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<li><a class="reference internal" href="#"><code class="xref py py-mod docutils literal notranslate"><span class="pre">sklearn.cluster</span></code>.ward_tree</a><ul>
<li><a class="reference internal" href="#sklearn.cluster.ward_tree"><code class="docutils literal notranslate"><span class="pre">ward_tree</span></code></a></li>
</ul>
</li>
</ul>

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  <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 notranslate"><span class="pre">sklearn.cluster</span></code></a>.ward_tree<a class="headerlink" href="#sklearn-cluster-ward-tree" title="Permalink to this heading">¶</a></h1>
<dl class="py function">
<dt class="sig sig-object py" id="sklearn.cluster.ward_tree">
<span class="sig-prename descclassname"><span class="pre">sklearn.cluster.</span></span><span class="sig-name descname"><span class="pre">ward_tree</span></span><span class="sig-paren">(</span><em class="sig-param"><span class="n"><span class="pre">X</span></span></em>, <em class="sig-param"><span class="o"><span class="pre">*</span></span></em>, <em class="sig-param"><span class="n"><span class="pre">connectivity</span></span><span class="o"><span class="pre">=</span></span><span class="default_value"><span class="pre">None</span></span></em>, <em class="sig-param"><span class="n"><span class="pre">n_clusters</span></span><span class="o"><span class="pre">=</span></span><span class="default_value"><span class="pre">None</span></span></em>, <em class="sig-param"><span class="n"><span class="pre">return_distance</span></span><span class="o"><span class="pre">=</span></span><span class="default_value"><span class="pre">False</span></span></em><span class="sig-paren">)</span><a class="reference external" href="https://github.com/scikit-learn/scikit-learn/blob/702316c27/sklearn/cluster/_agglomerative.py#L183"><span class="viewcode-link"><span class="pre">[source]</span></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>
<dl class="field-list">
<dt class="field-odd">Parameters<span class="colon">:</span></dt>
<dd class="field-odd"><dl class="simple">
<dt><strong>X</strong><span class="classifier">array-like of shape (n_samples, n_features)</span></dt><dd><p>Feature matrix representing <code class="docutils literal notranslate"><span class="pre">n_samples</span></code> samples to be clustered.</p>
</dd>
<dt><strong>connectivity</strong><span class="classifier">{array-like, sparse matrix}, default=None</span></dt><dd><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>
</dd>
<dt><strong>n_clusters</strong><span class="classifier">int, default=None</span></dt><dd><p><code class="docutils literal notranslate"><span class="pre">n_clusters</span></code> should be less than <code class="docutils literal notranslate"><span class="pre">n_samples</span></code>.  Stop early the
construction of the tree at <code class="docutils literal notranslate"><span class="pre">n_clusters.</span></code> 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>
</dd>
<dt><strong>return_distance</strong><span class="classifier">bool, default=False</span></dt><dd><p>If <code class="docutils literal notranslate"><span class="pre">True</span></code>, return the distance between the clusters.</p>
</dd>
</dl>
</dd>
<dt class="field-even">Returns<span class="colon">:</span></dt>
<dd class="field-even"><dl>
<dt><strong>children</strong><span class="classifier">ndarray of shape (n_nodes-1, 2)</span></dt><dd><p>The children of each non-leaf node. Values less than <code class="docutils literal notranslate"><span class="pre">n_samples</span></code>
correspond to leaves of the tree which are the original samples.
A node <code class="docutils literal notranslate"><span class="pre">i</span></code> greater than or equal to <code class="docutils literal notranslate"><span class="pre">n_samples</span></code> is a non-leaf
node and has children <code class="docutils literal notranslate"><span class="pre">children_[i</span> <span class="pre">-</span> <span class="pre">n_samples]</span></code>. Alternatively
at the i-th iteration, children[i][0] and children[i][1]
are merged to form node <code class="docutils literal notranslate"><span class="pre">n_samples</span> <span class="pre">+</span> <span class="pre">i</span></code>.</p>
</dd>
<dt><strong>n_connected_components</strong><span class="classifier">int</span></dt><dd><p>The number of connected components in the graph.</p>
</dd>
<dt><strong>n_leaves</strong><span class="classifier">int</span></dt><dd><p>The number of leaves in the tree.</p>
</dd>
<dt><strong>parents</strong><span class="classifier">ndarray of shape (n_nodes,) or None</span></dt><dd><p>The parent of each node. Only returned when a connectivity matrix
is specified, elsewhere ‘None’ is returned.</p>
</dd>
<dt><strong>distances</strong><span class="classifier">ndarray of shape (n_nodes-1,)</span></dt><dd><p>Only returned if <code class="docutils literal notranslate"><span class="pre">return_distance</span></code> is set to <code class="docutils literal notranslate"><span class="pre">True</span></code> (for compatibility).
The distances between the centers of the nodes. <code class="docutils literal notranslate"><span class="pre">distances[i]</span></code>
corresponds to a weighted Euclidean distance between
the nodes <code class="docutils literal notranslate"><span class="pre">children[i,</span> <span class="pre">1]</span></code> and <code class="docutils literal notranslate"><span class="pre">children[i,</span> <span class="pre">2]</span></code>. If the nodes refer to
leaves of the tree, then <code class="docutils literal notranslate"><span class="pre">distances[i]</span></code> is their unweighted Euclidean
distance. Distances are updated in the following way
(from scipy.hierarchy.linkage):</p>
<p>The new entry <span class="math notranslate nohighlight">\(d(u,v)\)</span> is computed as follows,</p>
<div class="math notranslate nohighlight">
\[d(u,v) = \sqrt{\frac{|v|+|s|}
                    {T}d(v,s)^2
             + \frac{|v|+|t|}
                    {T}d(v,t)^2
             - \frac{|v|}
                    {T}d(s,t)^2}\]</div>
<p>where <span class="math notranslate nohighlight">\(u\)</span> is the newly joined cluster consisting of
clusters <span class="math notranslate nohighlight">\(s\)</span> and <span class="math notranslate nohighlight">\(t\)</span>, <span class="math notranslate nohighlight">\(v\)</span> is an unused
cluster in the forest, <span class="math notranslate nohighlight">\(T=|v|+|s|+|t|\)</span>, and
<span class="math notranslate nohighlight">\(|*|\)</span> is the cardinality of its argument. This is also
known as the incremental algorithm.</p>
</dd>
</dl>
</dd>
</dl>
</dd></dl>

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