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<h3>Contents</h3>
<ul>
<li><a class="reference internal" href="#">4.2. Clustering</a><ul>
<li><a class="reference internal" href="#affinity-propagation">4.2.1. Affinity propagation</a></li>
<li><a class="reference internal" href="#mean-shift">4.2.2. Mean Shift</a></li>
<li><a class="reference internal" href="#k-means">4.2.3. K-means</a></li>
<li><a class="reference internal" href="#spectral-clustering">4.2.4. Spectral clustering</a></li>
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<div class="section" id="clustering">
<span id="id1"></span><h1>4.2. Clustering<a class="headerlink" href="#clustering" title="Permalink to this headline">¶</a></h1>
<p><a class="reference external" href="http://en.wikipedia.org/wiki/Cluster_analysis">Clustering</a> of
unlabeled data can be performed with the module <cite>scikits.learn.cluster</cite>.</p>
<p>Each clustering algorithm comes in two variants: a class, that implements
the <cite>fit</cite> method to learn the clusters on train data, and a function,
that, given train data, returns an array of integer labels corresponding
to the different clusters. For the class, the labels over the training
data can be found in the <cite>labels_</cite> attribute.</p>
<p>Here, we only explain the different algorithms. For usage examples, click
on the class name to read the reference documentation.</p>
<div class="section" id="affinity-propagation">
<h2>4.2.1. Affinity propagation<a class="headerlink" href="#affinity-propagation" title="Permalink to this headline">¶</a></h2>
<p><tt class="xref py py-class docutils literal"><span class="pre">AffinityPropagation</span></tt> clusters data by diffusion in the similarity
matrix. This algorithm automatically sets its numbers of cluster. It
will have difficulties scaling to thousands of samples.</p>
<div class="figure align-center">
<a class="reference external image-reference" href="../auto_examples/cluster/plot_affinity_propagation.html"><img alt="auto_examples/cluster/images/plot_affinity_propagation.png" src="auto_examples/cluster/images/plot_affinity_propagation.png" /></a>
</div>
<div class="topic">
<p class="topic-title first">Examples:</p>
<ul class="simple">
<li><a class="reference internal" href="../auto_examples/cluster/plot_affinity_propagation.html#example-cluster-plot-affinity-propagation-py"><em>Demo of affinity propagation clustering algorithm</em></a>: Affinity
Propagation on a synthetic 2D datasets with 3 classes.</li>
<li><a class="reference internal" href="../auto_examples/applications/stock_market.html#example-applications-stock-market-py"><em>Finding structure in the stock market</em></a> Affinity Propagation on Financial
time series to find groups of companies</li>
</ul>
</div>
</div>
<div class="section" id="mean-shift">
<h2>4.2.2. Mean Shift<a class="headerlink" href="#mean-shift" title="Permalink to this headline">¶</a></h2>
<p><tt class="xref py py-class docutils literal"><span class="pre">MeanShift</span></tt> clusters data by estimating <em>blobs</em> in a smooth
density of points matrix. This algorithm automatically sets its numbers
of cluster. It will have difficulties scaling to thousands of samples.</p>
<div class="figure align-center">
<a class="reference external image-reference" href="../auto_examples/cluster/plot_mean_shift.html"><img alt="auto_examples/cluster/images/plot_mean_shift.png" src="auto_examples/cluster/images/plot_mean_shift.png" /></a>
</div>
<div class="topic">
<p class="topic-title first">Examples:</p>
<ul class="simple">
<li><a class="reference internal" href="../auto_examples/cluster/plot_mean_shift.html#example-cluster-plot-mean-shift-py"><em>A demo of the mean-shift clustering algorithm</em></a>: Mean Shift clustering
on a synthetic 2D datasets with 3 classes.</li>
</ul>
</div>
</div>
<div class="section" id="k-means">
<h2>4.2.3. K-means<a class="headerlink" href="#k-means" title="Permalink to this headline">¶</a></h2>
<p>The <tt class="xref py py-class docutils literal"><span class="pre">KMeans</span></tt> algorithm clusters data by trying to separate samples
in n groups of equal variance, minimizing a criterion known as the
‘inertia’ of the groups. This algorithm requires the number of cluster to
be specified. It scales well to large number of samples, however its
results may be dependent on an initialisation.</p>
</div>
<div class="section" id="spectral-clustering">
<h2>4.2.4. Spectral clustering<a class="headerlink" href="#spectral-clustering" title="Permalink to this headline">¶</a></h2>
<p><tt class="xref py py-class docutils literal"><span class="pre">SpectralClustering</span></tt> does an low-dimension embedding of the
affinity matrix between samples, followed by a KMeans in the low
dimensional space. It is especially efficient if the affinity matrix is
sparse and the <a class="reference external" href="http://code.google.com/p/pyamg/">pyamg</a> module is
installed. SpectralClustering requires the number of clusters to be
specified. It works well for a small number of clusters but is not
advised when using many clusters.</p>
<p>For two clusters, it solves a convex relaxation of the <a class="reference external" href="http://www.cs.berkeley.edu/~malik/papers/SM-ncut.pdf">normalised
cuts</a> problem on
the similarity graph: cutting the graph in two so that the weight of the
edges cut is small compared to the weights in of edges inside each
cluster. This criteria is especially interesting when working on images:
graph vertices are pixels, and edges of the similarity graph are a
function of the gradient of the image.</p>
<div class="figure align-center">
<a class="reference external image-reference" href="../auto_examples/cluster/plot_segmentation_toy.html"><img alt="auto_examples/cluster/images/plot_segmentation_toy.png" src="auto_examples/cluster/images/plot_segmentation_toy.png" /></a>
</div>
<div class="topic">
<p class="topic-title first">Examples:</p>
<ul class="simple">
<li><a class="reference internal" href="../auto_examples/cluster/plot_lena_segmentation.html#example-cluster-plot-lena-segmentation-py"><em>Segmenting the picture of Lena in regions</em></a>: Spectral clustering
to split the image of lena in regions.</li>
<li><a class="reference internal" href="../auto_examples/cluster/plot_segmentation_toy.html#example-cluster-plot-segmentation-toy-py"><em>Spectral clustering for image segmentation</em></a>: Segmenting objects
from a noisy background using spectral clustering.</li>
</ul>
</div>
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