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hyperplane</a></li> </ul> </div> <div class="content"> <div class="documentwrapper"> <div class="bodywrapper"> <div class="body"> <div class="section" id="sgd-maximum-margin-separating-hyperplane"> <span id="example-linear-model-plot-sgd-separating-hyperplane-py"></span><h1>SGD: Maximum margin separating hyperplane<a class="headerlink" href="#sgd-maximum-margin-separating-hyperplane" title="Permalink to this headline">ΒΆ</a></h1> <p>Plot the maximum margin separating hyperplane within a two-class separable dataset using a linear Support Vector Machines classifier trained using SGD.</p> <img alt="auto_examples/linear_model/images/plot_sgd_separating_hyperplane.png" class="align-center" src="auto_examples/linear_model/images/plot_sgd_separating_hyperplane.png" /> <p><strong>Python source code:</strong> <a class="reference download internal" href="../../_downloads/plot_sgd_separating_hyperplane.py"><tt class="xref download docutils literal"><span class="pre">plot_sgd_separating_hyperplane.py</span></tt></a></p> <div class="highlight-python"><div class="highlight"><pre><span class="k">print</span> <span class="n">__doc__</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">pylab</span> <span class="kn">as</span> <span class="nn">pl</span> <span class="kn">from</span> <span class="nn">scikits.learn.linear_model</span> <span class="kn">import</span> <span class="n">SGDClassifier</span> <span class="c"># we create 40 separable points</span> <span class="n">np</span><span class="o">.</span><span class="n">random</span><span class="o">.</span><span class="n">seed</span><span class="p">(</span><span class="mi">0</span><span class="p">)</span> <span class="n">X</span> <span class="o">=</span> <span class="n">np</span><span class="o">.</span><span class="n">r_</span><span class="p">[</span><span class="n">np</span><span class="o">.</span><span class="n">random</span><span class="o">.</span><span class="n">randn</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="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">np</span><span class="o">.</span><span class="n">random</span><span class="o">.</span><span class="n">randn</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="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="c"># fit the model</span> <span class="n">clf</span> <span class="o">=</span> <span class="n">SGDClassifier</span><span class="p">(</span><span class="n">loss</span><span class="o">=</span><span class="s">"hinge"</span><span class="p">,</span> <span class="n">alpha</span> <span class="o">=</span> <span class="mf">0.01</span><span class="p">,</span> <span class="n">n_iter</span><span class="o">=</span><span class="mi">50</span><span class="p">,</span> <span class="n">fit_intercept</span><span class="o">=</span><span class="bp">True</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="c"># plot the line, the points, and the nearest vectors to the plane</span> <span class="n">xx</span> <span class="o">=</span> <span class="n">np</span><span class="o">.</span><span class="n">linspace</span><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">10</span><span class="p">)</span> <span class="n">yy</span> <span class="o">=</span> <span class="n">np</span><span class="o">.</span><span class="n">linspace</span><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">10</span><span class="p">)</span> <span class="n">X1</span><span class="p">,</span> <span class="n">X2</span> <span class="o">=</span> <span class="n">np</span><span class="o">.</span><span class="n">meshgrid</span><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="o">=</span> <span class="n">np</span><span class="o">.</span><span class="n">empty</span><span class="p">(</span><span class="n">X1</span><span class="o">.</span><span class="n">shape</span><span class="p">)</span> <span class="k">for</span> <span class="p">(</span><span class="n">i</span><span class="p">,</span><span class="n">j</span><span class="p">),</span> <span class="n">val</span> <span class="ow">in</span> <span class="n">np</span><span class="o">.</span><span class="n">ndenumerate</span><span class="p">(</span><span class="n">X1</span><span class="p">):</span> <span class="n">x1</span> <span class="o">=</span> <span class="n">val</span> <span class="n">x2</span> <span class="o">=</span> <span class="n">X2</span><span class="p">[</span><span class="n">i</span><span class="p">,</span><span class="n">j</span><span class="p">]</span> <span class="n">p</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">x1</span><span class="p">,</span> <span class="n">x2</span><span class="p">])</span> <span class="n">Z</span><span class="p">[</span><span class="n">i</span><span class="p">,</span><span class="n">j</span><span class="p">]</span> <span class="o">=</span> <span class="n">p</span><span class="p">[</span><span class="mi">0</span><span class="p">]</span> <span class="n">levels</span> <span class="o">=</span> <span class="p">[</span><span class="o">-</span><span class="mf">1.0</span><span class="p">,</span> <span class="mf">0.0</span><span class="p">,</span> <span class="mf">1.0</span><span class="p">]</span> <span class="n">linestyles</span> <span class="o">=</span> <span class="p">[</span><span class="s">'dashed'</span><span class="p">,</span><span class="s">'solid'</span><span class="p">,</span> <span class="s">'dashed'</span><span class="p">]</span> <span class="n">colors</span> <span class="o">=</span> <span class="s">'k'</span> <span class="n">pl</span><span class="o">.</span><span class="n">set_cmap</span><span class="p">(</span><span class="n">pl</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">pl</span><span class="o">.</span><span class="n">contour</span><span class="p">(</span><span class="n">X1</span><span class="p">,</span> <span class="n">X2</span><span class="p">,</span> <span class="n">Z</span><span class="p">,</span> <span class="n">levels</span><span class="p">,</span> <span class="n">colors</span><span class="o">=</span><span class="n">colors</span><span class="p">,</span> <span class="n">linestyles</span><span class="o">=</span><span class="n">linestyles</span><span class="p">)</span> <span class="n">pl</span><span class="o">.</span><span class="n">scatter</span><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">pl</span><span class="o">.</span><span class="n">axis</span><span class="p">(</span><span class="s">'tight'</span><span class="p">)</span> <span class="n">pl</span><span class="o">.</span><span class="n">show</span><span class="p">()</span> </pre></div> </div> </div> </div> </div> </div> <div class="clearer"></div> </div> </div> <div class="footer"> <p style="text-align: center">This documentation is relative to scikits.learn version 0.6.0<p> © 2010, scikits.learn developers (BSD Lincense). 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