<!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>Blind source separation using FastICA — 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="FastICA on 2D point clouds" href="plot_ica_vs_pca.html" /> <link rel="prev" title="Univariate Feature Selection" href="plot_feature_selection.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_feature_selection.html" title="Univariate Feature Selection" accesskey="P">previous</a> | <a href="plot_ica_vs_pca.html" title="FastICA on 2D point clouds" 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="#">Blind source separation using FastICA</a></li> </ul> </div> <div class="content"> <div class="documentwrapper"> <div class="bodywrapper"> <div class="body"> <div class="section" id="blind-source-separation-using-fastica"> <span id="example-plot-ica-blind-source-separation-py"></span><h1>Blind source separation using FastICA<a class="headerlink" href="#blind-source-separation-using-fastica" title="Permalink to this headline">ΒΆ</a></h1> <p><a class="reference internal" href="../modules/decompositions.html#ica"><em>Independent component analysis (ICA)</em></a> is used to estimate sources given noisy measurements. Imagine 2 instruments playing simultaneously and 2 microphones recording the mixed signals. ICA is used to recover the sources ie. what is played by each instrument.</p> <img alt="auto_examples/images/plot_ica_blind_source_separation.png" class="align-center" src="auto_examples/images/plot_ica_blind_source_separation.png" /> <p><strong>Python source code:</strong> <a class="reference download internal" href="../_downloads/plot_ica_blind_source_separation.py"><tt class="xref download docutils literal"><span class="pre">plot_ica_blind_source_separation.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.fastica</span> <span class="kn">import</span> <span class="n">FastICA</span> <span class="c">###############################################################################</span> <span class="c"># Generate sample data</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</span> <span class="o">=</span> <span class="mi">2000</span> <span class="n">time</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="mi">0</span><span class="p">,</span> <span class="mi">10</span><span class="p">,</span> <span class="n">n_samples</span><span class="p">)</span> <span class="n">s1</span> <span class="o">=</span> <span class="n">np</span><span class="o">.</span><span class="n">sin</span><span class="p">(</span><span class="mi">2</span><span class="o">*</span><span class="n">time</span><span class="p">)</span> <span class="c"># Signal 1 : sinusoidal signal</span> <span class="n">s2</span> <span class="o">=</span> <span class="n">np</span><span class="o">.</span><span class="n">sign</span><span class="p">(</span><span class="n">np</span><span class="o">.</span><span class="n">sin</span><span class="p">(</span><span class="mi">3</span><span class="o">*</span><span class="n">time</span><span class="p">))</span> <span class="c"># Signal 2 : square signal</span> <span class="n">S</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">s1</span><span class="p">,</span><span class="n">s2</span><span class="p">]</span><span class="o">.</span><span class="n">T</span> <span class="n">S</span> <span class="o">+=</span> <span class="mf">0.2</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">normal</span><span class="p">(</span><span class="n">size</span><span class="o">=</span><span class="n">S</span><span class="o">.</span><span class="n">shape</span><span class="p">)</span> <span class="c"># Add noise</span> <span class="n">S</span> <span class="o">/=</span> <span class="n">S</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">1</span><span class="p">)[:,</span><span class="n">np</span><span class="o">.</span><span class="n">newaxis</span><span class="p">]</span> <span class="c"># Standardize data</span> <span class="c"># Mix data</span> <span class="n">A</span> <span class="o">=</span> <span class="p">[[</span><span class="mi">1</span><span class="p">,</span> <span class="mi">1</span><span class="p">],</span> <span class="p">[</span><span class="mf">0.5</span><span class="p">,</span> <span class="mi">2</span><span class="p">]]</span> <span class="c"># Mixing matrix</span> <span class="n">X</span> <span class="o">=</span> <span class="n">np</span><span class="o">.</span><span class="n">dot</span><span class="p">(</span><span class="n">A</span><span class="p">,</span> <span class="n">S</span><span class="p">)</span> <span class="c"># Generate observations</span> <span class="c"># Compute ICA</span> <span class="n">ica</span> <span class="o">=</span> <span class="n">FastICA</span><span class="p">()</span> <span class="n">S_</span> <span class="o">=</span> <span class="n">ica</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="o">.</span><span class="n">transform</span><span class="p">(</span><span class="n">X</span><span class="p">)</span> <span class="c"># Get the estimated sources</span> <span class="n">A_</span> <span class="o">=</span> <span class="n">ica</span><span class="o">.</span><span class="n">get_mixing_matrix</span><span class="p">()</span> <span class="c"># Get estimated mixing matrix</span> <span class="k">assert</span> <span class="n">np</span><span class="o">.</span><span class="n">allclose</span><span class="p">(</span><span class="n">X</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">A_</span><span class="p">,</span> <span class="n">S_</span><span class="p">))</span> <span class="c">###############################################################################</span> <span class="c"># Plot results</span> <span class="n">pl</span><span class="o">.</span><span class="n">figure</span><span class="p">()</span> <span class="n">pl</span><span class="o">.</span><span class="n">subplot</span><span class="p">(</span><span class="mi">3</span><span class="p">,</span> <span class="mi">1</span><span class="p">,</span> <span class="mi">1</span><span class="p">)</span> <span class="n">pl</span><span class="o">.</span><span class="n">plot</span><span class="p">(</span><span class="n">S</span><span class="o">.</span><span class="n">T</span><span class="p">)</span> <span class="n">pl</span><span class="o">.</span><span class="n">title</span><span class="p">(</span><span class="s">'True Sources'</span><span class="p">)</span> <span class="n">pl</span><span class="o">.</span><span class="n">subplot</span><span class="p">(</span><span class="mi">3</span><span class="p">,</span> <span class="mi">1</span><span class="p">,</span> <span class="mi">2</span><span class="p">)</span> <span class="n">pl</span><span class="o">.</span><span class="n">plot</span><span class="p">(</span><span class="n">X</span><span class="o">.</span><span class="n">T</span><span class="p">)</span> <span class="n">pl</span><span class="o">.</span><span class="n">title</span><span class="p">(</span><span class="s">'Observations (mixed signal)'</span><span class="p">)</span> <span class="n">pl</span><span class="o">.</span><span class="n">subplot</span><span class="p">(</span><span class="mi">3</span><span class="p">,</span> <span class="mi">1</span><span class="p">,</span> <span class="mi">3</span><span class="p">)</span> <span class="n">pl</span><span class="o">.</span><span class="n">plot</span><span class="p">(</span><span class="n">S_</span><span class="o">.</span><span class="n">T</span><span class="p">)</span> <span class="n">pl</span><span class="o">.</span><span class="n">title</span><span class="p">(</span><span class="s">'ICA estimated sources'</span><span class="p">)</span> <span class="n">pl</span><span class="o">.</span><span class="n">subplots_adjust</span><span class="p">(</span><span class="mf">0.09</span><span class="p">,</span> <span class="mf">0.04</span><span class="p">,</span> <span class="mf">0.94</span><span class="p">,</span> <span class="mf">0.94</span><span class="p">,</span> <span class="mf">0.26</span><span class="p">,</span> <span class="mf">0.36</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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