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  <section id="spectralclustering">
<h1>SpectralClustering<a class="headerlink" href="#spectralclustering" title="Link to this heading">#</a></h1>
<dl class="py class">
<dt class="sig sig-object py" id="sklearn.cluster.SpectralClustering">
<em class="property"><span class="pre">class</span><span class="w"> </span></em><span class="sig-prename descclassname"><span class="pre">sklearn.cluster.</span></span><span class="sig-name descname"><span class="pre">SpectralClustering</span></span><span class="sig-paren">(</span><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">8</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">eigen_solver</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_components</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">random_state</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_init</span></span><span class="o"><span class="pre">=</span></span><span class="default_value"><span class="pre">10</span></span></em>, <em class="sig-param"><span class="n"><span class="pre">gamma</span></span><span class="o"><span class="pre">=</span></span><span class="default_value"><span class="pre">1.0</span></span></em>, <em class="sig-param"><span class="n"><span class="pre">affinity</span></span><span class="o"><span class="pre">=</span></span><span class="default_value"><span class="pre">'rbf'</span></span></em>, <em class="sig-param"><span class="n"><span class="pre">n_neighbors</span></span><span class="o"><span class="pre">=</span></span><span class="default_value"><span class="pre">10</span></span></em>, <em class="sig-param"><span class="n"><span class="pre">eigen_tol</span></span><span class="o"><span class="pre">=</span></span><span class="default_value"><span class="pre">'auto'</span></span></em>, <em class="sig-param"><span class="n"><span class="pre">assign_labels</span></span><span class="o"><span class="pre">=</span></span><span class="default_value"><span class="pre">'kmeans'</span></span></em>, <em class="sig-param"><span class="n"><span class="pre">degree</span></span><span class="o"><span class="pre">=</span></span><span class="default_value"><span class="pre">3</span></span></em>, <em class="sig-param"><span class="n"><span class="pre">coef0</span></span><span class="o"><span class="pre">=</span></span><span class="default_value"><span class="pre">1</span></span></em>, <em class="sig-param"><span class="n"><span class="pre">kernel_params</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_jobs</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">verbose</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/86d099ec1/sklearn/cluster/_spectral.py#L379"><span class="viewcode-link"><span class="pre">[source]</span></span></a><a class="headerlink" href="#sklearn.cluster.SpectralClustering" title="Link to this definition">#</a></dt>
<dd><p>Apply clustering to a projection of the normalized Laplacian.</p>
<p>In practice Spectral Clustering is very useful when the structure of
the individual clusters is highly non-convex, or more generally when
a measure of the center and spread of the cluster is not a suitable
description of the complete cluster, such as when clusters are
nested circles on the 2D plane.</p>
<p>If the affinity matrix is the adjacency matrix of a graph, this method
can be used to find normalized graph cuts <a class="reference internal" href="#r5f6cbeb1558e-1" id="id1">[1]</a>, <a class="reference internal" href="#r5f6cbeb1558e-2" id="id2">[2]</a>.</p>
<p>When calling <code class="docutils literal notranslate"><span class="pre">fit</span></code>, an affinity matrix is constructed using either
a kernel function such the Gaussian (aka RBF) kernel with Euclidean
distance <code class="docutils literal notranslate"><span class="pre">d(X,</span> <span class="pre">X)</span></code>:</p>
<div class="highlight-default notranslate"><div class="highlight"><pre><span></span><span class="n">np</span><span class="o">.</span><span class="n">exp</span><span class="p">(</span><span class="o">-</span><span class="n">gamma</span> <span class="o">*</span> <span class="n">d</span><span class="p">(</span><span class="n">X</span><span class="p">,</span><span class="n">X</span><span class="p">)</span> <span class="o">**</span> <span class="mi">2</span><span class="p">)</span>
</pre></div>
</div>
<p>or a k-nearest neighbors connectivity matrix.</p>
<p>Alternatively, a user-provided affinity matrix can be specified by
setting <code class="docutils literal notranslate"><span class="pre">affinity='precomputed'</span></code>.</p>
<p>Read more in the <a class="reference internal" href="../clustering.html#spectral-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>
<dt><strong>n_clusters</strong><span class="classifier">int, default=8</span></dt><dd><p>The dimension of the projection subspace.</p>
</dd>
<dt><strong>eigen_solver</strong><span class="classifier">{‘arpack’, ‘lobpcg’, ‘amg’}, default=None</span></dt><dd><p>The eigenvalue decomposition strategy to use. AMG requires pyamg
to be installed. It can be faster on very large, sparse problems,
but may also lead to instabilities. If None, then <code class="docutils literal notranslate"><span class="pre">'arpack'</span></code> is
used. See <a class="reference internal" href="#r5f6cbeb1558e-4" id="id3">[4]</a> for more details regarding <code class="docutils literal notranslate"><span class="pre">'lobpcg'</span></code>.</p>
</dd>
<dt><strong>n_components</strong><span class="classifier">int, default=None</span></dt><dd><p>Number of eigenvectors to use for the spectral embedding. If None,
defaults to <code class="docutils literal notranslate"><span class="pre">n_clusters</span></code>.</p>
</dd>
<dt><strong>random_state</strong><span class="classifier">int, RandomState instance, default=None</span></dt><dd><p>A pseudo random number generator used for the initialization
of the lobpcg eigenvectors decomposition when <code class="docutils literal notranslate"><span class="pre">eigen_solver</span> <span class="pre">==</span>
<span class="pre">'amg'</span></code>, and for the K-Means initialization. Use an int to make
the results deterministic across calls (See
<a class="reference internal" href="../../glossary.html#term-random_state"><span class="xref std std-term">Glossary</span></a>).</p>
<div class="admonition note">
<p class="admonition-title">Note</p>
<p>When using <code class="docutils literal notranslate"><span class="pre">eigen_solver</span> <span class="pre">==</span> <span class="pre">'amg'</span></code>,
it is necessary to also fix the global numpy seed with
<code class="docutils literal notranslate"><span class="pre">np.random.seed(int)</span></code> to get deterministic results. See
<a class="github reference external" href="https://github.com/pyamg/pyamg/issues/139">pyamg/pyamg#139</a> for further
information.</p>
</div>
</dd>
<dt><strong>n_init</strong><span class="classifier">int, default=10</span></dt><dd><p>Number of time the k-means algorithm will be run with different
centroid seeds. The final results will be the best output of n_init
consecutive runs in terms of inertia. Only used if
<code class="docutils literal notranslate"><span class="pre">assign_labels='kmeans'</span></code>.</p>
</dd>
<dt><strong>gamma</strong><span class="classifier">float, default=1.0</span></dt><dd><p>Kernel coefficient for rbf, poly, sigmoid, laplacian and chi2 kernels.
Ignored for <code class="docutils literal notranslate"><span class="pre">affinity='nearest_neighbors'</span></code>, <code class="docutils literal notranslate"><span class="pre">affinity='precomputed'</span></code>
or <code class="docutils literal notranslate"><span class="pre">affinity='precomputed_nearest_neighbors'</span></code>.</p>
</dd>
<dt><strong>affinity</strong><span class="classifier">str or callable, default=’rbf’</span></dt><dd><dl class="simple">
<dt>How to construct the affinity matrix.</dt><dd><ul class="simple">
<li><p>‘nearest_neighbors’: construct the affinity matrix by computing a
graph of nearest neighbors.</p></li>
<li><p>‘rbf’: construct the affinity matrix using a radial basis function
(RBF) kernel.</p></li>
<li><p>‘precomputed’: interpret <code class="docutils literal notranslate"><span class="pre">X</span></code> as a precomputed affinity matrix,
where larger values indicate greater similarity between instances.</p></li>
<li><p>‘precomputed_nearest_neighbors’: interpret <code class="docutils literal notranslate"><span class="pre">X</span></code> as a sparse graph
of precomputed distances, and construct a binary affinity matrix
from the <code class="docutils literal notranslate"><span class="pre">n_neighbors</span></code> nearest neighbors of each instance.</p></li>
<li><p>one of the kernels supported by
<a class="reference internal" href="sklearn.metrics.pairwise.pairwise_kernels.html#sklearn.metrics.pairwise.pairwise_kernels" title="sklearn.metrics.pairwise.pairwise_kernels"><code class="xref py py-func docutils literal notranslate"><span class="pre">pairwise_kernels</span></code></a>.</p></li>
</ul>
</dd>
</dl>
<p>Only kernels that produce similarity scores (non-negative values that
increase with similarity) should be used. This property is not checked
by the clustering algorithm.</p>
</dd>
<dt><strong>n_neighbors</strong><span class="classifier">int, default=10</span></dt><dd><p>Number of neighbors to use when constructing the affinity matrix using
the nearest neighbors method. Ignored for <code class="docutils literal notranslate"><span class="pre">affinity='rbf'</span></code>.</p>
</dd>
<dt><strong>eigen_tol</strong><span class="classifier">float, default=”auto”</span></dt><dd><p>Stopping criterion for eigen decomposition of the Laplacian matrix.
If <code class="docutils literal notranslate"><span class="pre">eigen_tol=&quot;auto&quot;</span></code> then the passed tolerance will depend on the
<code class="docutils literal notranslate"><span class="pre">eigen_solver</span></code>:</p>
<ul class="simple">
<li><p>If <code class="docutils literal notranslate"><span class="pre">eigen_solver=&quot;arpack&quot;</span></code>, then <code class="docutils literal notranslate"><span class="pre">eigen_tol=0.0</span></code>;</p></li>
<li><p>If <code class="docutils literal notranslate"><span class="pre">eigen_solver=&quot;lobpcg&quot;</span></code> or <code class="docutils literal notranslate"><span class="pre">eigen_solver=&quot;amg&quot;</span></code>, then
<code class="docutils literal notranslate"><span class="pre">eigen_tol=None</span></code> which configures the underlying <code class="docutils literal notranslate"><span class="pre">lobpcg</span></code> solver to
automatically resolve the value according to their heuristics. See,
<a class="reference external" href="https://docs.scipy.org/doc/scipy/reference/generated/scipy.sparse.linalg.lobpcg.html#scipy.sparse.linalg.lobpcg" title="(in SciPy v1.15.2)"><code class="xref py py-func docutils literal notranslate"><span class="pre">scipy.sparse.linalg.lobpcg</span></code></a> for details.</p></li>
</ul>
<p>Note that when using <code class="docutils literal notranslate"><span class="pre">eigen_solver=&quot;lobpcg&quot;</span></code> or <code class="docutils literal notranslate"><span class="pre">eigen_solver=&quot;amg&quot;</span></code>
values of <code class="docutils literal notranslate"><span class="pre">tol&lt;1e-5</span></code> may lead to convergence issues and should be
avoided.</p>
<div class="versionadded">
<p><span class="versionmodified added">Added in version 1.2: </span>Added ‘auto’ option.</p>
</div>
</dd>
<dt><strong>assign_labels</strong><span class="classifier">{‘kmeans’, ‘discretize’, ‘cluster_qr’}, default=’kmeans’</span></dt><dd><p>The strategy for assigning labels in the embedding space. There are two
ways to assign labels after the Laplacian embedding. k-means is a
popular choice, but it can be sensitive to initialization.
Discretization is another approach which is less sensitive to random
initialization <a class="reference internal" href="#r5f6cbeb1558e-3" id="id4">[3]</a>.
The cluster_qr method <a class="reference internal" href="#r5f6cbeb1558e-5" id="id5">[5]</a> directly extract clusters from eigenvectors
in spectral clustering. In contrast to k-means and discretization, cluster_qr
has no tuning parameters and runs no iterations, yet may outperform
k-means and discretization in terms of both quality and speed.</p>
<div class="versionchanged">
<p><span class="versionmodified changed">Changed in version 1.1: </span>Added new labeling method ‘cluster_qr’.</p>
</div>
</dd>
<dt><strong>degree</strong><span class="classifier">float, default=3</span></dt><dd><p>Degree of the polynomial kernel. Ignored by other kernels.</p>
</dd>
<dt><strong>coef0</strong><span class="classifier">float, default=1</span></dt><dd><p>Zero coefficient for polynomial and sigmoid kernels.
Ignored by other kernels.</p>
</dd>
<dt><strong>kernel_params</strong><span class="classifier">dict of str to any, default=None</span></dt><dd><p>Parameters (keyword arguments) and values for kernel passed as
callable object. Ignored by other kernels.</p>
</dd>
<dt><strong>n_jobs</strong><span class="classifier">int, default=None</span></dt><dd><p>The number of parallel jobs to run when <code class="docutils literal notranslate"><span class="pre">affinity='nearest_neighbors'</span></code>
or <code class="docutils literal notranslate"><span class="pre">affinity='precomputed_nearest_neighbors'</span></code>. The neighbors search
will be done in parallel.
<code class="docutils literal notranslate"><span class="pre">None</span></code> means 1 unless in a <a class="reference external" href="https://joblib.readthedocs.io/en/latest/generated/joblib.parallel_backend.html#joblib.parallel_backend" title="(in joblib v1.5.dev0)"><code class="xref py py-obj docutils literal notranslate"><span class="pre">joblib.parallel_backend</span></code></a> context.
<code class="docutils literal notranslate"><span class="pre">-1</span></code> means using all processors. See <a class="reference internal" href="../../glossary.html#term-n_jobs"><span class="xref std std-term">Glossary</span></a>
for more details.</p>
</dd>
<dt><strong>verbose</strong><span class="classifier">bool, default=False</span></dt><dd><p>Verbosity mode.</p>
<div class="versionadded">
<p><span class="versionmodified added">Added in version 0.24.</span></p>
</div>
</dd>
</dl>
</dd>
<dt class="field-even">Attributes<span class="colon">:</span></dt>
<dd class="field-even"><dl>
<dt><strong>affinity_matrix_</strong><span class="classifier">array-like of shape (n_samples, n_samples)</span></dt><dd><p>Affinity matrix used for clustering. Available only after calling
<code class="docutils literal notranslate"><span class="pre">fit</span></code>.</p>
</dd>
<dt><strong>labels_</strong><span class="classifier">ndarray of shape (n_samples,)</span></dt><dd><p>Labels of each point</p>
</dd>
<dt><strong>n_features_in_</strong><span class="classifier">int</span></dt><dd><p>Number of features seen during <a class="reference internal" href="../../glossary.html#term-fit"><span class="xref std std-term">fit</span></a>.</p>
<div class="versionadded">
<p><span class="versionmodified added">Added in version 0.24.</span></p>
</div>
</dd>
<dt><strong>feature_names_in_</strong><span class="classifier">ndarray of shape (<code class="docutils literal notranslate"><span class="pre">n_features_in_</span></code>,)</span></dt><dd><p>Names of features seen during <a class="reference internal" href="../../glossary.html#term-fit"><span class="xref std std-term">fit</span></a>. Defined only when <code class="docutils literal notranslate"><span class="pre">X</span></code>
has feature names that are all strings.</p>
<div class="versionadded">
<p><span class="versionmodified added">Added in version 1.0.</span></p>
</div>
</dd>
</dl>
</dd>
</dl>
<div class="admonition seealso">
<p class="admonition-title">See also</p>
<dl class="simple">
<dt><a class="reference internal" href="sklearn.cluster.KMeans.html#sklearn.cluster.KMeans" title="sklearn.cluster.KMeans"><code class="xref py py-obj docutils literal notranslate"><span class="pre">sklearn.cluster.KMeans</span></code></a></dt><dd><p>K-Means clustering.</p>
</dd>
<dt><a class="reference internal" href="sklearn.cluster.DBSCAN.html#sklearn.cluster.DBSCAN" title="sklearn.cluster.DBSCAN"><code class="xref py py-obj docutils literal notranslate"><span class="pre">sklearn.cluster.DBSCAN</span></code></a></dt><dd><p>Density-Based Spatial Clustering of Applications with Noise.</p>
</dd>
</dl>
</div>
<p class="rubric">Notes</p>
<p>A distance matrix for which 0 indicates identical elements and high values
indicate very dissimilar elements can be transformed into an affinity /
similarity matrix that is well-suited for the algorithm by
applying the Gaussian (aka RBF, heat) kernel:</p>
<div class="highlight-default notranslate"><div class="highlight"><pre><span></span><span class="n">np</span><span class="o">.</span><span class="n">exp</span><span class="p">(</span><span class="o">-</span> <span class="n">dist_matrix</span> <span class="o">**</span> <span class="mi">2</span> <span class="o">/</span> <span class="p">(</span><span class="mf">2.</span> <span class="o">*</span> <span class="n">delta</span> <span class="o">**</span> <span class="mi">2</span><span class="p">))</span>
</pre></div>
</div>
<p>where <code class="docutils literal notranslate"><span class="pre">delta</span></code> is a free parameter representing the width of the Gaussian
kernel.</p>
<p>An alternative is to take a symmetric version of the k-nearest neighbors
connectivity matrix of the points.</p>
<p>If the pyamg package is installed, it is used: this greatly
speeds up computation.</p>
<p class="rubric">References</p>
<div role="list" class="citation-list">
<div class="citation" id="r5f6cbeb1558e-1" role="doc-biblioentry">
<span class="label"><span class="fn-bracket">[</span><a role="doc-backlink" href="#id1">1</a><span class="fn-bracket">]</span></span>
<p><a class="reference external" href="https://doi.org/10.1109/34.868688">Normalized cuts and image segmentation, 2000
Jianbo Shi, Jitendra Malik</a></p>
</div>
<div class="citation" id="r5f6cbeb1558e-2" role="doc-biblioentry">
<span class="label"><span class="fn-bracket">[</span><a role="doc-backlink" href="#id2">2</a><span class="fn-bracket">]</span></span>
<p><a class="reference external" href="https://doi.org/10.1007/s11222-007-9033-z">A Tutorial on Spectral Clustering, 2007
Ulrike von Luxburg</a></p>
</div>
<div class="citation" id="r5f6cbeb1558e-3" role="doc-biblioentry">
<span class="label"><span class="fn-bracket">[</span><a role="doc-backlink" href="#id4">3</a><span class="fn-bracket">]</span></span>
<p><a class="reference external" href="https://people.eecs.berkeley.edu/~jordan/courses/281B-spring04/readings/yu-shi.pdf">Multiclass spectral clustering, 2003
Stella X. Yu, Jianbo Shi</a></p>
</div>
<div class="citation" id="r5f6cbeb1558e-4" role="doc-biblioentry">
<span class="label"><span class="fn-bracket">[</span><a role="doc-backlink" href="#id3">4</a><span class="fn-bracket">]</span></span>
<p><a class="reference external" href="https://doi.org/10.1137/S1064827500366124">Toward the Optimal Preconditioned Eigensolver:
Locally Optimal Block Preconditioned Conjugate Gradient Method, 2001
A. V. Knyazev
SIAM Journal on Scientific Computing 23, no. 2, pp. 517-541.</a></p>
</div>
<div class="citation" id="r5f6cbeb1558e-5" role="doc-biblioentry">
<span class="label"><span class="fn-bracket">[</span><a role="doc-backlink" href="#id5">5</a><span class="fn-bracket">]</span></span>
<p><a class="reference external" href="https://doi.org/10.1093/imaiai/iay008">Simple, direct, and efficient multi-way spectral clustering, 2019
Anil Damle, Victor Minden, Lexing Ying</a></p>
</div>
</div>
<p class="rubric">Examples</p>
<div class="doctest highlight-default notranslate"><div class="highlight"><pre><span></span><span class="gp">&gt;&gt;&gt; </span><span class="kn">from</span><span class="w"> </span><span class="nn">sklearn.cluster</span><span class="w"> </span><span class="kn">import</span> <span class="n">SpectralClustering</span>
<span class="gp">&gt;&gt;&gt; </span><span class="kn">import</span><span class="w"> </span><span class="nn">numpy</span><span class="w"> </span><span class="k">as</span><span class="w"> </span><span class="nn">np</span>
<span class="gp">&gt;&gt;&gt; </span><span class="n">X</span> <span class="o">=</span> <span class="n">np</span><span class="o">.</span><span class="n">array</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="mi">2</span><span class="p">,</span> <span class="mi">1</span><span class="p">],</span> <span class="p">[</span><span class="mi">1</span><span class="p">,</span> <span class="mi">0</span><span class="p">],</span>
<span class="gp">... </span>              <span class="p">[</span><span class="mi">4</span><span class="p">,</span> <span class="mi">7</span><span class="p">],</span> <span class="p">[</span><span class="mi">3</span><span class="p">,</span> <span class="mi">5</span><span class="p">],</span> <span class="p">[</span><span class="mi">3</span><span class="p">,</span> <span class="mi">6</span><span class="p">]])</span>
<span class="gp">&gt;&gt;&gt; </span><span class="n">clustering</span> <span class="o">=</span> <span class="n">SpectralClustering</span><span class="p">(</span><span class="n">n_clusters</span><span class="o">=</span><span class="mi">2</span><span class="p">,</span>
<span class="gp">... </span>        <span class="n">assign_labels</span><span class="o">=</span><span class="s1">&#39;discretize&#39;</span><span class="p">,</span>
<span class="gp">... </span>        <span class="n">random_state</span><span class="o">=</span><span class="mi">0</span><span class="p">)</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="gp">&gt;&gt;&gt; </span><span class="n">clustering</span><span class="o">.</span><span class="n">labels_</span>
<span class="go">array([1, 1, 1, 0, 0, 0])</span>
<span class="gp">&gt;&gt;&gt; </span><span class="n">clustering</span>
<span class="go">SpectralClustering(assign_labels=&#39;discretize&#39;, n_clusters=2,</span>
<span class="go">    random_state=0)</span>
</pre></div>
</div>
<p>For a comparison of Spectral clustering with other clustering algorithms, see
<a class="reference internal" href="../../auto_examples/cluster/plot_cluster_comparison.html#sphx-glr-auto-examples-cluster-plot-cluster-comparison-py"><span class="std std-ref">Comparing different clustering algorithms on toy datasets</span></a></p>
<dl class="py method">
<dt class="sig sig-object py" id="sklearn.cluster.SpectralClustering.fit">
<span class="sig-name descname"><span class="pre">fit</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="n"><span class="pre">y</span></span><span class="o"><span class="pre">=</span></span><span class="default_value"><span class="pre">None</span></span></em><span class="sig-paren">)</span><a class="reference external" href="https://github.com/scikit-learn/scikit-learn/blob/86d099ec1/sklearn/cluster/_spectral.py#L671"><span class="viewcode-link"><span class="pre">[source]</span></span></a><a class="headerlink" href="#sklearn.cluster.SpectralClustering.fit" title="Link to this definition">#</a></dt>
<dd><p>Perform spectral clustering from features, or affinity matrix.</p>
<dl class="field-list simple">
<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, sparse matrix} of shape (n_samples, n_features) or                 (n_samples, n_samples)</span></dt><dd><p>Training instances to cluster, similarities / affinities between
instances if <code class="docutils literal notranslate"><span class="pre">affinity='precomputed'</span></code>, or distances between
instances if <code class="docutils literal notranslate"><span class="pre">affinity='precomputed_nearest_neighbors</span></code>. If a
sparse matrix is provided in a format other than <code class="docutils literal notranslate"><span class="pre">csr_matrix</span></code>,
<code class="docutils literal notranslate"><span class="pre">csc_matrix</span></code>, or <code class="docutils literal notranslate"><span class="pre">coo_matrix</span></code>, it will be converted into a
sparse <code class="docutils literal notranslate"><span class="pre">csr_matrix</span></code>.</p>
</dd>
<dt><strong>y</strong><span class="classifier">Ignored</span></dt><dd><p>Not used, present here for API consistency by convention.</p>
</dd>
</dl>
</dd>
<dt class="field-even">Returns<span class="colon">:</span></dt>
<dd class="field-even"><dl class="simple">
<dt><strong>self</strong><span class="classifier">object</span></dt><dd><p>A fitted instance of the estimator.</p>
</dd>
</dl>
</dd>
</dl>
</dd></dl>

<dl class="py method">
<dt class="sig sig-object py" id="sklearn.cluster.SpectralClustering.fit_predict">
<span class="sig-name descname"><span class="pre">fit_predict</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="n"><span class="pre">y</span></span><span class="o"><span class="pre">=</span></span><span class="default_value"><span class="pre">None</span></span></em><span class="sig-paren">)</span><a class="reference external" href="https://github.com/scikit-learn/scikit-learn/blob/86d099ec1/sklearn/cluster/_spectral.py#L774"><span class="viewcode-link"><span class="pre">[source]</span></span></a><a class="headerlink" href="#sklearn.cluster.SpectralClustering.fit_predict" title="Link to this definition">#</a></dt>
<dd><p>Perform spectral clustering on <code class="docutils literal notranslate"><span class="pre">X</span></code> and return cluster labels.</p>
<dl class="field-list simple">
<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, sparse matrix} of shape (n_samples, n_features) or                 (n_samples, n_samples)</span></dt><dd><p>Training instances to cluster, similarities / affinities between
instances if <code class="docutils literal notranslate"><span class="pre">affinity='precomputed'</span></code>, or distances between
instances if <code class="docutils literal notranslate"><span class="pre">affinity='precomputed_nearest_neighbors</span></code>. If a
sparse matrix is provided in a format other than <code class="docutils literal notranslate"><span class="pre">csr_matrix</span></code>,
<code class="docutils literal notranslate"><span class="pre">csc_matrix</span></code>, or <code class="docutils literal notranslate"><span class="pre">coo_matrix</span></code>, it will be converted into a
sparse <code class="docutils literal notranslate"><span class="pre">csr_matrix</span></code>.</p>
</dd>
<dt><strong>y</strong><span class="classifier">Ignored</span></dt><dd><p>Not used, present here for API consistency by convention.</p>
</dd>
</dl>
</dd>
<dt class="field-even">Returns<span class="colon">:</span></dt>
<dd class="field-even"><dl class="simple">
<dt><strong>labels</strong><span class="classifier">ndarray of shape (n_samples,)</span></dt><dd><p>Cluster labels.</p>
</dd>
</dl>
</dd>
</dl>
</dd></dl>

<dl class="py method">
<dt class="sig sig-object py" id="sklearn.cluster.SpectralClustering.get_metadata_routing">
<span class="sig-name descname"><span class="pre">get_metadata_routing</span></span><span class="sig-paren">(</span><span class="sig-paren">)</span><a class="reference external" href="https://github.com/scikit-learn/scikit-learn/blob/86d099ec1/sklearn/utils/_metadata_requests.py#L1508"><span class="viewcode-link"><span class="pre">[source]</span></span></a><a class="headerlink" href="#sklearn.cluster.SpectralClustering.get_metadata_routing" title="Link to this definition">#</a></dt>
<dd><p>Get metadata routing of this object.</p>
<p>Please check <a class="reference internal" href="../../metadata_routing.html#metadata-routing"><span class="std std-ref">User Guide</span></a> on how the routing
mechanism works.</p>
<dl class="field-list simple">
<dt class="field-odd">Returns<span class="colon">:</span></dt>
<dd class="field-odd"><dl class="simple">
<dt><strong>routing</strong><span class="classifier">MetadataRequest</span></dt><dd><p>A <a class="reference internal" href="sklearn.utils.metadata_routing.MetadataRequest.html#sklearn.utils.metadata_routing.MetadataRequest" title="sklearn.utils.metadata_routing.MetadataRequest"><code class="xref py py-class docutils literal notranslate"><span class="pre">MetadataRequest</span></code></a> encapsulating
routing information.</p>
</dd>
</dl>
</dd>
</dl>
</dd></dl>

<dl class="py method">
<dt class="sig sig-object py" id="sklearn.cluster.SpectralClustering.get_params">
<span class="sig-name descname"><span class="pre">get_params</span></span><span class="sig-paren">(</span><em class="sig-param"><span class="n"><span class="pre">deep</span></span><span class="o"><span class="pre">=</span></span><span class="default_value"><span class="pre">True</span></span></em><span class="sig-paren">)</span><a class="reference external" href="https://github.com/scikit-learn/scikit-learn/blob/86d099ec1/sklearn/base.py#L228"><span class="viewcode-link"><span class="pre">[source]</span></span></a><a class="headerlink" href="#sklearn.cluster.SpectralClustering.get_params" title="Link to this definition">#</a></dt>
<dd><p>Get parameters for this estimator.</p>
<dl class="field-list simple">
<dt class="field-odd">Parameters<span class="colon">:</span></dt>
<dd class="field-odd"><dl class="simple">
<dt><strong>deep</strong><span class="classifier">bool, default=True</span></dt><dd><p>If True, will return the parameters for this estimator and
contained subobjects that are estimators.</p>
</dd>
</dl>
</dd>
<dt class="field-even">Returns<span class="colon">:</span></dt>
<dd class="field-even"><dl class="simple">
<dt><strong>params</strong><span class="classifier">dict</span></dt><dd><p>Parameter names mapped to their values.</p>
</dd>
</dl>
</dd>
</dl>
</dd></dl>

<dl class="py method">
<dt class="sig sig-object py" id="sklearn.cluster.SpectralClustering.set_params">
<span class="sig-name descname"><span class="pre">set_params</span></span><span class="sig-paren">(</span><em class="sig-param"><span class="o"><span class="pre">**</span></span><span class="n"><span class="pre">params</span></span></em><span class="sig-paren">)</span><a class="reference external" href="https://github.com/scikit-learn/scikit-learn/blob/86d099ec1/sklearn/base.py#L252"><span class="viewcode-link"><span class="pre">[source]</span></span></a><a class="headerlink" href="#sklearn.cluster.SpectralClustering.set_params" title="Link to this definition">#</a></dt>
<dd><p>Set the parameters of this estimator.</p>
<p>The method works on simple estimators as well as on nested objects
(such as <a class="reference internal" href="sklearn.pipeline.Pipeline.html#sklearn.pipeline.Pipeline" title="sklearn.pipeline.Pipeline"><code class="xref py py-class docutils literal notranslate"><span class="pre">Pipeline</span></code></a>). The latter have
parameters of the form <code class="docutils literal notranslate"><span class="pre">&lt;component&gt;__&lt;parameter&gt;</span></code> so that it’s
possible to update each component of a nested object.</p>
<dl class="field-list simple">
<dt class="field-odd">Parameters<span class="colon">:</span></dt>
<dd class="field-odd"><dl class="simple">
<dt><strong>**params</strong><span class="classifier">dict</span></dt><dd><p>Estimator parameters.</p>
</dd>
</dl>
</dd>
<dt class="field-even">Returns<span class="colon">:</span></dt>
<dd class="field-even"><dl class="simple">
<dt><strong>self</strong><span class="classifier">estimator instance</span></dt><dd><p>Estimator instance.</p>
</dd>
</dl>
</dd>
</dl>
</dd></dl>

</dd></dl>

<section id="gallery-examples">
<h2>Gallery examples<a class="headerlink" href="#gallery-examples" title="Link to this heading">#</a></h2>
<div class="sphx-glr-thumbnails"><div class="sphx-glr-thumbcontainer" tooltip="This example shows characteristics of different clustering algorithms on datasets that are &quot;interesting&quot; but still in 2D. With the exception of the last dataset, the parameters of each of these dataset-algorithm pairs has been tuned to produce good clustering results. Some algorithms are more sensitive to parameter values than others."><img alt="" src="../../_images/sphx_glr_plot_cluster_comparison_thumb.png" />
<p><a class="reference internal" href="../../auto_examples/cluster/plot_cluster_comparison.html#sphx-glr-auto-examples-cluster-plot-cluster-comparison-py"><span class="std std-ref">Comparing different clustering algorithms on toy datasets</span></a></p>
  <div class="sphx-glr-thumbnail-title">Comparing different clustering algorithms on toy datasets</div>
</div></div></section>
</section>


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<li class="toc-h2 nav-item toc-entry"><a class="reference internal nav-link" href="#sklearn.cluster.SpectralClustering"><code class="docutils literal notranslate"><span class="pre">SpectralClustering</span></code></a><ul class="nav section-nav flex-column visible">
<li class="toc-h3 nav-item toc-entry"><a class="reference internal nav-link" href="#sklearn.cluster.SpectralClustering.fit"><code class="docutils literal notranslate"><span class="pre">fit</span></code></a></li>
<li class="toc-h3 nav-item toc-entry"><a class="reference internal nav-link" href="#sklearn.cluster.SpectralClustering.fit_predict"><code class="docutils literal notranslate"><span class="pre">fit_predict</span></code></a></li>
<li class="toc-h3 nav-item toc-entry"><a class="reference internal nav-link" href="#sklearn.cluster.SpectralClustering.get_metadata_routing"><code class="docutils literal notranslate"><span class="pre">get_metadata_routing</span></code></a></li>
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