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<span id="sphx-glr-auto-examples-svm-plot-svm-margin-py"></span><h1>SVM Margins Example<a class="headerlink" href="#svm-margins-example" title="Permalink to this headline">¶</a></h1>
<p>The plots below illustrate the effect the parameter <cite>C</cite> has
on the separation line. A large value of <cite>C</cite> 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 <cite>C</cite> includes more/all the observations, allowing
the margins to be calculated using all the data in the area.</p>
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<li><img alt="../../_images/sphx_glr_plot_svm_margin_001.png" class="sphx-glr-multi-img first" src="../../_images/sphx_glr_plot_svm_margin_001.png" />
</li>
<li><img alt="../../_images/sphx_glr_plot_svm_margin_002.png" class="sphx-glr-multi-img first" src="../../_images/sphx_glr_plot_svm_margin_002.png" />
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<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="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">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="c1"># we create 40 separable points</span>
<a href="https://docs.scipy.org/doc/numpy/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="https://docs.scipy.org/doc/numpy/reference/generated/numpy.r_.html#numpy.r_" title="View documentation for numpy.r_"><span class="n">np</span><span class="o">.</span><span class="n">r_</span></a><span class="p">[</span><a href="https://docs.scipy.org/doc/numpy/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">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://docs.scipy.org/doc/numpy/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">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="s1">'unreg'</span><span class="p">,</span> <span class="mi">1</span><span class="p">),</span> <span class="p">(</span><span class="s1">'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="View documentation for sklearn.svm.SVC"><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="s1">'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://docs.scipy.org/doc/numpy/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">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://docs.scipy.org/doc/numpy/reference/generated/numpy.sqrt.html#numpy.sqrt" title="View documentation for numpy.sqrt"><span class="n">np</span><span class="o">.</span><span class="n">sqrt</span></a><span class="p">(</span><a href="https://docs.scipy.org/doc/numpy/reference/generated/numpy.sum.html#numpy.sum" title="View documentation for numpy.sum"><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://docs.scipy.org/doc/numpy/reference/generated/numpy.sqrt.html#numpy.sqrt" title="View documentation for numpy.sqrt"><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://docs.scipy.org/doc/numpy/reference/generated/numpy.sqrt.html#numpy.sqrt" title="View documentation for numpy.sqrt"><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/api/_as_gen/matplotlib.pyplot.figure.html#matplotlib.pyplot.figure" title="View documentation for matplotlib.pyplot.figure"><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/api/_as_gen/matplotlib.pyplot.clf.html#matplotlib.pyplot.clf" title="View documentation for matplotlib.pyplot.clf"><span class="n">plt</span><span class="o">.</span><span class="n">clf</span></a><span class="p">()</span>
<a href="https://matplotlib.org/api/_as_gen/matplotlib.pyplot.plot.html#matplotlib.pyplot.plot" title="View documentation for matplotlib.pyplot.plot"><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="s1">'k-'</span><span class="p">)</span>
<a href="https://matplotlib.org/api/_as_gen/matplotlib.pyplot.plot.html#matplotlib.pyplot.plot" title="View documentation for matplotlib.pyplot.plot"><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="s1">'k--'</span><span class="p">)</span>
<a href="https://matplotlib.org/api/_as_gen/matplotlib.pyplot.plot.html#matplotlib.pyplot.plot" title="View documentation for matplotlib.pyplot.plot"><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="s1">'k--'</span><span class="p">)</span>
<a href="https://matplotlib.org/api/_as_gen/matplotlib.pyplot.scatter.html#matplotlib.pyplot.scatter" title="View documentation for matplotlib.pyplot.scatter"><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="s1">'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="s1">'k'</span><span class="p">)</span>
<a href="https://matplotlib.org/api/_as_gen/matplotlib.pyplot.scatter.html#matplotlib.pyplot.scatter" title="View documentation for matplotlib.pyplot.scatter"><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><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="s1">'k'</span><span class="p">)</span>
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<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">XX</span><span class="p">,</span> <span class="n">YY</span> <span class="o">=</span> <a href="https://docs.scipy.org/doc/numpy/reference/generated/numpy.mgrid.html#numpy.mgrid" title="View documentation for numpy.mgrid"><span class="n">np</span><span class="o">.</span><span class="n">mgrid</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><span class="mi">200j</span><span class="p">,</span> <span class="n">y_min</span><span class="p">:</span><span class="n">y_max</span><span class="p">:</span><span class="mi">200j</span><span class="p">]</span>
<span class="n">Z</span> <span class="o">=</span> <span class="n">clf</span><span class="o">.</span><span class="n">predict</span><span class="p">(</span><a href="https://docs.scipy.org/doc/numpy/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="c1"># Put the result into a color plot</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>
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<a href="https://matplotlib.org/api/_as_gen/matplotlib.pyplot.pcolormesh.html#matplotlib.pyplot.pcolormesh" title="View documentation for matplotlib.pyplot.pcolormesh"><span class="n">plt</span><span class="o">.</span><span class="n">pcolormesh</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><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>
<a href="https://matplotlib.org/api/_as_gen/matplotlib.pyplot.xlim.html#matplotlib.pyplot.xlim" title="View documentation for matplotlib.pyplot.xlim"><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/api/_as_gen/matplotlib.pyplot.ylim.html#matplotlib.pyplot.ylim" title="View documentation for matplotlib.pyplot.ylim"><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>
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<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/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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