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<ul>
<li><a class="reference internal" href="#"><code class="docutils literal"><span class="pre">sklearn.cluster</span></code>.ward_tree</a></li>
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<div class="section" id="sklearn-cluster-ward-tree">
<h1><a class="reference internal" href="../classes.html#module-sklearn.cluster" title="sklearn.cluster"><code class="xref py py-mod docutils literal"><span class="pre">sklearn.cluster</span></code></a>.ward_tree<a class="headerlink" href="#sklearn-cluster-ward-tree" title="Permalink to this headline">¶</a></h1>
<dl class="function">
<dt id="sklearn.cluster.ward_tree">
<code class="descclassname">sklearn.cluster.</code><code class="descname">ward_tree</code><span class="sig-paren">(</span><em>X</em>, <em>connectivity=None</em>, <em>n_clusters=None</em>, <em>return_distance=False</em><span class="sig-paren">)</span><a class="reference external" href="https://github.com/scikit-learn/scikit-learn/blob/474b5e0/sklearn/cluster/hierarchical.py#L136"><span class="viewcode-link">[source]</span></a><a class="headerlink" href="#sklearn.cluster.ward_tree" title="Permalink to this definition">¶</a></dt>
<dd><p>Ward clustering based on a Feature matrix.</p>
<p>Recursively merges the pair of clusters that minimally increases
within-cluster variance.</p>
<p>The inertia matrix uses a Heapq-based representation.</p>
<p>This is the structured version, that takes into account some topological
structure between samples.</p>
<p>Read more in the <a class="reference internal" href="../clustering.html#hierarchical-clustering"><span class="std std-ref">User Guide</span></a>.</p>
<table class="docutils field-list" frame="void" rules="none">
<col class="field-name" />
<col class="field-body" />
<tbody valign="top">
<tr class="field-odd field"><th class="field-name">Parameters:</th><td class="field-body"><p class="first"><strong>X</strong> : array, shape (n_samples, n_features)</p>
<blockquote>
<div><p>feature matrix representing n_samples samples to be clustered</p>
</div></blockquote>
<p><strong>connectivity</strong> : sparse matrix (optional).</p>
<blockquote>
<div><p>connectivity matrix. Defines for each sample the neighboring samples
following a given structure of the data. The matrix is assumed to
be symmetric and only the upper triangular half is used.
Default is None, i.e, the Ward algorithm is unstructured.</p>
</div></blockquote>
<p><strong>n_clusters</strong> : int (optional)</p>
<blockquote>
<div><p>Stop early the construction of the tree at n_clusters. This is
useful to decrease computation time if the number of clusters is
not small compared to the number of samples. In this case, the
complete tree is not computed, thus the ‘children’ output is of
limited use, and the ‘parents’ output should rather be used.
This option is valid only when specifying a connectivity matrix.</p>
</div></blockquote>
<p><strong>return_distance</strong> : bool (optional)</p>
<blockquote>
<div><p>If True, return the distance between the clusters.</p>
</div></blockquote>
</td>
</tr>
<tr class="field-even field"><th class="field-name">Returns:</th><td class="field-body"><p class="first"><strong>children</strong> : 2D array, shape (n_nodes-1, 2)</p>
<blockquote>
<div><p>The children of each non-leaf node. Values less than <cite>n_samples</cite>
correspond to leaves of the tree which are the original samples.
A node <cite>i</cite> greater than or equal to <cite>n_samples</cite> is a non-leaf
node and has children <cite>children_[i - n_samples]</cite>. Alternatively
at the i-th iteration, children[i][0] and children[i][1]
are merged to form node <cite>n_samples + i</cite></p>
</div></blockquote>
<p><strong>n_components</strong> : int</p>
<blockquote>
<div><p>The number of connected components in the graph.</p>
</div></blockquote>
<p><strong>n_leaves</strong> : int</p>
<blockquote>
<div><p>The number of leaves in the tree</p>
</div></blockquote>
<p><strong>parents</strong> : 1D array, shape (n_nodes, ) or None</p>
<blockquote>
<div><p>The parent of each node. Only returned when a connectivity matrix
is specified, elsewhere ‘None’ is returned.</p>
</div></blockquote>
<p><strong>distances</strong> : 1D array, shape (n_nodes-1, )</p>
<blockquote class="last">
<div><p>Only returned if return_distance is set to True (for compatibility).
The distances between the centers of the nodes. <cite>distances[i]</cite>
corresponds to a weighted euclidean distance between
the nodes <cite>children[i, 1]</cite> and <cite>children[i, 2]</cite>. If the nodes refer to
leaves of the tree, then <cite>distances[i]</cite> is their unweighted euclidean
distance. Distances are updated in the following way
(from scipy.hierarchy.linkage):</p>
<p>The new entry <span class="math">\(d(u,v)\)</span> is computed as follows,</p>
<div class="math">
\[d(u,v) = \sqrt{\frac{|v|+|s|}
{T}d(v,s)^2
+ \frac{|v|+|t|}
{T}d(v,t)^2
- \frac{|v|}
{T}d(s,t)^2}\]</div>
<p>where <span class="math">\(u\)</span> is the newly joined cluster consisting of
clusters <span class="math">\(s\)</span> and <span class="math">\(t\)</span>, <span class="math">\(v\)</span> is an unused
cluster in the forest, <span class="math">\(T=|v|+|s|+|t|\)</span>, and
<span class="math">\(|*|\)</span> is the cardinality of its argument. This is also
known as the incremental algorithm.</p>
</div></blockquote>
</td>
</tr>
</tbody>
</table>
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