<!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>Density Estimation for a mixture of Gaussians — 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="SVM with custom kernel" href="../svm/plot_custom_kernel.html" />
<link rel="prev" title="GMM classification" href="plot_gmm_classifier.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_gmm_classifier.html" title="GMM classification"
accesskey="P">previous</a> |
<a href="../svm/plot_custom_kernel.html" title="SVM with custom kernel"
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="#">Density Estimation for a mixture of Gaussians</a></li>
</ul>
</div>
<div class="content">
<div class="documentwrapper">
<div class="bodywrapper">
<div class="body">
<div class="section" id="density-estimation-for-a-mixture-of-gaussians">
<span id="example-mixture-plot-gmm-pdf-py"></span><h1>Density Estimation for a mixture of Gaussians<a class="headerlink" href="#density-estimation-for-a-mixture-of-gaussians" title="Permalink to this headline">ΒΆ</a></h1>
<p>Plot the density estimation of a mixture of two gaussians. Data is
generated from two gaussians with different centers and covariance
matrices.</p>
<img alt="auto_examples/mixture/images/plot_gmm_pdf.png" class="align-center" src="auto_examples/mixture/images/plot_gmm_pdf.png" />
<p><strong>Python source code:</strong> <a class="reference download internal" href="../../_downloads/plot_gmm_pdf.py"><tt class="xref download docutils literal"><span class="pre">plot_gmm_pdf.py</span></tt></a></p>
<div class="highlight-python"><div class="highlight"><pre><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</span> <span class="kn">import</span> <span class="n">mixture</span>
<span class="n">n_samples</span> <span class="o">=</span> <span class="mi">300</span>
<span class="c"># generate random sample, two components</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">C</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="mf">0.</span><span class="p">,</span> <span class="o">-</span><span class="mf">0.7</span><span class="p">],</span> <span class="p">[</span><span class="mf">3.5</span><span class="p">,</span> <span class="o">.</span><span class="mi">7</span><span class="p">]])</span>
<span class="n">X_train</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">dot</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="n">n_samples</span><span class="p">,</span> <span class="mi">2</span><span class="p">),</span> <span class="n">C</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="n">n_samples</span><span class="p">,</span> <span class="mi">2</span><span class="p">)</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">20</span><span class="p">,</span> <span class="mi">20</span><span class="p">])]</span>
<span class="n">clf</span> <span class="o">=</span> <span class="n">mixture</span><span class="o">.</span><span class="n">GMM</span><span class="p">(</span><span class="n">n_states</span><span class="o">=</span><span class="mi">2</span><span class="p">,</span> <span class="n">cvtype</span><span class="o">=</span><span class="s">'full'</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">x</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="mf">20.0</span><span class="p">,</span> <span class="mf">30.0</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">linspace</span><span class="p">(</span><span class="o">-</span><span class="mf">20.0</span><span class="p">,</span> <span class="mf">40.0</span><span class="p">)</span>
<span class="n">X</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">meshgrid</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">XX</span> <span class="o">=</span> <span class="n">np</span><span class="o">.</span><span class="n">c_</span><span class="p">[</span><span class="n">X</span><span class="o">.</span><span class="n">ravel</span><span class="p">(),</span> <span class="n">Y</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">np</span><span class="o">.</span><span class="n">log</span><span class="p">(</span><span class="o">-</span><span class="n">clf</span><span class="o">.</span><span class="n">eval</span><span class="p">(</span><span class="n">XX</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">Z</span><span class="o">.</span><span class="n">reshape</span><span class="p">(</span><span class="n">X</span><span class="o">.</span><span class="n">shape</span><span class="p">)</span>
<span class="n">CS</span> <span class="o">=</span> <span class="n">pl</span><span class="o">.</span><span class="n">contour</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">Z</span><span class="p">)</span>
<span class="n">CB</span> <span class="o">=</span> <span class="n">pl</span><span class="o">.</span><span class="n">colorbar</span><span class="p">(</span><span class="n">CS</span><span class="p">,</span> <span class="n">shrink</span><span class="o">=</span><span class="mf">0.8</span><span class="p">,</span> <span class="n">extend</span><span class="o">=</span><span class="s">'both'</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_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="o">.</span><span class="mi">8</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).
Created using <a href="http://sphinx.pocoo.org/">Sphinx</a> 1.0.5. Design by <a href="http://webylimonada.com">Web y Limonada</a>.
</div>
</body>
</html>
