,</span> <span class="n">c</span><span class="p">],</span>
<span class="p">[</span>
<span class="s2">"learned frontier"</span><span class="p">,</span>
<span class="s2">"training observations"</span><span class="p">,</span>
<span class="s2">"new regular observations"</span><span class="p">,</span>
<span class="s2">"new abnormal observations"</span><span class="p">,</span>
<span class="p">],</span>
<span class="n">loc</span><span class="o">=</span><span class="s2">"upper left"</span><span class="p">,</span>
<span class="n">prop</span><span class="o">=</span><a href="https://matplotlib.org/stable/api/font_manager_api.html#matplotlib.font_manager.FontProperties" title="matplotlib.font_manager.FontProperties" class="sphx-glr-backref-module-matplotlib-font_manager sphx-glr-backref-type-py-class sphx-glr-backref-instance"><span class="n">matplotlib</span><span class="o">.</span><span class="n">font_manager</span><span class="o">.</span><span class="n">FontProperties</span></a><span class="p">(</span><span class="n">size</span><span class="o">=</span><span class="mi">11</span><span class="p">),</span>
<span class="p">)</span>
<a href="https://matplotlib.org/stable/api/_as_gen/matplotlib.pyplot.xlabel.html#matplotlib.pyplot.xlabel" title="matplotlib.pyplot.xlabel" 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">xlabel</span></a><span class="p">(</span>
<span class="s2">"error train: </span><span class="si">%d</span><span class="s2">/200 ; errors novel regular: </span><span class="si">%d</span><span class="s2">/40 ; errors novel abnormal: </span><span class="si">%d</span><span class="s2">/40"</span>
<span class="o">%</span> <span class="p">(</span><span class="n">n_error_train</span><span class="p">,</span> <span class="n">n_error_test</span><span class="p">,</span> <span class="n">n_error_outliers</span><span class="p">)</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>
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