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<section id="k-means">
<h1>k_means<a class="headerlink" href="#k-means" title="Link to this heading">#</a></h1>
<dl class="py function">
<dt class="sig sig-object py" id="sklearn.cluster.k_means">
<span class="sig-prename descclassname"><span class="pre">sklearn.cluster.</span></span><span class="sig-name descname"><span class="pre">k_means</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">n_clusters</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">sample_weight</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">init</span></span><span class="o"><span class="pre">=</span></span><span class="default_value"><span class="pre">'k-means++'</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">'auto'</span></span></em>, <em class="sig-param"><span class="n"><span class="pre">max_iter</span></span><span class="o"><span class="pre">=</span></span><span class="default_value"><span class="pre">300</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>, <em class="sig-param"><span class="n"><span class="pre">tol</span></span><span class="o"><span class="pre">=</span></span><span class="default_value"><span class="pre">0.0001</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">copy_x</span></span><span class="o"><span class="pre">=</span></span><span class="default_value"><span class="pre">True</span></span></em>, <em class="sig-param"><span class="n"><span class="pre">algorithm</span></span><span class="o"><span class="pre">=</span></span><span class="default_value"><span class="pre">'lloyd'</span></span></em>, <em class="sig-param"><span class="n"><span class="pre">return_n_iter</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/4ee3afa55/sklearn/cluster/_kmeans.py#L290"><span class="viewcode-link"><span class="pre">[source]</span></span></a><a class="headerlink" href="#sklearn.cluster.k_means" title="Link to this definition">#</a></dt>
<dd><p>Perform K-means clustering algorithm.</p>
<p>Read more in the <a class="reference internal" href="../clustering.html#k-means"><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>X</strong><span class="classifier">{array-like, sparse matrix} of shape (n_samples, n_features)</span></dt><dd><p>The observations to cluster. It must be noted that the data
will be converted to C ordering, which will cause a memory copy
if the given data is not C-contiguous.</p>
</dd>
<dt><strong>n_clusters</strong><span class="classifier">int</span></dt><dd><p>The number of clusters to form as well as the number of
centroids to generate.</p>
</dd>
<dt><strong>sample_weight</strong><span class="classifier">array-like of shape (n_samples,), default=None</span></dt><dd><p>The weights for each observation in <code class="docutils literal notranslate"><span class="pre">X</span></code>. If <code class="docutils literal notranslate"><span class="pre">None</span></code>, all observations
are assigned equal weight. <code class="docutils literal notranslate"><span class="pre">sample_weight</span></code> is not used during
initialization if <code class="docutils literal notranslate"><span class="pre">init</span></code> is a callable or a user provided array.</p>
</dd>
<dt><strong>init</strong><span class="classifier">{‘k-means++’, ‘random’}, callable or array-like of shape (n_clusters, n_features), default=’k-means++’</span></dt><dd><p>Method for initialization:</p>
<ul class="simple">
<li><p><code class="docutils literal notranslate"><span class="pre">'k-means++'</span></code> : selects initial cluster centers for k-mean
clustering in a smart way to speed up convergence. See section
Notes in k_init for more details.</p></li>
<li><p><code class="docutils literal notranslate"><span class="pre">'random'</span></code>: choose <code class="docutils literal notranslate"><span class="pre">n_clusters</span></code> observations (rows) at random from data
for the initial centroids.</p></li>
<li><p>If an array is passed, it should be of shape <code class="docutils literal notranslate"><span class="pre">(n_clusters,</span> <span class="pre">n_features)</span></code>
and gives the initial centers.</p></li>
<li><p>If a callable is passed, it should take arguments <code class="docutils literal notranslate"><span class="pre">X</span></code>, <code class="docutils literal notranslate"><span class="pre">n_clusters</span></code> and a
random state and return an initialization.</p></li>
</ul>
</dd>
<dt><strong>n_init</strong><span class="classifier">‘auto’ or int, default=”auto”</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.</p>
<p>When <code class="docutils literal notranslate"><span class="pre">n_init='auto'</span></code>, the number of runs depends on the value of init:
10 if using <code class="docutils literal notranslate"><span class="pre">init='random'</span></code> or <code class="docutils literal notranslate"><span class="pre">init</span></code> is a callable;
1 if using <code class="docutils literal notranslate"><span class="pre">init='k-means++'</span></code> or <code class="docutils literal notranslate"><span class="pre">init</span></code> is an array-like.</p>
<div class="versionadded">
<p><span class="versionmodified added">Added in version 1.2: </span>Added ‘auto’ option for <code class="docutils literal notranslate"><span class="pre">n_init</span></code>.</p>
</div>
<div class="versionchanged">
<p><span class="versionmodified changed">Changed in version 1.4: </span>Default value for <code class="docutils literal notranslate"><span class="pre">n_init</span></code> changed to <code class="docutils literal notranslate"><span class="pre">'auto'</span></code>.</p>
</div>
</dd>
<dt><strong>max_iter</strong><span class="classifier">int, default=300</span></dt><dd><p>Maximum number of iterations of the k-means algorithm to run.</p>
</dd>
<dt><strong>verbose</strong><span class="classifier">bool, default=False</span></dt><dd><p>Verbosity mode.</p>
</dd>
<dt><strong>tol</strong><span class="classifier">float, default=1e-4</span></dt><dd><p>Relative tolerance with regards to Frobenius norm of the difference
in the cluster centers of two consecutive iterations to declare
convergence.</p>
</dd>
<dt><strong>random_state</strong><span class="classifier">int, RandomState instance or None, default=None</span></dt><dd><p>Determines random number generation for centroid initialization. Use
an int to make the randomness deterministic.
See <a class="reference internal" href="../../glossary.html#term-random_state"><span class="xref std std-term">Glossary</span></a>.</p>
</dd>
<dt><strong>copy_x</strong><span class="classifier">bool, default=True</span></dt><dd><p>When pre-computing distances it is more numerically accurate to center
the data first. If <code class="docutils literal notranslate"><span class="pre">copy_x</span></code> is True (default), then the original data is
not modified. If False, the original data is modified, and put back
before the function returns, but small numerical differences may be
introduced by subtracting and then adding the data mean. Note that if
the original data is not C-contiguous, a copy will be made even if
<code class="docutils literal notranslate"><span class="pre">copy_x</span></code> is False. If the original data is sparse, but not in CSR format,
a copy will be made even if <code class="docutils literal notranslate"><span class="pre">copy_x</span></code> is False.</p>
</dd>
<dt><strong>algorithm</strong><span class="classifier">{“lloyd”, “elkan”}, default=”lloyd”</span></dt><dd><p>K-means algorithm to use. The classical EM-style algorithm is <code class="docutils literal notranslate"><span class="pre">"lloyd"</span></code>.
The <code class="docutils literal notranslate"><span class="pre">"elkan"</span></code> variation can be more efficient on some datasets with
well-defined clusters, by using the triangle inequality. However it’s
more memory intensive due to the allocation of an extra array of shape
<code class="docutils literal notranslate"><span class="pre">(n_samples,</span> <span class="pre">n_clusters)</span></code>.</p>
<div class="versionchanged">
<p><span class="versionmodified changed">Changed in version 0.18: </span>Added Elkan algorithm</p>
</div>
<div class="versionchanged">
<p><span class="versionmodified changed">Changed in version 1.1: </span>Renamed “full” to “lloyd”, and deprecated “auto” and “full”.
Changed “auto” to use “lloyd” instead of “elkan”.</p>
</div>
</dd>
<dt><strong>return_n_iter</strong><span class="classifier">bool, default=False</span></dt><dd><p>Whether or not to return the number of iterations.</p>
</dd>
</dl>
</dd>
<dt class="field-even">Returns<span class="colon">:</span></dt>
<dd class="field-even"><dl class="simple">
<dt><strong>centroid</strong><span class="classifier">ndarray of shape (n_clusters, n_features)</span></dt><dd><p>Centroids found at the last iteration of k-means.</p>
</dd>
<dt><strong>label</strong><span class="classifier">ndarray of shape (n_samples,)</span></dt><dd><p>The <code class="docutils literal notranslate"><span class="pre">label[i]</span></code> is the code or index of the centroid the
i’th observation is closest to.</p>
</dd>
<dt><strong>inertia</strong><span class="classifier">float</span></dt><dd><p>The final value of the inertia criterion (sum of squared distances to
the closest centroid for all observations in the training set).</p>
</dd>
<dt><strong>best_n_iter</strong><span class="classifier">int</span></dt><dd><p>Number of iterations corresponding to the best results.
Returned only if <code class="docutils literal notranslate"><span class="pre">return_n_iter</span></code> is set to True.</p>
</dd>
</dl>
</dd>
</dl>
<p class="rubric">Examples</p>
<div class="doctest highlight-default notranslate"><div class="highlight"><pre><span></span><span class="gp">>>> </span><span class="kn">import</span> <span class="nn">numpy</span> <span class="k">as</span> <span class="nn">np</span>
<span class="gp">>>> </span><span class="kn">from</span> <span class="nn">sklearn.cluster</span> <span class="kn">import</span> <span class="n">k_means</span>
<span class="gp">>>> </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">2</span><span class="p">],</span> <span class="p">[</span><span class="mi">1</span><span class="p">,</span> <span class="mi">4</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">10</span><span class="p">,</span> <span class="mi">2</span><span class="p">],</span> <span class="p">[</span><span class="mi">10</span><span class="p">,</span> <span class="mi">4</span><span class="p">],</span> <span class="p">[</span><span class="mi">10</span><span class="p">,</span> <span class="mi">0</span><span class="p">]])</span>
<span class="gp">>>> </span><span class="n">centroid</span><span class="p">,</span> <span class="n">label</span><span class="p">,</span> <span class="n">inertia</span> <span class="o">=</span> <span class="n">k_means</span><span class="p">(</span>
<span class="gp">... </span> <span class="n">X</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="n">n_init</span><span class="o">=</span><span class="s2">"auto"</span><span class="p">,</span> <span class="n">random_state</span><span class="o">=</span><span class="mi">0</span>
<span class="gp">... </span><span class="p">)</span>
<span class="gp">>>> </span><span class="n">centroid</span>
<span class="go">array([[10., 2.],</span>
<span class="go"> [ 1., 2.]])</span>
<span class="gp">>>> </span><span class="n">label</span>
<span class="go">array([1, 1, 1, 0, 0, 0], dtype=int32)</span>
<span class="gp">>>> </span><span class="n">inertia</span>
<span class="go">16.0</span>
</pre></div>
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