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        <h3>Contents</h3>
         <ul>
<li><a class="reference internal" href="#">4.3. Decomposing signals in components (matrix factorization problems)</a><ul>
<li><a class="reference internal" href="#principal-component-analysis-pca">4.3.1. Principal component analysis (PCA)</a></li>
<li><a class="reference internal" href="#independent-component-analysis-ica">4.3.2. Independent component analysis (ICA)</a></li>
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  <div class="section" id="decomposing-signals-in-components-matrix-factorization-problems">
<h1>4.3. Decomposing signals in components (matrix factorization problems)<a class="headerlink" href="#decomposing-signals-in-components-matrix-factorization-problems" title="Permalink to this headline">¶</a></h1>
<div class="section" id="principal-component-analysis-pca">
<span id="pca"></span><h2>4.3.1. Principal component analysis (PCA)<a class="headerlink" href="#principal-component-analysis-pca" title="Permalink to this headline">¶</a></h2>
<p>PCA is used to decompose a multivariate dataset in a set of successive
orthogonal components that explain a maximum amount of the variance. In
the scikit-learn, <tt class="xref py py-class docutils literal"><span class="pre">PCA</span></tt> is implemented as a <cite>transformer</cite> object
that learns n components in its <cite>fit</cite> method, and can be used on new data
to project it on these components.</p>
<p>In addition, the <tt class="xref py py-class docutils literal"><span class="pre">ProbabilisticPCA</span></tt> object provides a
probabilistic interpretation of the PCA that can give a likelihood of
data based on the amount of variance it explains. As such it implements a
<cite>score</cite> method that can be used in cross-validation.</p>
<p>Below is an example of the iris dataset, which is comprised of 4
features, projected on the 2 dimensions that explain most variance:</p>
<div class="figure align-center">
<a class="reference external image-reference" href="../auto_examples/plot_pca.html"><img alt="auto_examples/images/plot_pca.png" src="auto_examples/images/plot_pca.png" /></a>
</div>
<div class="topic">
<p class="topic-title first">Examples:</p>
<ul class="simple">
<li><a class="reference internal" href="../auto_examples/plot_pca.html#example-plot-pca-py"><em>PCA 2d projection of of Iris dataset</em></a></li>
</ul>
</div>
</div>
<div class="section" id="independent-component-analysis-ica">
<span id="ica"></span><h2>4.3.2. Independent component analysis (ICA)<a class="headerlink" href="#independent-component-analysis-ica" title="Permalink to this headline">¶</a></h2>
<p>ICA finds components that are maximally independent. It is classically
used to separate mixed signals (a problem know as <em>blind source
separation</em>), as in the example below:</p>
<div class="figure align-center">
<a class="reference external image-reference" href="../auto_examples/plot_ica_blind_source_separation.html"><img alt="auto_examples/images/plot_ica_blind_source_separation.png" src="auto_examples/images/plot_ica_blind_source_separation.png" /></a>
</div>
<div class="topic">
<p class="topic-title first">Examples:</p>
<ul class="simple">
<li><a class="reference internal" href="../auto_examples/plot_ica_blind_source_separation.html#example-plot-ica-blind-source-separation-py"><em>Blind source separation using FastICA</em></a></li>
<li><a class="reference internal" href="../auto_examples/plot_ica_vs_pca.html#example-plot-ica-vs-pca-py"><em>FastICA on 2D point clouds</em></a></li>
</ul>
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