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<li><a class="reference internal" href="#">SVM Margins Example</a></li>
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<p><a class="reference internal" href="#sphx-glr-download-auto-examples-svm-plot-svm-margin-py"><span class="std std-ref">Go to the end</span></a>
to download the full example code or to run this example in your browser via JupyterLite or Binder</p>
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<section class="sphx-glr-example-title" id="svm-margins-example">
<span id="sphx-glr-auto-examples-svm-plot-svm-margin-py"></span><h1>SVM Margins Example<a class="headerlink" href="#svm-margins-example" title="Link to this heading">¶</a></h1>
<p>The plots below illustrate the effect the parameter <code class="docutils literal notranslate"><span class="pre">C</span></code> has
on the separation line. A large value of <code class="docutils literal notranslate"><span class="pre">C</span></code> basically tells
our model that we do not have that much faith in our data’s
distribution, and will only consider points close to line
of separation.</p>
<p>A small value of <code class="docutils literal notranslate"><span class="pre">C</span></code> includes more/all the observations, allowing
the margins to be calculated using all the data in the area.</p>
<ul class="sphx-glr-horizontal">
<li><img src="../../_images/sphx_glr_plot_svm_margin_001.png" srcset="../../_images/sphx_glr_plot_svm_margin_001.png" alt="plot svm margin" class = "sphx-glr-multi-img"/></li>
<li><img src="../../_images/sphx_glr_plot_svm_margin_002.png" srcset="../../_images/sphx_glr_plot_svm_margin_002.png" alt="plot svm margin" class = "sphx-glr-multi-img"/></li>
</ul>
<div class="sphx-glr-script-out highlight-none notranslate"><div class="highlight"><pre><span></span>/home/circleci/project/examples/svm/plot_svm_margin.py:59: UserWarning:
No data for colormapping provided via 'c'. Parameters 'cmap' will be ignored
/home/circleci/project/examples/svm/plot_svm_margin.py:59: UserWarning:
No data for colormapping provided via 'c'. Parameters 'cmap' will be ignored
</pre></div>
</div>
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<div class="highlight-Python notranslate"><div class="highlight"><pre><span></span><span class="c1"># Code source: Gaël Varoquaux</span>
<span class="c1"># Modified for documentation by Jaques Grobler</span>
<span class="c1"># License: BSD 3 clause</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="c1"># we create 40 separable points</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/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><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="o">-</span> <span class="p">[</span><span class="mi">2</span><span class="p">,</span> <span class="mi">2</span><span class="p">],</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="o">+</span> <span class="p">[</span><span class="mi">2</span><span class="p">,</span> <span class="mi">2</span><span class="p">]]</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">20</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">20</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">name</span><span class="p">,</span> <span class="n">penalty</span> <span class="ow">in</span> <span class="p">((</span><span class="s2">"unreg"</span><span class="p">,</span> <span class="mi">1</span><span class="p">),</span> <span class="p">(</span><span class="s2">"reg"</span><span class="p">,</span> <span class="mf">0.05</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="sklearn.svm.SVC" 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">SVC</span></a><span class="p">(</span><span class="n">kernel</span><span class="o">=</span><span class="s2">"linear"</span><span class="p">,</span> <span class="n">C</span><span class="o">=</span><span class="n">penalty</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"># get the separating hyperplane</span>
<span class="n">w</span> <span class="o">=</span> <span class="n">clf</span><span class="o">.</span><span class="n">coef_</span><span class="p">[</span><span class="mi">0</span><span class="p">]</span>
<span class="n">a</span> <span class="o">=</span> <span class="o">-</span><span class="n">w</span><span class="p">[</span><span class="mi">0</span><span class="p">]</span> <span class="o">/</span> <span class="n">w</span><span class="p">[</span><span class="mi">1</span><span class="p">]</span>
<span class="n">xx</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="o">-</span><span class="mi">5</span><span class="p">,</span> <span class="mi">5</span><span class="p">)</span>
<span class="n">yy</span> <span class="o">=</span> <span class="n">a</span> <span class="o">*</span> <span class="n">xx</span> <span class="o">-</span> <span class="p">(</span><span class="n">clf</span><span class="o">.</span><span class="n">intercept_</span><span class="p">[</span><span class="mi">0</span><span class="p">])</span> <span class="o">/</span> <span class="n">w</span><span class="p">[</span><span class="mi">1</span><span class="p">]</span>
<span class="c1"># plot the parallels to the separating hyperplane that pass through the</span>
<span class="c1"># support vectors (margin away from hyperplane in direction</span>
<span class="c1"># perpendicular to hyperplane). This is sqrt(1+a^2) away vertically in</span>
<span class="c1"># 2-d.</span>
<span class="n">margin</span> <span class="o">=</span> <span class="mi">1</span> <span class="o">/</span> <a href="https://numpy.org/doc/stable/reference/generated/numpy.sqrt.html#numpy.sqrt" title="numpy.sqrt" class="sphx-glr-backref-module-numpy sphx-glr-backref-type-py-data"><span class="n">np</span><span class="o">.</span><span class="n">sqrt</span></a><span class="p">(</span><a href="https://numpy.org/doc/stable/reference/generated/numpy.sum.html#numpy.sum" title="numpy.sum" class="sphx-glr-backref-module-numpy sphx-glr-backref-type-py-function"><span class="n">np</span><span class="o">.</span><span class="n">sum</span></a><span class="p">(</span><span class="n">clf</span><span class="o">.</span><span class="n">coef_</span><span class="o">**</span><span class="mi">2</span><span class="p">))</span>
<span class="n">yy_down</span> <span class="o">=</span> <span class="n">yy</span> <span class="o">-</span> <a href="https://numpy.org/doc/stable/reference/generated/numpy.sqrt.html#numpy.sqrt" title="numpy.sqrt" class="sphx-glr-backref-module-numpy sphx-glr-backref-type-py-data"><span class="n">np</span><span class="o">.</span><span class="n">sqrt</span></a><span class="p">(</span><span class="mi">1</span> <span class="o">+</span> <span class="n">a</span><span class="o">**</span><span class="mi">2</span><span class="p">)</span> <span class="o">*</span> <span class="n">margin</span>
<span class="n">yy_up</span> <span class="o">=</span> <span class="n">yy</span> <span class="o">+</span> <a href="https://numpy.org/doc/stable/reference/generated/numpy.sqrt.html#numpy.sqrt" title="numpy.sqrt" class="sphx-glr-backref-module-numpy sphx-glr-backref-type-py-data"><span class="n">np</span><span class="o">.</span><span class="n">sqrt</span></a><span class="p">(</span><span class="mi">1</span> <span class="o">+</span> <span class="n">a</span><span class="o">**</span><span class="mi">2</span><span class="p">)</span> <span class="o">*</span> <span class="n">margin</span>
<span class="c1"># plot the line, the points, and the nearest vectors to the plane</span>
<a href="https://matplotlib.org/stable/api/_as_gen/matplotlib.pyplot.figure.html#matplotlib.pyplot.figure" title="matplotlib.pyplot.figure" 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">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="https://matplotlib.org/stable/api/_as_gen/matplotlib.pyplot.clf.html#matplotlib.pyplot.clf" title="matplotlib.pyplot.clf" 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">clf</span></a><span class="p">()</span>
<a href="https://matplotlib.org/stable/api/_as_gen/matplotlib.pyplot.plot.html#matplotlib.pyplot.plot" title="matplotlib.pyplot.plot" 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">plot</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="s2">"k-"</span><span class="p">)</span>
<a href="https://matplotlib.org/stable/api/_as_gen/matplotlib.pyplot.plot.html#matplotlib.pyplot.plot" title="matplotlib.pyplot.plot" 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">plot</span></a><span class="p">(</span><span class="n">xx</span><span class="p">,</span> <span class="n">yy_down</span><span class="p">,</span> <span class="s2">"k--"</span><span class="p">)</span>
<a href="https://matplotlib.org/stable/api/_as_gen/matplotlib.pyplot.plot.html#matplotlib.pyplot.plot" title="matplotlib.pyplot.plot" 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">plot</span></a><span class="p">(</span><span class="n">xx</span><span class="p">,</span> <span class="n">yy_up</span><span class="p">,</span> <span class="s2">"k--"</span><span class="p">)</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">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="s2">"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="s2">"k"</span><span class="p">,</span>
<span class="n">cmap</span><span class="o">=</span><a href="https://matplotlib.org/stable/api/_as_gen/matplotlib.pyplot.get_cmap.html#matplotlib.pyplot.get_cmap" title="matplotlib.pyplot.get_cmap" 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">get_cmap</span></a><span class="p">(</span><span class="s2">"RdBu"</span><span class="p">),</span>
<span class="p">)</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">zorder</span><span class="o">=</span><span class="mi">10</span><span class="p">,</span> <span class="n">cmap</span><span class="o">=</span><a href="https://matplotlib.org/stable/api/_as_gen/matplotlib.pyplot.get_cmap.html#matplotlib.pyplot.get_cmap" title="matplotlib.pyplot.get_cmap" 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">get_cmap</span></a><span class="p">(</span><span class="s2">"RdBu"</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>
<span class="n">x_min</span> <span class="o">=</span> <span class="o">-</span><span class="mf">4.8</span>
<span class="n">x_max</span> <span class="o">=</span> <span class="mf">4.2</span>
<span class="n">y_min</span> <span class="o">=</span> <span class="o">-</span><span class="mi">6</span>
<span class="n">y_max</span> <span class="o">=</span> <span class="mi">6</span>
<span class="n">YY</span><span class="p">,</span> <span class="n">XX</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><span class="n">yy</span><span class="p">,</span> <span class="n">xx</span><span class="p">)</span>
<span class="n">xy</span> <span class="o">=</span> <a href="https://numpy.org/doc/stable/reference/generated/numpy.vstack.html#numpy.vstack" title="numpy.vstack" class="sphx-glr-backref-module-numpy sphx-glr-backref-type-py-function"><span class="n">np</span><span class="o">.</span><span class="n">vstack</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="o">.</span><span class="n">T</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><span class="n">xy</span><span class="p">)</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>
<span class="c1"># Put the result into a contour plot</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">cmap</span><span class="o">=</span><a href="https://matplotlib.org/stable/api/_as_gen/matplotlib.pyplot.get_cmap.html#matplotlib.pyplot.get_cmap" title="matplotlib.pyplot.get_cmap" 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">get_cmap</span></a><span class="p">(</span><span class="s2">"RdBu"</span><span class="p">),</span> <span class="n">alpha</span><span class="o">=</span><span class="mf">0.5</span><span class="p">,</span> <span class="n">linestyles</span><span class="o">=</span><span class="p">[</span><span class="s2">"-"</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="n">x_min</span><span class="p">,</span> <span class="n">x_max</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="n">y_min</span><span class="p">,</span> <span class="n">y_max</span><span class="p">)</span>
<a href="https://matplotlib.org/stable/api/_as_gen/matplotlib.pyplot.xticks.html#matplotlib.pyplot.xticks" title="matplotlib.pyplot.xticks" 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">xticks</span></a><span class="p">(())</span>
<a href="https://matplotlib.org/stable/api/_as_gen/matplotlib.pyplot.yticks.html#matplotlib.pyplot.yticks" title="matplotlib.pyplot.yticks" 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">yticks</span></a><span class="p">(())</span>
<span class="n">fignum</span> <span class="o">=</span> <span class="n">fignum</span> <span class="o">+</span> <span class="mi">1</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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