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<meta property="og:description" content="Clustering of unlabeled data can be performed with the module sklearn.cluster. Each clustering algorithm comes in two variants: a class, that implements the fit method to learn the clusters on trai..." />
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<li class="toctree-l1 has-children"><a class="reference internal" href="../supervised_learning.html">1. Supervised learning</a><details><summary><span class="toctree-toggle" role="presentation"><i class="fa-solid fa-chevron-down"></i></span></summary><ul>
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<li class="toctree-l2"><a class="reference internal" href="preprocessing_targets.html">6.9. Transforming the prediction target (<code class="docutils literal notranslate"><span class="pre">y</span></code>)</a></li>
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<li class="toctree-l2"><a class="reference internal" href="../datasets/toy_dataset.html">7.1. Toy datasets</a></li>
<li class="toctree-l2"><a class="reference internal" href="../datasets/real_world.html">7.2. Real world datasets</a></li>
<li class="toctree-l2"><a class="reference internal" href="../datasets/sample_generators.html">7.3. Generated datasets</a></li>
<li class="toctree-l2"><a class="reference internal" href="../datasets/loading_other_datasets.html">7.4. Loading other datasets</a></li>
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<li class="toctree-l2"><a class="reference internal" href="../computing/scaling_strategies.html">8.1. Strategies to scale computationally: bigger data</a></li>
<li class="toctree-l2"><a class="reference internal" href="../computing/computational_performance.html">8.2. Computational Performance</a></li>
<li class="toctree-l2"><a class="reference internal" href="../computing/parallelism.html">8.3. Parallelism, resource management, and configuration</a></li>
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</details></li>
<li class="toctree-l1"><a class="reference internal" href="../model_persistence.html">9. Model persistence</a></li>
<li class="toctree-l1"><a class="reference internal" href="../common_pitfalls.html">10. Common pitfalls and recommended practices</a></li>
<li class="toctree-l1 has-children"><a class="reference internal" href="../dispatching.html">11. Dispatching</a><details><summary><span class="toctree-toggle" role="presentation"><i class="fa-solid fa-chevron-down"></i></span></summary><ul>
<li class="toctree-l2"><a class="reference internal" href="array_api.html">11.1. Array API support (experimental)</a></li>
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</details></li>
<li class="toctree-l1"><a class="reference internal" href="../machine_learning_map.html">12. Choosing the right estimator</a></li>
<li class="toctree-l1"><a class="reference internal" href="../presentations.html">13. External Resources, Videos and Talks</a></li>
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<section id="clustering">
<span id="id1"></span><h1><span class="section-number">2.3. </span>Clustering<a class="headerlink" href="#clustering" title="Link to this heading">#</a></h1>
<p><a class="reference external" href="https://en.wikipedia.org/wiki/Cluster_analysis">Clustering</a> of
unlabeled data can be performed with the module <a class="reference internal" href="../api/sklearn.cluster.html#module-sklearn.cluster" title="sklearn.cluster"><code class="xref py py-mod docutils literal notranslate"><span class="pre">sklearn.cluster</span></code></a>.</p>
<p>Each clustering algorithm comes in two variants: a class, that implements
the <code class="docutils literal notranslate"><span class="pre">fit</span></code> 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 <code class="docutils literal notranslate"><span class="pre">labels_</span></code> attribute.</p>
<aside class="topic">
<p class="topic-title">Input data</p>
<p>One important thing to note is that the algorithms implemented in
this module can take different kinds of matrix as input. All the
methods accept standard data matrices of shape <code class="docutils literal notranslate"><span class="pre">(n_samples,</span> <span class="pre">n_features)</span></code>.
These can be obtained from the classes in the <a class="reference internal" href="../api/sklearn.feature_extraction.html#module-sklearn.feature_extraction" title="sklearn.feature_extraction"><code class="xref py py-mod docutils literal notranslate"><span class="pre">sklearn.feature_extraction</span></code></a>
module. For <a class="reference internal" href="generated/sklearn.cluster.AffinityPropagation.html#sklearn.cluster.AffinityPropagation" title="sklearn.cluster.AffinityPropagation"><code class="xref py py-class docutils literal notranslate"><span class="pre">AffinityPropagation</span></code></a>, <a class="reference internal" href="generated/sklearn.cluster.SpectralClustering.html#sklearn.cluster.SpectralClustering" title="sklearn.cluster.SpectralClustering"><code class="xref py py-class docutils literal notranslate"><span class="pre">SpectralClustering</span></code></a>
and <a class="reference internal" href="generated/sklearn.cluster.DBSCAN.html#sklearn.cluster.DBSCAN" title="sklearn.cluster.DBSCAN"><code class="xref py py-class docutils literal notranslate"><span class="pre">DBSCAN</span></code></a> one can also input similarity matrices of shape
<code class="docutils literal notranslate"><span class="pre">(n_samples,</span> <span class="pre">n_samples)</span></code>. These can be obtained from the functions
in the <a class="reference internal" href="../api/sklearn.metrics.html#module-sklearn.metrics.pairwise" title="sklearn.metrics.pairwise"><code class="xref py py-mod docutils literal notranslate"><span class="pre">sklearn.metrics.pairwise</span></code></a> module.</p>
</aside>
<section id="overview-of-clustering-methods">
<h2><span class="section-number">2.3.1. </span>Overview of clustering methods<a class="headerlink" href="#overview-of-clustering-methods" title="Link to this heading">#</a></h2>
<figure class="align-center" id="id24">
<a class="reference external image-reference" href="../auto_examples/cluster/plot_cluster_comparison.html"><img alt="../_images/sphx_glr_plot_cluster_comparison_001.png" src="../_images/sphx_glr_plot_cluster_comparison_001.png" style="width: 1050.0px; height: 650.0px;" />
</a>
<figcaption>
<p><span class="caption-text">A comparison of the clustering algorithms in scikit-learn</span><a class="headerlink" href="#id24" title="Link to this image">#</a></p>
</figcaption>
</figure>
<div class="pst-scrollable-table-container"><table class="table">
<colgroup>
<col style="width: 15.1%" />
<col style="width: 16.1%" />
<col style="width: 20.4%" />
<col style="width: 26.9%" />
<col style="width: 21.5%" />
</colgroup>
<thead>
<tr class="row-odd"><th class="head"><p>Method name</p></th>
<th class="head"><p>Parameters</p></th>
<th class="head"><p>Scalability</p></th>
<th class="head"><p>Usecase</p></th>
<th class="head"><p>Geometry (metric used)</p></th>
</tr>
</thead>
<tbody>
<tr class="row-even"><td><p><a class="reference internal" href="#k-means"><span class="std std-ref">K-Means</span></a></p></td>
<td><p>number of clusters</p></td>
<td><p>Very large <code class="docutils literal notranslate"><span class="pre">n_samples</span></code>, medium <code class="docutils literal notranslate"><span class="pre">n_clusters</span></code> with
<a class="reference internal" href="#mini-batch-kmeans"><span class="std std-ref">MiniBatch code</span></a></p></td>
<td><p>General-purpose, even cluster size, flat geometry,
not too many clusters, inductive</p></td>
<td><p>Distances between points</p></td>
</tr>
<tr class="row-odd"><td><p><a class="reference internal" href="#affinity-propagation"><span class="std std-ref">Affinity propagation</span></a></p></td>
<td><p>damping, sample preference</p></td>
<td><p>Not scalable with n_samples</p></td>
<td><p>Many clusters, uneven cluster size, non-flat geometry, inductive</p></td>
<td><p>Graph distance (e.g. nearest-neighbor graph)</p></td>
</tr>
<tr class="row-even"><td><p><a class="reference internal" href="#mean-shift"><span class="std std-ref">Mean-shift</span></a></p></td>
<td><p>bandwidth</p></td>
<td><p>Not scalable with <code class="docutils literal notranslate"><span class="pre">n_samples</span></code></p></td>
<td><p>Many clusters, uneven cluster size, non-flat geometry, inductive</p></td>
<td><p>Distances between points</p></td>
</tr>
<tr class="row-odd"><td><p><a class="reference internal" href="#spectral-clustering"><span class="std std-ref">Spectral clustering</span></a></p></td>
<td><p>number of clusters</p></td>
<td><p>Medium <code class="docutils literal notranslate"><span class="pre">n_samples</span></code>, small <code class="docutils literal notranslate"><span class="pre">n_clusters</span></code></p></td>
<td><p>Few clusters, even cluster size, non-flat geometry, transductive</p></td>
<td><p>Graph distance (e.g. nearest-neighbor graph)</p></td>
</tr>
<tr class="row-even"><td><p><a class="reference internal" href="#hierarchical-clustering"><span class="std std-ref">Ward hierarchical clustering</span></a></p></td>
<td><p>number of clusters or distance threshold</p></td>
<td><p>Large <code class="docutils literal notranslate"><span class="pre">n_samples</span></code> and <code class="docutils literal notranslate"><span class="pre">n_clusters</span></code></p></td>
<td><p>Many clusters, possibly connectivity constraints, transductive</p></td>
<td><p>Distances between points</p></td>
</tr>
<tr class="row-odd"><td><p><a class="reference internal" href="#hierarchical-clustering"><span class="std std-ref">Agglomerative clustering</span></a></p></td>
<td><p>number of clusters or distance threshold, linkage type, distance</p></td>
<td><p>Large <code class="docutils literal notranslate"><span class="pre">n_samples</span></code> and <code class="docutils literal notranslate"><span class="pre">n_clusters</span></code></p></td>
<td><p>Many clusters, possibly connectivity constraints, non Euclidean
distances, transductive</p></td>
<td><p>Any pairwise distance</p></td>
</tr>
<tr class="row-even"><td><p><a class="reference internal" href="#dbscan"><span class="std std-ref">DBSCAN</span></a></p></td>
<td><p>neighborhood size</p></td>
<td><p>Very large <code class="docutils literal notranslate"><span class="pre">n_samples</span></code>, medium <code class="docutils literal notranslate"><span class="pre">n_clusters</span></code></p></td>
<td><p>Non-flat geometry, uneven cluster sizes, outlier removal,
transductive</p></td>
<td><p>Distances between nearest points</p></td>
</tr>
<tr class="row-odd"><td><p><a class="reference internal" href="#hdbscan"><span class="std std-ref">HDBSCAN</span></a></p></td>
<td><p>minimum cluster membership, minimum point neighbors</p></td>
<td><p>large <code class="docutils literal notranslate"><span class="pre">n_samples</span></code>, medium <code class="docutils literal notranslate"><span class="pre">n_clusters</span></code></p></td>
<td><p>Non-flat geometry, uneven cluster sizes, outlier removal,
transductive, hierarchical, variable cluster density</p></td>
<td><p>Distances between nearest points</p></td>
</tr>
<tr class="row-even"><td><p><a class="reference internal" href="#optics"><span class="std std-ref">OPTICS</span></a></p></td>
<td><p>minimum cluster membership</p></td>
<td><p>Very large <code class="docutils literal notranslate"><span class="pre">n_samples</span></code>, large <code class="docutils literal notranslate"><span class="pre">n_clusters</span></code></p></td>
<td><p>Non-flat geometry, uneven cluster sizes, variable cluster density,
outlier removal, transductive</p></td>
<td><p>Distances between points</p></td>
</tr>
<tr class="row-odd"><td><p><a class="reference internal" href="mixture.html#mixture"><span class="std std-ref">Gaussian mixtures</span></a></p></td>
<td><p>many</p></td>
<td><p>Not scalable</p></td>
<td><p>Flat geometry, good for density estimation, inductive</p></td>
<td><p>Mahalanobis distances to centers</p></td>
</tr>
<tr class="row-even"><td><p><a class="reference internal" href="#birch"><span class="std std-ref">BIRCH</span></a></p></td>
<td><p>branching factor, threshold, optional global clusterer.</p></td>
<td><p>Large <code class="docutils literal notranslate"><span class="pre">n_clusters</span></code> and <code class="docutils literal notranslate"><span class="pre">n_samples</span></code></p></td>
<td><p>Large dataset, outlier removal, data reduction, inductive</p></td>
<td><p>Euclidean distance between points</p></td>
</tr>
<tr class="row-odd"><td><p><a class="reference internal" href="#bisect-k-means"><span class="std std-ref">Bisecting K-Means</span></a></p></td>
<td><p>number of clusters</p></td>
<td><p>Very large <code class="docutils literal notranslate"><span class="pre">n_samples</span></code>, medium <code class="docutils literal notranslate"><span class="pre">n_clusters</span></code></p></td>
<td><p>General-purpose, even cluster size, flat geometry,
no empty clusters, inductive, hierarchical</p></td>
<td><p>Distances between points</p></td>
</tr>
</tbody>
</table>
</div>
<p>Non-flat geometry clustering is useful when the clusters have a specific
shape, i.e. a non-flat manifold, and the standard euclidean distance is
not the right metric. This case arises in the two top rows of the figure
above.</p>
<p>Gaussian mixture models, useful for clustering, are described in
<a class="reference internal" href="mixture.html#mixture"><span class="std std-ref">another chapter of the documentation</span></a> dedicated to
mixture models. KMeans can be seen as a special case of Gaussian mixture
model with equal covariance per component.</p>
<p><a class="reference internal" href="../glossary.html#term-transductive"><span class="xref std std-term">Transductive</span></a> clustering methods (in contrast to
<a class="reference internal" href="../glossary.html#term-inductive"><span class="xref std std-term">inductive</span></a> clustering methods) are not designed to be applied to new,
unseen data.</p>
<p class="rubric">Examples</p>
<ul class="simple">
<li><p><a class="reference internal" href="../auto_examples/cluster/plot_inductive_clustering.html#sphx-glr-auto-examples-cluster-plot-inductive-clustering-py"><span class="std std-ref">Inductive Clustering</span></a>: An example
of an inductive clustering model for handling new data.</p></li>
</ul>
</section>
<section id="k-means">
<span id="id2"></span><h2><span class="section-number">2.3.2. </span>K-means<a class="headerlink" href="#k-means" title="Link to this heading">#</a></h2>
<p>The <a class="reference internal" href="generated/sklearn.cluster.KMeans.html#sklearn.cluster.KMeans" title="sklearn.cluster.KMeans"><code class="xref py py-class docutils literal notranslate"><span class="pre">KMeans</span></code></a> algorithm clusters data by trying to separate samples in n
groups of equal variance, minimizing a criterion known as the <em>inertia</em> or
within-cluster sum-of-squares (see below). This algorithm requires the number
of clusters to be specified. It scales well to large numbers of samples and has
been used across a large range of application areas in many different fields.</p>
<p>The k-means algorithm divides a set of <span class="math notranslate nohighlight">\(N\)</span> samples <span class="math notranslate nohighlight">\(X\)</span> into
<span class="math notranslate nohighlight">\(K\)</span> disjoint clusters <span class="math notranslate nohighlight">\(C\)</span>, each described by the mean <span class="math notranslate nohighlight">\(\mu_j\)</span>
of the samples in the cluster. The means are commonly called the cluster
“centroids”; note that they are not, in general, points from <span class="math notranslate nohighlight">\(X\)</span>,
although they live in the same space.</p>
<p>The K-means algorithm aims to choose centroids that minimise the <strong>inertia</strong>,
or <strong>within-cluster sum-of-squares criterion</strong>:</p>
<div class="math notranslate nohighlight">
\[\sum_{i=0}^{n}\min_{\mu_j \in C}(||x_i - \mu_j||^2)\]</div>
<p>Inertia can be recognized as a measure of how internally coherent clusters are.
It suffers from various drawbacks:</p>
<ul class="simple">
<li><p>Inertia makes the assumption that clusters are convex and isotropic,
which is not always the case. It responds poorly to elongated clusters,
or manifolds with irregular shapes.</p></li>
<li><p>Inertia is not a normalized metric: we just know that lower values are
better and zero is optimal. But in very high-dimensional spaces, Euclidean
distances tend to become inflated
(this is an instance of the so-called “curse of dimensionality”).
Running a dimensionality reduction algorithm such as <a class="reference internal" href="decomposition.html#pca"><span class="std std-ref">Principal component analysis (PCA)</span></a> prior to
k-means clustering can alleviate this problem and speed up the
computations.</p></li>
</ul>
<a class="reference external image-reference" href="../auto_examples/cluster/plot_kmeans_assumptions.html"><img alt="../_images/sphx_glr_plot_kmeans_assumptions_002.png" class="align-center" src="../_images/sphx_glr_plot_kmeans_assumptions_002.png" style="width: 600.0px; height: 600.0px;" />
</a>
<p>For more detailed descriptions of the issues shown above and how to address them,
refer to the examples <a class="reference internal" href="../auto_examples/cluster/plot_kmeans_assumptions.html#sphx-glr-auto-examples-cluster-plot-kmeans-assumptions-py"><span class="std std-ref">Demonstration of k-means assumptions</span></a>
and <a class="reference internal" href="../auto_examples/cluster/plot_kmeans_silhouette_analysis.html#sphx-glr-auto-examples-cluster-plot-kmeans-silhouette-analysis-py"><span class="std std-ref">Selecting the number of clusters with silhouette analysis on KMeans clustering</span></a>.</p>
<p>K-means is often referred to as Lloyd’s algorithm. In basic terms, the
algorithm has three steps. The first step chooses the initial centroids, with
the most basic method being to choose <span class="math notranslate nohighlight">\(k\)</span> samples from the dataset
<span class="math notranslate nohighlight">\(X\)</span>. After initialization, K-means consists of looping between the
two other steps. The first step assigns each sample to its nearest centroid.
The second step creates new centroids by taking the mean value of all of the
samples assigned to each previous centroid. The difference between the old
and the new centroids are computed and the algorithm repeats these last two
steps until this value is less than a threshold. In other words, it repeats
until the centroids do not move significantly.</p>
<a class="reference external image-reference" href="../auto_examples/cluster/plot_kmeans_digits.html"><img alt="../_images/sphx_glr_plot_kmeans_digits_001.png" class="align-right" src="../_images/sphx_glr_plot_kmeans_digits_001.png" style="width: 224.0px; height: 168.0px;" />
</a>
<p>K-means is equivalent to the expectation-maximization algorithm
with a small, all-equal, diagonal covariance matrix.</p>
<p>The algorithm can also be understood through the concept of <a class="reference external" href="https://en.wikipedia.org/wiki/Voronoi_diagram">Voronoi diagrams</a>. First the Voronoi diagram of
the points is calculated using the current centroids. Each segment in the
Voronoi diagram becomes a separate cluster. Secondly, the centroids are updated
to the mean of each segment. The algorithm then repeats this until a stopping
criterion is fulfilled. Usually, the algorithm stops when the relative decrease
in the objective function between iterations is less than the given tolerance
value. This is not the case in this implementation: iteration stops when
centroids move less than the tolerance.</p>
<p>Given enough time, K-means will always converge, however this may be to a local
minimum. This is highly dependent on the initialization of the centroids.
As a result, the computation is often done several times, with different
initializations of the centroids. One method to help address this issue is the
k-means++ initialization scheme, which has been implemented in scikit-learn
(use the <code class="docutils literal notranslate"><span class="pre">init='k-means++'</span></code> parameter). This initializes the centroids to be
(generally) distant from each other, leading to probably better results than
random initialization, as shown in the reference. For detailed examples of
comparing different initialization schemes, refer to
<a class="reference internal" href="../auto_examples/cluster/plot_kmeans_digits.html#sphx-glr-auto-examples-cluster-plot-kmeans-digits-py"><span class="std std-ref">A demo of K-Means clustering on the handwritten digits data</span></a> and
<a class="reference internal" href="../auto_examples/cluster/plot_kmeans_stability_low_dim_dense.html#sphx-glr-auto-examples-cluster-plot-kmeans-stability-low-dim-dense-py"><span class="std std-ref">Empirical evaluation of the impact of k-means initialization</span></a>.</p>
<p>K-means++ can also be called independently to select seeds for other
clustering algorithms, see <a class="reference internal" href="generated/sklearn.cluster.kmeans_plusplus.html#sklearn.cluster.kmeans_plusplus" title="sklearn.cluster.kmeans_plusplus"><code class="xref py py-func docutils literal notranslate"><span class="pre">sklearn.cluster.kmeans_plusplus</span></code></a> for details
and example usage.</p>
<p>The algorithm supports sample weights, which can be given by a parameter
<code class="docutils literal notranslate"><span class="pre">sample_weight</span></code>. This allows to assign more weight to some samples when
computing cluster centers and values of inertia. For example, assigning a
weight of 2 to a sample is equivalent to adding a duplicate of that sample
to the dataset <span class="math notranslate nohighlight">\(X\)</span>.</p>
<p class="rubric">Examples</p>
<ul class="simple">
<li><p><a class="reference internal" href="../auto_examples/text/plot_document_clustering.html#sphx-glr-auto-examples-text-plot-document-clustering-py"><span class="std std-ref">Clustering text documents using k-means</span></a>: Document clustering
using <a class="reference internal" href="generated/sklearn.cluster.KMeans.html#sklearn.cluster.KMeans" title="sklearn.cluster.KMeans"><code class="xref py py-class docutils literal notranslate"><span class="pre">KMeans</span></code></a> and <a class="reference internal" href="generated/sklearn.cluster.MiniBatchKMeans.html#sklearn.cluster.MiniBatchKMeans" title="sklearn.cluster.MiniBatchKMeans"><code class="xref py py-class docutils literal notranslate"><span class="pre">MiniBatchKMeans</span></code></a> based on sparse data</p></li>
<li><p><a class="reference internal" href="../auto_examples/cluster/plot_kmeans_plusplus.html#sphx-glr-auto-examples-cluster-plot-kmeans-plusplus-py"><span class="std std-ref">An example of K-Means++ initialization</span></a>: Using K-means++
to select seeds for other clustering algorithms.</p></li>
</ul>
<section id="low-level-parallelism">
<h3><span class="section-number">2.3.2.1. </span>Low-level parallelism<a class="headerlink" href="#low-level-parallelism" title="Link to this heading">#</a></h3>
<p><a class="reference internal" href="generated/sklearn.cluster.KMeans.html#sklearn.cluster.KMeans" title="sklearn.cluster.KMeans"><code class="xref py py-class docutils literal notranslate"><span class="pre">KMeans</span></code></a> benefits from OpenMP based parallelism through Cython. Small
chunks of data (256 samples) are processed in parallel, which in addition
yields a low memory footprint. For more details on how to control the number of
threads, please refer to our <a class="reference internal" href="../computing/parallelism.html#parallelism"><span class="std std-ref">Parallelism</span></a> notes.</p>
<p class="rubric">Examples</p>
<ul class="simple">
<li><p><a class="reference internal" href="../auto_examples/cluster/plot_kmeans_assumptions.html#sphx-glr-auto-examples-cluster-plot-kmeans-assumptions-py"><span class="std std-ref">Demonstration of k-means assumptions</span></a>: Demonstrating when
k-means performs intuitively and when it does not</p></li>
<li><p><a class="reference internal" href="../auto_examples/cluster/plot_kmeans_digits.html#sphx-glr-auto-examples-cluster-plot-kmeans-digits-py"><span class="std std-ref">A demo of K-Means clustering on the handwritten digits data</span></a>: Clustering handwritten digits</p></li>
</ul>
<details class="sd-sphinx-override sd-dropdown sd-card sd-mb-3" id="references">
<summary class="sd-summary-title sd-card-header">
<span class="sd-summary-text">References<a class="headerlink" href="#references" title="Link to this dropdown">#</a></span><span class="sd-summary-state-marker sd-summary-chevron-right"><svg version="1.1" width="1.5em" height="1.5em" class="sd-octicon sd-octicon-chevron-right" viewBox="0 0 24 24" aria-hidden="true"><path d="M8.72 18.78a.75.75 0 0 1 0-1.06L14.44 12 8.72 6.28a.751.751 0 0 1 .018-1.042.751.751 0 0 1 1.042-.018l6.25 6.25a.75.75 0 0 1 0 1.06l-6.25 6.25a.75.75 0 0 1-1.06 0Z"></path></svg></span></summary><div class="sd-summary-content sd-card-body docutils">
<ul class="simple">
<li><p class="sd-card-text"><a class="reference external" href="http://ilpubs.stanford.edu:8090/778/1/2006-13.pdf">“k-means++: The advantages of careful seeding”</a>
Arthur, David, and Sergei Vassilvitskii,
<em>Proceedings of the eighteenth annual ACM-SIAM symposium on Discrete
algorithms</em>, Society for Industrial and Applied Mathematics (2007)</p></li>
</ul>
</div>
</details></section>
<section id="mini-batch-k-means">
<span id="mini-batch-kmeans"></span><h3><span class="section-number">2.3.2.2. </span>Mini Batch K-Means<a class="headerlink" href="#mini-batch-k-means" title="Link to this heading">#</a></h3>
<p>The <a class="reference internal" href="generated/sklearn.cluster.MiniBatchKMeans.html#sklearn.cluster.MiniBatchKMeans" title="sklearn.cluster.MiniBatchKMeans"><code class="xref py py-class docutils literal notranslate"><span class="pre">MiniBatchKMeans</span></code></a> is a variant of the <a class="reference internal" href="generated/sklearn.cluster.KMeans.html#sklearn.cluster.KMeans" title="sklearn.cluster.KMeans"><code class="xref py py-class docutils literal notranslate"><span class="pre">KMeans</span></code></a> algorithm
which uses mini-batches to reduce the computation time, while still attempting
to optimise the same objective function. Mini-batches are subsets of the input
data, randomly sampled in each training iteration. These mini-batches
drastically reduce the amount of computation required to converge to a local
solution. In contrast to other algorithms that reduce the convergence time of
k-means, mini-batch k-means produces results that are generally only slightly
worse than the standard algorithm.</p>
<p>The algorithm iterates between two major steps, similar to vanilla k-means.
In the first step, <span class="math notranslate nohighlight">\(b\)</span> samples are drawn randomly from the dataset, to form
a mini-batch. These are then assigned to the nearest centroid. In the second
step, the centroids are updated. In contrast to k-means, this is done on a
per-sample basis. For each sample in the mini-batch, the assigned centroid
is updated by taking the streaming average of the sample and all previous
samples assigned to that centroid. This has the effect of decreasing the
rate of change for a centroid over time. These steps are performed until
convergence or a predetermined number of iterations is reached.</p>
<p><a class="reference internal" href="generated/sklearn.cluster.MiniBatchKMeans.html#sklearn.cluster.MiniBatchKMeans" title="sklearn.cluster.MiniBatchKMeans"><code class="xref py py-class docutils literal notranslate"><span class="pre">MiniBatchKMeans</span></code></a> converges faster than <a class="reference internal" href="generated/sklearn.cluster.KMeans.html#sklearn.cluster.KMeans" title="sklearn.cluster.KMeans"><code class="xref py py-class docutils literal notranslate"><span class="pre">KMeans</span></code></a>, but the quality
of the results is reduced. In practice this difference in quality can be quite
small, as shown in the example and cited reference.</p>
<figure class="align-center">
<a class="reference external image-reference" href="../auto_examples/cluster/plot_mini_batch_kmeans.html"><img alt="../_images/sphx_glr_plot_mini_batch_kmeans_001.png" src="../_images/sphx_glr_plot_mini_batch_kmeans_001.png" style="width: 800.0px; height: 300.0px;" />
</a>
</figure>
<p class="rubric">Examples</p>
<ul class="simple">
<li><p><a class="reference internal" href="../auto_examples/cluster/plot_mini_batch_kmeans.html#sphx-glr-auto-examples-cluster-plot-mini-batch-kmeans-py"><span class="std std-ref">Comparison of the K-Means and MiniBatchKMeans clustering algorithms</span></a>: Comparison of
<a class="reference internal" href="generated/sklearn.cluster.KMeans.html#sklearn.cluster.KMeans" title="sklearn.cluster.KMeans"><code class="xref py py-class docutils literal notranslate"><span class="pre">KMeans</span></code></a> and <a class="reference internal" href="generated/sklearn.cluster.MiniBatchKMeans.html#sklearn.cluster.MiniBatchKMeans" title="sklearn.cluster.MiniBatchKMeans"><code class="xref py py-class docutils literal notranslate"><span class="pre">MiniBatchKMeans</span></code></a></p></li>
<li><p><a class="reference internal" href="../auto_examples/text/plot_document_clustering.html#sphx-glr-auto-examples-text-plot-document-clustering-py"><span class="std std-ref">Clustering text documents using k-means</span></a>: Document clustering
using <a class="reference internal" href="generated/sklearn.cluster.KMeans.html#sklearn.cluster.KMeans" title="sklearn.cluster.KMeans"><code class="xref py py-class docutils literal notranslate"><span class="pre">KMeans</span></code></a> and <a class="reference internal" href="generated/sklearn.cluster.MiniBatchKMeans.html#sklearn.cluster.MiniBatchKMeans" title="sklearn.cluster.MiniBatchKMeans"><code class="xref py py-class docutils literal notranslate"><span class="pre">MiniBatchKMeans</span></code></a> based on sparse data</p></li>
<li><p><a class="reference internal" href="../auto_examples/cluster/plot_dict_face_patches.html#sphx-glr-auto-examples-cluster-plot-dict-face-patches-py"><span class="std std-ref">Online learning of a dictionary of parts of faces</span></a></p></li>
</ul>
<details class="sd-sphinx-override sd-dropdown sd-card sd-mb-3" id="references-2">
<summary class="sd-summary-title sd-card-header">
<span class="sd-summary-text">References<a class="headerlink" href="#references-2" title="Link to this dropdown">#</a></span><span class="sd-summary-state-marker sd-summary-chevron-right"><svg version="1.1" width="1.5em" height="1.5em" class="sd-octicon sd-octicon-chevron-right" viewBox="0 0 24 24" aria-hidden="true"><path d="M8.72 18.78a.75.75 0 0 1 0-1.06L14.44 12 8.72 6.28a.751.751 0 0 1 .018-1.042.751.751 0 0 1 1.042-.018l6.25 6.25a.75.75 0 0 1 0 1.06l-6.25 6.25a.75.75 0 0 1-1.06 0Z"></path></svg></span></summary><div class="sd-summary-content sd-card-body docutils">
<ul class="simple">
<li><p class="sd-card-text"><a class="reference external" href="https://www.eecs.tufts.edu/~dsculley/papers/fastkmeans.pdf">“Web Scale K-Means clustering”</a>
D. Sculley, <em>Proceedings of the 19th international conference on World
wide web</em> (2010)</p></li>
</ul>
</div>
</details></section>
</section>
<section id="affinity-propagation">
<span id="id3"></span><h2><span class="section-number">2.3.3. </span>Affinity Propagation<a class="headerlink" href="#affinity-propagation" title="Link to this heading">#</a></h2>
<p><a class="reference internal" href="generated/sklearn.cluster.AffinityPropagation.html#sklearn.cluster.AffinityPropagation" title="sklearn.cluster.AffinityPropagation"><code class="xref py py-class docutils literal notranslate"><span class="pre">AffinityPropagation</span></code></a> creates clusters by sending messages between
pairs of samples until convergence. A dataset is then described using a small
number of exemplars, which are identified as those most representative of other
samples. The messages sent between pairs represent the suitability for one
sample to be the exemplar of the other, which is updated in response to the
values from other pairs. This updating happens iteratively until convergence,
at which point the final exemplars are chosen, and hence the final clustering
is given.</p>
<figure class="align-center">
<a class="reference external image-reference" href="../auto_examples/cluster/plot_affinity_propagation.html"><img alt="../_images/sphx_glr_plot_affinity_propagation_001.png" src="../_images/sphx_glr_plot_affinity_propagation_001.png" style="width: 320.0px; height: 240.0px;" />
</a>