<!DOCTYPE html PUBLIC "-//W3C//DTD XHTML 1.0 Transitional//EN" "http://www.w3.org/TR/xhtml1/DTD/xhtml1-transitional.dtd"> <html xmlns="http://www.w3.org/1999/xhtml"> <head> <meta http-equiv="Content-Type" content="text/html; charset=utf-8" /> <title>SGD: Separating hyperplane with weighted classes — scikits.learn v0.6.0 documentation</title> <link rel="stylesheet" href="../../_static/nature.css" type="text/css" /> <link rel="stylesheet" href="../../_static/pygments.css" type="text/css" /> <script type="text/javascript"> var DOCUMENTATION_OPTIONS = { URL_ROOT: '../../', VERSION: '0.6.0', COLLAPSE_INDEX: false, FILE_SUFFIX: '.html', HAS_SOURCE: true }; </script> <script type="text/javascript" src="../../_static/jquery.js"></script> <script type="text/javascript" src="../../_static/underscore.js"></script> <script type="text/javascript" src="../../_static/doctools.js"></script> <link rel="shortcut icon" href="../../_static/favicon.ico"/> <link rel="author" title="About these documents" href="../../about.html" /> <link rel="top" title="scikits.learn v0.6.0 documentation" href="../../index.html" /> <link rel="up" title="Examples" href="../index.html" /> <link rel="next" title="Gaussian Mixture Model Ellipsoids" href="../mixture/plot_gmm.html" /> <link rel="prev" title="SGD: Maximum margin separating hyperplane" href="plot_sgd_separating_hyperplane.html" /> </head> <body> <div class="header-wrapper"> <div class="header"> <p class="logo"><a href="../../index.html"> <img src="../../_static/scikit-learn-logo-small.png" alt="Logo"/> </a> </p><div class="navbar"> <ul> <li><a href="../../install.html">Download</a></li> <li><a href="../../support.html">Support</a></li> <li><a href="../../user_guide.html">User Guide</a></li> <li><a href="../index.html">Examples</a></li> <li><a href="../../developers/index.html">Development</a></li> </ul> <div class="search_form"> <div id="cse" style="width: 100%;"></div> <script src="http://www.google.com/jsapi" type="text/javascript"></script> <script type="text/javascript"> google.load('search', '1', {language : 'en'}); google.setOnLoadCallback(function() { var customSearchControl = new google.search.CustomSearchControl('016639176250731907682:tjtqbvtvij0'); customSearchControl.setResultSetSize(google.search.Search.FILTERED_CSE_RESULTSET); var options = new google.search.DrawOptions(); options.setAutoComplete(true); customSearchControl.draw('cse', options); }, true); </script> </div> </div> <!-- end navbar --></div> </div> <div class="content-wrapper"> <!-- <div id="blue_tile"></div> --> <div class="sphinxsidebar"> <div class="rel"> <a href="plot_sgd_separating_hyperplane.html" title="SGD: Maximum margin separating hyperplane" accesskey="P">previous</a> | <a href="../mixture/plot_gmm.html" title="Gaussian Mixture Model Ellipsoids" accesskey="N">next</a> | <a href="../../genindex.html" title="General Index" accesskey="I">index</a> </div> <h3>Contents</h3> <ul> <li><a class="reference internal" href="#">SGD: Separating hyperplane with weighted classes</a></li> </ul> </div> <div class="content"> <div class="documentwrapper"> <div class="bodywrapper"> <div class="body"> <div class="section" id="sgd-separating-hyperplane-with-weighted-classes"> <span id="example-linear-model-plot-sgd-weighted-classes-py"></span><h1>SGD: Separating hyperplane with weighted classes<a class="headerlink" href="#sgd-separating-hyperplane-with-weighted-classes" title="Permalink to this headline">ΒΆ</a></h1> <p>Fit linear SVMs with and without class weighting. Allows to handle problems with unbalanced classes.</p> <img alt="auto_examples/linear_model/images/plot_sgd_weighted_classes.png" class="align-center" src="auto_examples/linear_model/images/plot_sgd_weighted_classes.png" /> <p><strong>Python source code:</strong> <a class="reference download internal" href="../../_downloads/plot_sgd_weighted_classes.py"><tt class="xref download docutils literal"><span class="pre">plot_sgd_weighted_classes.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">n_samples_1</span> <span class="o">=</span> <span class="mi">1000</span> <span class="n">n_samples_2</span> <span class="o">=</span> <span class="mi">100</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="mf">1.5</span><span class="o">*</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="n">n_samples_1</span><span class="p">,</span> <span class="mi">2</span><span class="p">),</span> <span class="mf">0.5</span><span class="o">*</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="n">n_samples_2</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="n">np</span><span class="o">.</span><span class="n">array</span><span class="p">([</span><span class="mi">0</span><span class="p">]</span><span class="o">*</span><span class="p">(</span><span class="n">n_samples_1</span><span class="p">)</span> <span class="o">+</span> <span class="p">[</span><span class="mi">1</span><span class="p">]</span><span class="o">*</span><span class="p">(</span><span class="n">n_samples_2</span><span class="p">),</span> <span class="n">dtype</span><span class="o">=</span><span class="n">np</span><span class="o">.</span><span class="n">float64</span><span class="p">)</span> <span class="n">idx</span> <span class="o">=</span> <span class="n">np</span><span class="o">.</span><span class="n">arange</span><span class="p">(</span><span class="n">y</span><span class="o">.</span><span class="n">shape</span><span class="p">[</span><span class="mi">0</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">shuffle</span><span class="p">(</span><span class="n">idx</span><span class="p">)</span> <span class="n">X</span> <span class="o">=</span> <span class="n">X</span><span class="p">[</span><span class="n">idx</span><span class="p">]</span> <span class="n">y</span> <span class="o">=</span> <span class="n">y</span><span class="p">[</span><span class="n">idx</span><span class="p">]</span> <span class="n">mean</span> <span class="o">=</span> <span class="n">X</span><span class="o">.</span><span class="n">mean</span><span class="p">(</span><span class="n">axis</span><span class="o">=</span><span class="mi">0</span><span class="p">)</span> <span class="n">std</span> <span class="o">=</span> <span class="n">X</span><span class="o">.</span><span class="n">std</span><span class="p">(</span><span class="n">axis</span><span class="o">=</span><span class="mi">0</span><span class="p">)</span> <span class="n">X</span> <span class="o">=</span> <span class="p">(</span><span class="n">X</span> <span class="o">-</span> <span class="n">mean</span><span class="p">)</span> <span class="o">/</span> <span class="n">std</span> <span class="c"># fit the model and get the separating hyperplane</span> <span class="n">clf</span> <span class="o">=</span> <span class="n">SGDClassifier</span><span class="p">(</span><span class="n">n_iter</span><span class="o">=</span><span class="mi">100</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">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">w</span> <span class="o">=</span> <span class="n">clf</span><span class="o">.</span><span class="n">coef_</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> <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="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="n">clf</span><span class="o">.</span><span class="n">intercept_</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="c"># get the separating hyperplane using weighted classes</span> <span class="n">wclf</span> <span class="o">=</span> <span class="n">SGDClassifier</span><span class="p">(</span><span class="n">n_iter</span><span class="o">=</span><span class="mi">100</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">wclf</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">class_weight</span><span class="o">=</span><span class="p">{</span><span class="mi">1</span><span class="p">:</span> <span class="mi">10</span><span class="p">})</span> <span class="n">ww</span> <span class="o">=</span> <span class="n">wclf</span><span class="o">.</span><span class="n">coef_</span> <span class="n">wa</span> <span class="o">=</span> <span class="o">-</span><span class="n">ww</span><span class="p">[</span><span class="mi">0</span><span class="p">]</span> <span class="o">/</span> <span class="n">ww</span><span class="p">[</span><span class="mi">1</span><span class="p">]</span> <span class="n">wyy</span> <span class="o">=</span> <span class="n">wa</span> <span class="o">*</span> <span class="n">xx</span> <span class="o">-</span> <span class="n">wclf</span><span class="o">.</span><span class="n">intercept_</span> <span class="o">/</span> <span class="n">ww</span><span class="p">[</span><span class="mi">1</span><span class="p">]</span> <span class="c"># plot separating hyperplanes and samples</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">h0</span> <span class="o">=</span> <span class="n">pl</span><span class="o">.</span><span class="n">plot</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="s">'k-'</span><span class="p">)</span> <span class="n">h1</span> <span class="o">=</span> <span class="n">pl</span><span class="o">.</span><span class="n">plot</span><span class="p">(</span><span class="n">xx</span><span class="p">,</span> <span class="n">wyy</span><span class="p">,</span> <span class="s">'k--'</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">legend</span><span class="p">((</span><span class="n">h0</span><span class="p">,</span> <span class="n">h1</span><span class="p">),</span> <span class="p">(</span><span class="s">'no weights'</span><span class="p">,</span> <span class="s">'with weights'</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 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