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                         <h1 class="title">Clustering</h1>


                     <p>This page describes clustering algorithms in MLlib.
 The <a href="mllib-clustering.html">guide for clustering in the RDD-based API</a> also has relevant information
 about these algorithms.</p>

 <p><strong>Table of Contents</strong></p>

 <ul id="markdown-toc">
   <li><a href="#k-means" id="markdown-toc-k-means">K-means</a>    <ul>
       <li><a href="#input-columns" id="markdown-toc-input-columns">Input Columns</a></li>
       <li><a href="#output-columns" id="markdown-toc-output-columns">Output Columns</a></li>
     </ul>
   </li>
   <li><a href="#latent-dirichlet-allocation-lda" id="markdown-toc-latent-dirichlet-allocation-lda">Latent Dirichlet allocation (LDA)</a></li>
   <li><a href="#bisecting-k-means" id="markdown-toc-bisecting-k-means">Bisecting k-means</a></li>
   <li><a href="#gaussian-mixture-model-gmm" id="markdown-toc-gaussian-mixture-model-gmm">Gaussian Mixture Model (GMM)</a>    <ul>
       <li><a href="#input-columns-1" id="markdown-toc-input-columns-1">Input Columns</a></li>
       <li><a href="#output-columns-1" id="markdown-toc-output-columns-1">Output Columns</a></li>
     </ul>
   </li>
 </ul>

 <h2 id="k-means">K-means</h2>

 <p><a href="http://en.wikipedia.org/wiki/K-means_clustering">k-means</a> is one of the
 most commonly used clustering algorithms that clusters the data points into a
 predefined number of clusters. The MLlib implementation includes a parallelized
 variant of the <a href="http://en.wikipedia.org/wiki/K-means%2B%2B">k-means++</a> method
 called <a href="http://theory.stanford.edu/~sergei/papers/vldb12-kmpar.pdf">kmeans||</a>.</p>

 <p><code>KMeans</code> is implemented as an <code>Estimator</code> and generates a <code>KMeansModel</code> as the base model.</p>

 <h3 id="input-columns">Input Columns</h3>

 <table class="table">
   <thead>
     <tr>
       <th align="left">Param name</th>
       <th align="left">Type(s)</th>
       <th align="left">Default</th>
       <th align="left">Description</th>
     </tr>
   </thead>
   <tbody>
     <tr>
       <td>featuresCol</td>
       <td>Vector</td>
       <td>"features"</td>
       <td>Feature vector</td>
     </tr>
   </tbody>
 </table>

 <h3 id="output-columns">Output Columns</h3>

 <table class="table">
   <thead>
     <tr>
       <th align="left">Param name</th>
       <th align="left">Type(s)</th>
       <th align="left">Default</th>
       <th align="left">Description</th>
     </tr>
   </thead>
   <tbody>
     <tr>
       <td>predictionCol</td>
       <td>Int</td>
       <td>"prediction"</td>
       <td>Predicted cluster center</td>
     </tr>
   </tbody>
 </table>

 <p><strong>Examples</strong></p>

 <div class="codetabs">

 <div data-lang="scala">
     <p>Refer to the <a href="api/scala/index.html#org.apache.spark.ml.clustering.KMeans">Scala API docs</a> for more details.</p>

     <div class="highlight"><pre><span></span><span class="k">import</span> <span class="nn">org.apache.spark.ml.clustering.KMeans</span>
 <span class="k">import</span> <span class="nn">org.apache.spark.ml.evaluation.ClusteringEvaluator</span>

 <span class="c1">// Loads data.</span>
 <span class="k">val</span> <span class="n">dataset</span> <span class="k">=</span> <span class="n">spark</span><span class="o">.</span><span class="n">read</span><span class="o">.</span><span class="n">format</span><span class="o">(</span><span class="s">&quot;libsvm&quot;</span><span class="o">).</span><span class="n">load</span><span class="o">(</span><span class="s">&quot;data/mllib/sample_kmeans_data.txt&quot;</span><span class="o">)</span>

 <span class="c1">// Trains a k-means model.</span>
 <span class="k">val</span> <span class="n">kmeans</span> <span class="k">=</span> <span class="k">new</span> <span class="nc">KMeans</span><span class="o">().</span><span class="n">setK</span><span class="o">(</span><span class="mi">2</span><span class="o">).</span><span class="n">setSeed</span><span class="o">(</span><span class="mi">1L</span><span class="o">)</span>
 <span class="k">val</span> <span class="n">model</span> <span class="k">=</span> <span class="n">kmeans</span><span class="o">.</span><span class="n">fit</span><span class="o">(</span><span class="n">dataset</span><span class="o">)</span>

 <span class="c1">// Make predictions</span>
 <span class="k">val</span> <span class="n">predictions</span> <span class="k">=</span> <span class="n">model</span><span class="o">.</span><span class="n">transform</span><span class="o">(</span><span class="n">dataset</span><span class="o">)</span>

 <span class="c1">// Evaluate clustering by computing Silhouette score</span>
 <span class="k">val</span> <span class="n">evaluator</span> <span class="k">=</span> <span class="k">new</span> <span class="nc">ClusteringEvaluator</span><span class="o">()</span>

 <span class="k">val</span> <span class="n">silhouette</span> <span class="k">=</span> <span class="n">evaluator</span><span class="o">.</span><span class="n">evaluate</span><span class="o">(</span><span class="n">predictions</span><span class="o">)</span>
 <span class="n">println</span><span class="o">(</span><span class="s">s&quot;Silhouette with squared euclidean distance = </span><span class="si">$silhouette</span><span class="s">&quot;</span><span class="o">)</span>

 <span class="c1">// Shows the result.</span>
 <span class="n">println</span><span class="o">(</span><span class="s">&quot;Cluster Centers: &quot;</span><span class="o">)</span>
 <span class="n">model</span><span class="o">.</span><span class="n">clusterCenters</span><span class="o">.</span><span class="n">foreach</span><span class="o">(</span><span class="n">println</span><span class="o">)</span>
 </pre></div>
     <div><small>Find full example code at "examples/src/main/scala/org/apache/spark/examples/ml/KMeansExample.scala" in the Spark repo.</small></div>
   </div>

 <div data-lang="java">
     <p>Refer to the <a href="api/java/org/apache/spark/ml/clustering/KMeans.html">Java API docs</a> for more details.</p>

     <div class="highlight"><pre><span></span><span class="kn">import</span> <span class="nn">org.apache.spark.ml.clustering.KMeansModel</span><span class="o">;</span>
 <span class="kn">import</span> <span class="nn">org.apache.spark.ml.clustering.KMeans</span><span class="o">;</span>
 <span class="kn">import</span> <span class="nn">org.apache.spark.ml.evaluation.ClusteringEvaluator</span><span class="o">;</span>
 <span class="kn">import</span> <span class="nn">org.apache.spark.ml.linalg.Vector</span><span class="o">;</span>
 <span class="kn">import</span> <span class="nn">org.apache.spark.sql.Dataset</span><span class="o">;</span>
 <span class="kn">import</span> <span class="nn">org.apache.spark.sql.Row</span><span class="o">;</span>

 <span class="c1">// Loads data.</span>
 <span class="n">Dataset</span><span class="o">&lt;</span><span class="n">Row</span><span class="o">&gt;</span> <span class="n">dataset</span> <span class="o">=</span> <span class="n">spark</span><span class="o">.</span><span class="na">read</span><span class="o">().</span><span class="na">format</span><span class="o">(</span><span class="s">&quot;libsvm&quot;</span><span class="o">).</span><span class="na">load</span><span class="o">(</span><span class="s">&quot;data/mllib/sample_kmeans_data.txt&quot;</span><span class="o">);</span>

 <span class="c1">// Trains a k-means model.</span>
 <span class="n">KMeans</span> <span class="n">kmeans</span> <span class="o">=</span> <span class="k">new</span> <span class="n">KMeans</span><span class="o">().</span><span class="na">setK</span><span class="o">(</span><span class="mi">2</span><span class="o">).</span><span class="na">setSeed</span><span class="o">(</span><span class="mi">1L</span><span class="o">);</span>
 <span class="n">KMeansModel</span> <span class="n">model</span> <span class="o">=</span> <span class="n">kmeans</span><span class="o">.</span><span class="na">fit</span><span class="o">(</span><span class="n">dataset</span><span class="o">);</span>

 <span class="c1">// Make predictions</span>
 <span class="n">Dataset</span><span class="o">&lt;</span><span class="n">Row</span><span class="o">&gt;</span> <span class="n">predictions</span> <span class="o">=</span> <span class="n">model</span><span class="o">.</span><span class="na">transform</span><span class="o">(</span><span class="n">dataset</span><span class="o">);</span>

 <span class="c1">// Evaluate clustering by computing Silhouette score</span>
 <span class="n">ClusteringEvaluator</span> <span class="n">evaluator</span> <span class="o">=</span> <span class="k">new</span> <span class="n">ClusteringEvaluator</span><span class="o">();</span>

 <span class="kt">double</span> <span class="n">silhouette</span> <span class="o">=</span> <span class="n">evaluator</span><span class="o">.</span><span class="na">evaluate</span><span class="o">(</span><span class="n">predictions</span><span class="o">);</span>
 <span class="n">System</span><span class="o">.</span><span class="na">out</span><span class="o">.</span><span class="na">println</span><span class="o">(</span><span class="s">&quot;Silhouette with squared euclidean distance = &quot;</span> <span class="o">+</span> <span class="n">silhouette</span><span class="o">);</span>

 <span class="c1">// Shows the result.</span>
 <span class="n">Vector</span><span class="o">[]</span> <span class="n">centers</span> <span class="o">=</span> <span class="n">model</span><span class="o">.</span><span class="na">clusterCenters</span><span class="o">();</span>
 <span class="n">System</span><span class="o">.</span><span class="na">out</span><span class="o">.</span><span class="na">println</span><span class="o">(</span><span class="s">&quot;Cluster Centers: &quot;</span><span class="o">);</span>
 <span class="k">for</span> <span class="o">(</span><span class="n">Vector</span> <span class="n">center</span><span class="o">:</span> <span class="n">centers</span><span class="o">)</span> <span class="o">{</span>
   <span class="n">System</span><span class="o">.</span><span class="na">out</span><span class="o">.</span><span class="na">println</span><span class="o">(</span><span class="n">center</span><span class="o">);</span>
 <span class="o">}</span>
 </pre></div>
     <div><small>Find full example code at "examples/src/main/java/org/apache/spark/examples/ml/JavaKMeansExample.java" in the Spark repo.</small></div>
   </div>

 <div data-lang="python">
     <p>Refer to the <a href="api/python/pyspark.ml.html#pyspark.ml.clustering.KMeans">Python API docs</a> for more details.</p>

     <div class="highlight"><pre><span></span><span class="kn">from</span> <span class="nn">pyspark.ml.clustering</span> <span class="kn">import</span> <span class="n">KMeans</span>
 <span class="kn">from</span> <span class="nn">pyspark.ml.evaluation</span> <span class="kn">import</span> <span class="n">ClusteringEvaluator</span>

 <span class="c1"># Loads data.</span>
 <span class="n">dataset</span> <span class="o">=</span> <span class="n">spark</span><span class="o">.</span><span class="n">read</span><span class="o">.</span><span class="n">format</span><span class="p">(</span><span class="s2">&quot;libsvm&quot;</span><span class="p">)</span><span class="o">.</span><span class="n">load</span><span class="p">(</span><span class="s2">&quot;data/mllib/sample_kmeans_data.txt&quot;</span><span class="p">)</span>

 <span class="c1"># Trains a k-means model.</span>
 <span class="n">kmeans</span> <span class="o">=</span> <span class="n">KMeans</span><span class="p">()</span><span class="o">.</span><span class="n">setK</span><span class="p">(</span><span class="mi">2</span><span class="p">)</span><span class="o">.</span><span class="n">setSeed</span><span class="p">(</span><span class="mi">1</span><span class="p">)</span>
 <span class="n">model</span> <span class="o">=</span> <span class="n">kmeans</span><span class="o">.</span><span class="n">fit</span><span class="p">(</span><span class="n">dataset</span><span class="p">)</span>

 <span class="c1"># Make predictions</span>
 <span class="n">predictions</span> <span class="o">=</span> <span class="n">model</span><span class="o">.</span><span class="n">transform</span><span class="p">(</span><span class="n">dataset</span><span class="p">)</span>

 <span class="c1"># Evaluate clustering by computing Silhouette score</span>
 <span class="n">evaluator</span> <span class="o">=</span> <span class="n">ClusteringEvaluator</span><span class="p">()</span>

 <span class="n">silhouette</span> <span class="o">=</span> <span class="n">evaluator</span><span class="o">.</span><span class="n">evaluate</span><span class="p">(</span><span class="n">predictions</span><span class="p">)</span>
 <span class="k">print</span><span class="p">(</span><span class="s2">&quot;Silhouette with squared euclidean distance = &quot;</span> <span class="o">+</span> <span class="nb">str</span><span class="p">(</span><span class="n">silhouette</span><span class="p">))</span>

 <span class="c1"># Shows the result.</span>
 <span class="n">centers</span> <span class="o">=</span> <span class="n">model</span><span class="o">.</span><span class="n">clusterCenters</span><span class="p">()</span>
 <span class="k">print</span><span class="p">(</span><span class="s2">&quot;Cluster Centers: &quot;</span><span class="p">)</span>
 <span class="k">for</span> <span class="n">center</span> <span class="ow">in</span> <span class="n">centers</span><span class="p">:</span>
     <span class="k">print</span><span class="p">(</span><span class="n">center</span><span class="p">)</span>
 </pre></div>
     <div><small>Find full example code at "examples/src/main/python/ml/kmeans_example.py" in the Spark repo.</small></div>
   </div>

 <div data-lang="r">

     <p>Refer to the <a href="api/R/spark.kmeans.html">R API docs</a> for more details.</p>

     <div class="highlight"><pre><span></span><span class="c1"># Fit a k-means model with spark.kmeans</span>
 t <span class="o">&lt;-</span> <span class="kp">as.data.frame</span><span class="p">(</span>Titanic<span class="p">)</span>
 training <span class="o">&lt;-</span> createDataFrame<span class="p">(</span><span class="kp">t</span><span class="p">)</span>
 df_list <span class="o">&lt;-</span> randomSplit<span class="p">(</span>training<span class="p">,</span> <span class="kt">c</span><span class="p">(</span><span class="m">7</span><span class="p">,</span><span class="m">3</span><span class="p">),</span> <span class="m">2</span><span class="p">)</span>
 kmeansDF <span class="o">&lt;-</span> df_list<span class="p">[[</span><span class="m">1</span><span class="p">]]</span>
 kmeansTestDF <span class="o">&lt;-</span> df_list<span class="p">[[</span><span class="m">2</span><span class="p">]]</span>
 kmeansModel <span class="o">&lt;-</span> spark.kmeans<span class="p">(</span>kmeansDF<span class="p">,</span> <span class="o">~</span> Class <span class="o">+</span> Sex <span class="o">+</span> Age <span class="o">+</span> Freq<span class="p">,</span>
                             k <span class="o">=</span> <span class="m">3</span><span class="p">)</span>

 <span class="c1"># Model summary</span>
 <span class="kp">summary</span><span class="p">(</span>kmeansModel<span class="p">)</span>

 <span class="c1"># Get fitted result from the k-means model</span>
 <span class="kp">head</span><span class="p">(</span>fitted<span class="p">(</span>kmeansModel<span class="p">))</span>

 <span class="c1"># Prediction</span>
 kmeansPredictions <span class="o">&lt;-</span> predict<span class="p">(</span>kmeansModel<span class="p">,</span> kmeansTestDF<span class="p">)</span>
 <span class="kp">head</span><span class="p">(</span>kmeansPredictions<span class="p">)</span>
 </pre></div>
     <div><small>Find full example code at "examples/src/main/r/ml/kmeans.R" in the Spark repo.</small></div>
   </div>

 </div>

 <h2 id="latent-dirichlet-allocation-lda">Latent Dirichlet allocation (LDA)</h2>

 <p><code>LDA</code> is implemented as an <code>Estimator</code> that supports both <code>EMLDAOptimizer</code> and <code>OnlineLDAOptimizer</code>,
 and generates a <code>LDAModel</code> as the base model. Expert users may cast a <code>LDAModel</code> generated by
 <code>EMLDAOptimizer</code> to a <code>DistributedLDAModel</code> if needed.</p>

 <p><strong>Examples</strong></p>

 <div class="codetabs">

 <div data-lang="scala">

     <p>Refer to the <a href="api/scala/index.html#org.apache.spark.ml.clustering.LDA">Scala API docs</a> for more details.</p>

     <div class="highlight"><pre><span></span><span class="k">import</span> <span class="nn">org.apache.spark.ml.clustering.LDA</span>

 <span class="c1">// Loads data.</span>
 <span class="k">val</span> <span class="n">dataset</span> <span class="k">=</span> <span class="n">spark</span><span class="o">.</span><span class="n">read</span><span class="o">.</span><span class="n">format</span><span class="o">(</span><span class="s">&quot;libsvm&quot;</span><span class="o">)</span>
   <span class="o">.</span><span class="n">load</span><span class="o">(</span><span class="s">&quot;data/mllib/sample_lda_libsvm_data.txt&quot;</span><span class="o">)</span>

 <span class="c1">// Trains a LDA model.</span>
 <span class="k">val</span> <span class="n">lda</span> <span class="k">=</span> <span class="k">new</span> <span class="nc">LDA</span><span class="o">().</span><span class="n">setK</span><span class="o">(</span><span class="mi">10</span><span class="o">).</span><span class="n">setMaxIter</span><span class="o">(</span><span class="mi">10</span><span class="o">)</span>
 <span class="k">val</span> <span class="n">model</span> <span class="k">=</span> <span class="n">lda</span><span class="o">.</span><span class="n">fit</span><span class="o">(</span><span class="n">dataset</span><span class="o">)</span>

 <span class="k">val</span> <span class="n">ll</span> <span class="k">=</span> <span class="n">model</span><span class="o">.</span><span class="n">logLikelihood</span><span class="o">(</span><span class="n">dataset</span><span class="o">)</span>
 <span class="k">val</span> <span class="n">lp</span> <span class="k">=</span> <span class="n">model</span><span class="o">.</span><span class="n">logPerplexity</span><span class="o">(</span><span class="n">dataset</span><span class="o">)</span>
 <span class="n">println</span><span class="o">(</span><span class="s">s&quot;The lower bound on the log likelihood of the entire corpus: </span><span class="si">$ll</span><span class="s">&quot;</span><span class="o">)</span>
 <span class="n">println</span><span class="o">(</span><span class="s">s&quot;The upper bound on perplexity: </span><span class="si">$lp</span><span class="s">&quot;</span><span class="o">)</span>

 <span class="c1">// Describe topics.</span>
 <span class="k">val</span> <span class="n">topics</span> <span class="k">=</span> <span class="n">model</span><span class="o">.</span><span class="n">describeTopics</span><span class="o">(</span><span class="mi">3</span><span class="o">)</span>
 <span class="n">println</span><span class="o">(</span><span class="s">&quot;The topics described by their top-weighted terms:&quot;</span><span class="o">)</span>
 <span class="n">topics</span><span class="o">.</span><span class="n">show</span><span class="o">(</span><span class="kc">false</span><span class="o">)</span>

 <span class="c1">// Shows the result.</span>
 <span class="k">val</span> <span class="n">transformed</span> <span class="k">=</span> <span class="n">model</span><span class="o">.</span><span class="n">transform</span><span class="o">(</span><span class="n">dataset</span><span class="o">)</span>
 <span class="n">transformed</span><span class="o">.</span><span class="n">show</span><span class="o">(</span><span class="kc">false</span><span class="o">)</span>
 </pre></div>
     <div><small>Find full example code at "examples/src/main/scala/org/apache/spark/examples/ml/LDAExample.scala" in the Spark repo.</small></div>
   </div>

 <div data-lang="java">

     <p>Refer to the <a href="api/java/org/apache/spark/ml/clustering/LDA.html">Java API docs</a> for more details.</p>

     <div class="highlight"><pre><span></span><span class="kn">import</span> <span class="nn">org.apache.spark.ml.clustering.LDA</span><span class="o">;</span>
 <span class="kn">import</span> <span class="nn">org.apache.spark.ml.clustering.LDAModel</span><span class="o">;</span>
 <span class="kn">import</span> <span class="nn">org.apache.spark.sql.Dataset</span><span class="o">;</span>
 <span class="kn">import</span> <span class="nn">org.apache.spark.sql.Row</span><span class="o">;</span>
 <span class="kn">import</span> <span class="nn">org.apache.spark.sql.SparkSession</span><span class="o">;</span>

 <span class="c1">// Loads data.</span>
 <span class="n">Dataset</span><span class="o">&lt;</span><span class="n">Row</span><span class="o">&gt;</span> <span class="n">dataset</span> <span class="o">=</span> <span class="n">spark</span><span class="o">.</span><span class="na">read</span><span class="o">().</span><span class="na">format</span><span class="o">(</span><span class="s">&quot;libsvm&quot;</span><span class="o">)</span>
   <span class="o">.</span><span class="na">load</span><span class="o">(</span><span class="s">&quot;data/mllib/sample_lda_libsvm_data.txt&quot;</span><span class="o">);</span>

 <span class="c1">// Trains a LDA model.</span>
 <span class="n">LDA</span> <span class="n">lda</span> <span class="o">=</span> <span class="k">new</span> <span class="n">LDA</span><span class="o">().</span><span class="na">setK</span><span class="o">(</span><span class="mi">10</span><span class="o">).</span><span class="na">setMaxIter</span><span class="o">(</span><span class="mi">10</span><span class="o">);</span>
 <span class="n">LDAModel</span> <span class="n">model</span> <span class="o">=</span> <span class="n">lda</span><span class="o">.</span><span class="na">fit</span><span class="o">(</span><span class="n">dataset</span><span class="o">);</span>

 <span class="kt">double</span> <span class="n">ll</span> <span class="o">=</span> <span class="n">model</span><span class="o">.</span><span class="na">logLikelihood</span><span class="o">(</span><span class="n">dataset</span><span class="o">);</span>
 <span class="kt">double</span> <span class="n">lp</span> <span class="o">=</span> <span class="n">model</span><span class="o">.</span><span class="na">logPerplexity</span><span class="o">(</span><span class="n">dataset</span><span class="o">);</span>
 <span class="n">System</span><span class="o">.</span><span class="na">out</span><span class="o">.</span><span class="na">println</span><span class="o">(</span><span class="s">&quot;The lower bound on the log likelihood of the entire corpus: &quot;</span> <span class="o">+</span> <span class="n">ll</span><span class="o">);</span>
 <span class="n">System</span><span class="o">.</span><span class="na">out</span><span class="o">.</span><span class="na">println</span><span class="o">(</span><span class="s">&quot;The upper bound on perplexity: &quot;</span> <span class="o">+</span> <span class="n">lp</span><span class="o">);</span>

 <span class="c1">// Describe topics.</span>
 <span class="n">Dataset</span><span class="o">&lt;</span><span class="n">Row</span><span class="o">&gt;</span> <span class="n">topics</span> <span class="o">=</span> <span class="n">model</span><span class="o">.</span><span class="na">describeTopics</span><span class="o">(</span><span class="mi">3</span><span class="o">);</span>
 <span class="n">System</span><span class="o">.</span><span class="na">out</span><span class="o">.</span><span class="na">println</span><span class="o">(</span><span class="s">&quot;The topics described by their top-weighted terms:&quot;</span><span class="o">);</span>
 <span class="n">topics</span><span class="o">.</span><span class="na">show</span><span class="o">(</span><span class="kc">false</span><span class="o">);</span>

 <span class="c1">// Shows the result.</span>
 <span class="n">Dataset</span><span class="o">&lt;</span><span class="n">Row</span><span class="o">&gt;</span> <span class="n">transformed</span> <span class="o">=</span> <span class="n">model</span><span class="o">.</span><span class="na">transform</span><span class="o">(</span><span class="n">dataset</span><span class="o">);</span>
 <span class="n">transformed</span><span class="o">.</span><span class="na">show</span><span class="o">(</span><span class="kc">false</span><span class="o">);</span>
 </pre></div>
     <div><small>Find full example code at "examples/src/main/java/org/apache/spark/examples/ml/JavaLDAExample.java" in the Spark repo.</small></div>
   </div>

 <div data-lang="python">

     <p>Refer to the <a href="api/python/pyspark.ml.html#pyspark.ml.clustering.LDA">Python API docs</a> for more details.</p>

     <div class="highlight"><pre><span></span><span class="kn">from</span> <span class="nn">pyspark.ml.clustering</span> <span class="kn">import</span> <span class="n">LDA</span>

 <span class="c1"># Loads data.</span>
 <span class="n">dataset</span> <span class="o">=</span> <span class="n">spark</span><span class="o">.</span><span class="n">read</span><span class="o">.</span><span class="n">format</span><span class="p">(</span><span class="s2">&quot;libsvm&quot;</span><span class="p">)</span><span class="o">.</span><span class="n">load</span><span class="p">(</span><span class="s2">&quot;data/mllib/sample_lda_libsvm_data.txt&quot;</span><span class="p">)</span>

 <span class="c1"># Trains a LDA model.</span>
 <span class="n">lda</span> <span class="o">=</span> <span class="n">LDA</span><span class="p">(</span><span class="n">k</span><span class="o">=</span><span class="mi">10</span><span class="p">,</span> <span class="n">maxIter</span><span class="o">=</span><span class="mi">10</span><span class="p">)</span>
 <span class="n">model</span> <span class="o">=</span> <span class="n">lda</span><span class="o">.</span><span class="n">fit</span><span class="p">(</span><span class="n">dataset</span><span class="p">)</span>

 <span class="n">ll</span> <span class="o">=</span> <span class="n">model</span><span class="o">.</span><span class="n">logLikelihood</span><span class="p">(</span><span class="n">dataset</span><span class="p">)</span>
 <span class="n">lp</span> <span class="o">=</span> <span class="n">model</span><span class="o">.</span><span class="n">logPerplexity</span><span class="p">(</span><span class="n">dataset</span><span class="p">)</span>
 <span class="k">print</span><span class="p">(</span><span class="s2">&quot;The lower bound on the log likelihood of the entire corpus: &quot;</span> <span class="o">+</span> <span class="nb">str</span><span class="p">(</span><span class="n">ll</span><span class="p">))</span>
 <span class="k">print</span><span class="p">(</span><span class="s2">&quot;The upper bound on perplexity: &quot;</span> <span class="o">+</span> <span class="nb">str</span><span class="p">(</span><span class="n">lp</span><span class="p">))</span>

 <span class="c1"># Describe topics.</span>
 <span class="n">topics</span> <span class="o">=</span> <span class="n">model</span><span class="o">.</span><span class="n">describeTopics</span><span class="p">(</span><span class="mi">3</span><span class="p">)</span>
 <span class="k">print</span><span class="p">(</span><span class="s2">&quot;The topics described by their top-weighted terms:&quot;</span><span class="p">)</span>
 <span class="n">topics</span><span class="o">.</span><span class="n">show</span><span class="p">(</span><span class="n">truncate</span><span class="o">=</span><span class="bp">False</span><span class="p">)</span>

 <span class="c1"># Shows the result</span>
 <span class="n">transformed</span> <span class="o">=</span> <span class="n">model</span><span class="o">.</span><span class="n">transform</span><span class="p">(</span><span class="n">dataset</span><span class="p">)</span>
 <span class="n">transformed</span><span class="o">.</span><span class="n">show</span><span class="p">(</span><span class="n">truncate</span><span class="o">=</span><span class="bp">False</span><span class="p">)</span>
 </pre></div>
     <div><small>Find full example code at "examples/src/main/python/ml/lda_example.py" in the Spark repo.</small></div>
   </div>

 <div data-lang="r">

     <p>Refer to the <a href="api/R/spark.lda.html">R API docs</a> for more details.</p>

     <div class="highlight"><pre><span></span><span class="c1"># Load training data</span>
 df <span class="o">&lt;-</span> read.df<span class="p">(</span><span class="s">&quot;data/mllib/sample_lda_libsvm_data.txt&quot;</span><span class="p">,</span> <span class="kn">source</span> <span class="o">=</span> <span class="s">&quot;libsvm&quot;</span><span class="p">)</span>
 training <span class="o">&lt;-</span> df
 test <span class="o">&lt;-</span> df

 <span class="c1"># Fit a latent dirichlet allocation model with spark.lda</span>
 model <span class="o">&lt;-</span> spark.lda<span class="p">(</span>training<span class="p">,</span> k <span class="o">=</span> <span class="m">10</span><span class="p">,</span> maxIter <span class="o">=</span> <span class="m">10</span><span class="p">)</span>

 <span class="c1"># Model summary</span>
 <span class="kp">summary</span><span class="p">(</span>model<span class="p">)</span>

 <span class="c1"># Posterior probabilities</span>
 posterior <span class="o">&lt;-</span> spark.posterior<span class="p">(</span>model<span class="p">,</span> test<span class="p">)</span>
 <span class="kp">head</span><span class="p">(</span>posterior<span class="p">)</span>

 <span class="c1"># The log perplexity of the LDA model</span>
 logPerplexity <span class="o">&lt;-</span> spark.perplexity<span class="p">(</span>model<span class="p">,</span> test<span class="p">)</span>
 <span class="kp">print</span><span class="p">(</span><span class="kp">paste0</span><span class="p">(</span><span class="s">&quot;The upper bound bound on perplexity: &quot;</span><span class="p">,</span> logPerplexity<span class="p">))</span>
 </pre></div>
     <div><small>Find full example code at "examples/src/main/r/ml/lda.R" in the Spark repo.</small></div>
   </div>

 </div>

 <h2 id="bisecting-k-means">Bisecting k-means</h2>

 <p>Bisecting k-means is a kind of <a href="https://en.wikipedia.org/wiki/Hierarchical_clustering">hierarchical clustering</a> using a
 divisive (or &#8220;top-down&#8221;) approach: all observations start in one cluster, and splits are performed recursively as one
 moves down the hierarchy.</p>

 <p>Bisecting K-means can often be much faster than regular K-means, but it will generally produce a different clustering.</p>

 <p><code>BisectingKMeans</code> is implemented as an <code>Estimator</code> and generates a <code>BisectingKMeansModel</code> as the base model.</p>

 <p><strong>Examples</strong></p>

 <div class="codetabs">

 <div data-lang="scala">
     <p>Refer to the <a href="api/scala/index.html#org.apache.spark.ml.clustering.BisectingKMeans">Scala API docs</a> for more details.</p>

     <div class="highlight"><pre><span></span><span class="k">import</span> <span class="nn">org.apache.spark.ml.clustering.BisectingKMeans</span>

 <span class="c1">// Loads data.</span>
 <span class="k">val</span> <span class="n">dataset</span> <span class="k">=</span> <span class="n">spark</span><span class="o">.</span><span class="n">read</span><span class="o">.</span><span class="n">format</span><span class="o">(</span><span class="s">&quot;libsvm&quot;</span><span class="o">).</span><span class="n">load</span><span class="o">(</span><span class="s">&quot;data/mllib/sample_kmeans_data.txt&quot;</span><span class="o">)</span>

 <span class="c1">// Trains a bisecting k-means model.</span>
 <span class="k">val</span> <span class="n">bkm</span> <span class="k">=</span> <span class="k">new</span> <span class="nc">BisectingKMeans</span><span class="o">().</span><span class="n">setK</span><span class="o">(</span><span class="mi">2</span><span class="o">).</span><span class="n">setSeed</span><span class="o">(</span><span class="mi">1</span><span class="o">)</span>
 <span class="k">val</span> <span class="n">model</span> <span class="k">=</span> <span class="n">bkm</span><span class="o">.</span><span class="n">fit</span><span class="o">(</span><span class="n">dataset</span><span class="o">)</span>

 <span class="c1">// Evaluate clustering.</span>
 <span class="k">val</span> <span class="n">cost</span> <span class="k">=</span> <span class="n">model</span><span class="o">.</span><span class="n">computeCost</span><span class="o">(</span><span class="n">dataset</span><span class="o">)</span>
 <span class="n">println</span><span class="o">(</span><span class="s">s&quot;Within Set Sum of Squared Errors = </span><span class="si">$cost</span><span class="s">&quot;</span><span class="o">)</span>

 <span class="c1">// Shows the result.</span>
 <span class="n">println</span><span class="o">(</span><span class="s">&quot;Cluster Centers: &quot;</span><span class="o">)</span>
 <span class="k">val</span> <span class="n">centers</span> <span class="k">=</span> <span class="n">model</span><span class="o">.</span><span class="n">clusterCenters</span>
 <span class="n">centers</span><span class="o">.</span><span class="n">foreach</span><span class="o">(</span><span class="n">println</span><span class="o">)</span>
 </pre></div>
     <div><small>Find full example code at "examples/src/main/scala/org/apache/spark/examples/ml/BisectingKMeansExample.scala" in the Spark repo.</small></div>
   </div>

 <div data-lang="java">
     <p>Refer to the <a href="api/java/org/apache/spark/ml/clustering/BisectingKMeans.html">Java API docs</a> for more details.</p>

     <div class="highlight"><pre><span></span><span class="kn">import</span> <span class="nn">org.apache.spark.ml.clustering.BisectingKMeans</span><span class="o">;</span>
 <span class="kn">import</span> <span class="nn">org.apache.spark.ml.clustering.BisectingKMeansModel</span><span class="o">;</span>
 <span class="kn">import</span> <span class="nn">org.apache.spark.ml.linalg.Vector</span><span class="o">;</span>
 <span class="kn">import</span> <span class="nn">org.apache.spark.sql.Dataset</span><span class="o">;</span>
 <span class="kn">import</span> <span class="nn">org.apache.spark.sql.Row</span><span class="o">;</span>

 <span class="c1">// Loads data.</span>
 <span class="n">Dataset</span><span class="o">&lt;</span><span class="n">Row</span><span class="o">&gt;</span> <span class="n">dataset</span> <span class="o">=</span> <span class="n">spark</span><span class="o">.</span><span class="na">read</span><span class="o">().</span><span class="na">format</span><span class="o">(</span><span class="s">&quot;libsvm&quot;</span><span class="o">).</span><span class="na">load</span><span class="o">(</span><span class="s">&quot;data/mllib/sample_kmeans_data.txt&quot;</span><span class="o">);</span>

 <span class="c1">// Trains a bisecting k-means model.</span>
 <span class="n">BisectingKMeans</span> <span class="n">bkm</span> <span class="o">=</span> <span class="k">new</span> <span class="n">BisectingKMeans</span><span class="o">().</span><span class="na">setK</span><span class="o">(</span><span class="mi">2</span><span class="o">).</span><span class="na">setSeed</span><span class="o">(</span><span class="mi">1</span><span class="o">);</span>
 <span class="n">BisectingKMeansModel</span> <span class="n">model</span> <span class="o">=</span> <span class="n">bkm</span><span class="o">.</span><span class="na">fit</span><span class="o">(</span><span class="n">dataset</span><span class="o">);</span>

 <span class="c1">// Evaluate clustering.</span>
 <span class="kt">double</span> <span class="n">cost</span> <span class="o">=</span> <span class="n">model</span><span class="o">.</span><span class="na">computeCost</span><span class="o">(</span><span class="n">dataset</span><span class="o">);</span>
 <span class="n">System</span><span class="o">.</span><span class="na">out</span><span class="o">.</span><span class="na">println</span><span class="o">(</span><span class="s">&quot;Within Set Sum of Squared Errors = &quot;</span> <span class="o">+</span> <span class="n">cost</span><span class="o">);</span>

 <span class="c1">// Shows the result.</span>
 <span class="n">System</span><span class="o">.</span><span class="na">out</span><span class="o">.</span><span class="na">println</span><span class="o">(</span><span class="s">&quot;Cluster Centers: &quot;</span><span class="o">);</span>
 <span class="n">Vector</span><span class="o">[]</span> <span class="n">centers</span> <span class="o">=</span> <span class="n">model</span><span class="o">.</span><span class="na">clusterCenters</span><span class="o">();</span>
 <span class="k">for</span> <span class="o">(</span><span class="n">Vector</span> <span class="n">center</span> <span class="o">:</span> <span class="n">centers</span><span class="o">)</span> <span class="o">{</span>
   <span class="n">System</span><span class="o">.</span><span class="na">out</span><span class="o">.</span><span class="na">println</span><span class="o">(</span><span class="n">center</span><span class="o">);</span>
 <span class="o">}</span>
 </pre></div>
     <div><small>Find full example code at "examples/src/main/java/org/apache/spark/examples/ml/JavaBisectingKMeansExample.java" in the Spark repo.</small></div>
   </div>

 <div data-lang="python">
     <p>Refer to the <a href="api/python/pyspark.ml.html#pyspark.ml.clustering.BisectingKMeans">Python API docs</a> for more details.</p>

     <div class="highlight"><pre><span></span><span class="kn">from</span> <span class="nn">pyspark.ml.clustering</span> <span class="kn">import</span> <span class="n">BisectingKMeans</span>

 <span class="c1"># Loads data.</span>
 <span class="n">dataset</span> <span class="o">=</span> <span class="n">spark</span><span class="o">.</span><span class="n">read</span><span class="o">.</span><span class="n">format</span><span class="p">(</span><span class="s2">&quot;libsvm&quot;</span><span class="p">)</span><span class="o">.</span><span class="n">load</span><span class="p">(</span><span class="s2">&quot;data/mllib/sample_kmeans_data.txt&quot;</span><span class="p">)</span>

 <span class="c1"># Trains a bisecting k-means model.</span>
 <span class="n">bkm</span> <span class="o">=</span> <span class="n">BisectingKMeans</span><span class="p">()</span><span class="o">.</span><span class="n">setK</span><span class="p">(</span><span class="mi">2</span><span class="p">)</span><span class="o">.</span><span class="n">setSeed</span><span class="p">(</span><span class="mi">1</span><span class="p">)</span>
 <span class="n">model</span> <span class="o">=</span> <span class="n">bkm</span><span class="o">.</span><span class="n">fit</span><span class="p">(</span><span class="n">dataset</span><span class="p">)</span>

 <span class="c1"># Evaluate clustering.</span>
 <span class="n">cost</span> <span class="o">=</span> <span class="n">model</span><span class="o">.</span><span class="n">computeCost</span><span class="p">(</span><span class="n">dataset</span><span class="p">)</span>
 <span class="k">print</span><span class="p">(</span><span class="s2">&quot;Within Set Sum of Squared Errors = &quot;</span> <span class="o">+</span> <span class="nb">str</span><span class="p">(</span><span class="n">cost</span><span class="p">))</span>

 <span class="c1"># Shows the result.</span>
 <span class="k">print</span><span class="p">(</span><span class="s2">&quot;Cluster Centers: &quot;</span><span class="p">)</span>
 <span class="n">centers</span> <span class="o">=</span> <span class="n">model</span><span class="o">.</span><span class="n">clusterCenters</span><span class="p">()</span>
 <span class="k">for</span> <span class="n">center</span> <span class="ow">in</span> <span class="n">centers</span><span class="p">:</span>
     <span class="k">print</span><span class="p">(</span><span class="n">center</span><span class="p">)</span>
 </pre></div>
     <div><small>Find full example code at "examples/src/main/python/ml/bisecting_k_means_example.py" in the Spark repo.</small></div>
   </div>

 <div data-lang="r">

     <p>Refer to the <a href="api/R/spark.bisectingKmeans.html">R API docs</a> for more details.</p>

     <div class="highlight"><pre><span></span>t <span class="o">&lt;-</span> <span class="kp">as.data.frame</span><span class="p">(</span>Titanic<span class="p">)</span>
 training <span class="o">&lt;-</span> createDataFrame<span class="p">(</span><span class="kp">t</span><span class="p">)</span>

 <span class="c1"># Fit bisecting k-means model with four centers</span>
 model <span class="o">&lt;-</span> spark.bisectingKmeans<span class="p">(</span>training<span class="p">,</span> Class <span class="o">~</span> Survived<span class="p">,</span> k <span class="o">=</span> <span class="m">4</span><span class="p">)</span>

 <span class="c1"># get fitted result from a bisecting k-means model</span>
 fitted.model <span class="o">&lt;-</span> fitted<span class="p">(</span>model<span class="p">,</span> <span class="s">&quot;centers&quot;</span><span class="p">)</span>

 <span class="c1"># Model summary</span>
 <span class="kp">head</span><span class="p">(</span><span class="kp">summary</span><span class="p">(</span>fitted.model<span class="p">))</span>

 <span class="c1"># fitted values on training data</span>
 fitted <span class="o">&lt;-</span> predict<span class="p">(</span>model<span class="p">,</span> training<span class="p">)</span>
 <span class="kp">head</span><span class="p">(</span>select<span class="p">(</span>fitted<span class="p">,</span> <span class="s">&quot;Class&quot;</span><span class="p">,</span> <span class="s">&quot;prediction&quot;</span><span class="p">))</span>
 </pre></div>
     <div><small>Find full example code at "examples/src/main/r/ml/bisectingKmeans.R" in the Spark repo.</small></div>
   </div>
 </div>

 <h2 id="gaussian-mixture-model-gmm">Gaussian Mixture Model (GMM)</h2>

 <p>A <a href="http://en.wikipedia.org/wiki/Mixture_model#Multivariate_Gaussian_mixture_model">Gaussian Mixture Model</a>
 represents a composite distribution whereby points are drawn from one of <em>k</em> Gaussian sub-distributions,
 each with its own probability. The <code>spark.ml</code> implementation uses the
 <a href="http://en.wikipedia.org/wiki/Expectation%E2%80%93maximization_algorithm">expectation-maximization</a>
 algorithm to induce the maximum-likelihood model given a set of samples.</p>

 <p><code>GaussianMixture</code> is implemented as an <code>Estimator</code> and generates a <code>GaussianMixtureModel</code> as the base
 model.</p>

 <h3 id="input-columns-1">Input Columns</h3>

 <table class="table">
   <thead>
     <tr>
       <th align="left">Param name</th>
       <th align="left">Type(s)</th>
       <th align="left">Default</th>
       <th align="left">Description</th>
     </tr>
   </thead>
   <tbody>
     <tr>
       <td>featuresCol</td>
       <td>Vector</td>
       <td>"features"</td>
       <td>Feature vector</td>
     </tr>
   </tbody>
 </table>

 <h3 id="output-columns-1">Output Columns</h3>

 <table class="table">
   <thead>
     <tr>
       <th align="left">Param name</th>
       <th align="left">Type(s)</th>
       <th align="left">Default</th>
       <th align="left">Description</th>
     </tr>
   </thead>
   <tbody>
     <tr>
       <td>predictionCol</td>
       <td>Int</td>
       <td>"prediction"</td>
       <td>Predicted cluster center</td>
     </tr>
     <tr>
       <td>probabilityCol</td>
       <td>Vector</td>
       <td>"probability"</td>
       <td>Probability of each cluster</td>
     </tr>
   </tbody>
 </table>

 <p><strong>Examples</strong></p>

 <div class="codetabs">

 <div data-lang="scala">
     <p>Refer to the <a href="api/scala/index.html#org.apache.spark.ml.clustering.GaussianMixture">Scala API docs</a> for more details.</p>

     <div class="highlight"><pre><span></span><span class="k">import</span> <span class="nn">org.apache.spark.ml.clustering.GaussianMixture</span>

 <span class="c1">// Loads data</span>
 <span class="k">val</span> <span class="n">dataset</span> <span class="k">=</span> <span class="n">spark</span><span class="o">.</span><span class="n">read</span><span class="o">.</span><span class="n">format</span><span class="o">(</span><span class="s">&quot;libsvm&quot;</span><span class="o">).</span><span class="n">load</span><span class="o">(</span><span class="s">&quot;data/mllib/sample_kmeans_data.txt&quot;</span><span class="o">)</span>

 <span class="c1">// Trains Gaussian Mixture Model</span>
 <span class="k">val</span> <span class="n">gmm</span> <span class="k">=</span> <span class="k">new</span> <span class="nc">GaussianMixture</span><span class="o">()</span>
   <span class="o">.</span><span class="n">setK</span><span class="o">(</span><span class="mi">2</span><span class="o">)</span>
 <span class="k">val</span> <span class="n">model</span> <span class="k">=</span> <span class="n">gmm</span><span class="o">.</span><span class="n">fit</span><span class="o">(</span><span class="n">dataset</span><span class="o">)</span>

 <span class="c1">// output parameters of mixture model model</span>
 <span class="k">for</span> <span class="o">(</span><span class="n">i</span> <span class="k">&lt;-</span> <span class="mi">0</span> <span class="n">until</span> <span class="n">model</span><span class="o">.</span><span class="n">getK</span><span class="o">)</span> <span class="o">{</span>
   <span class="n">println</span><span class="o">(</span><span class="s">s&quot;Gaussian </span><span class="si">$i</span><span class="s">:\nweight=</span><span class="si">${</span><span class="n">model</span><span class="o">.</span><span class="n">weights</span><span class="o">(</span><span class="n">i</span><span class="o">)</span><span class="si">}</span><span class="s">\n&quot;</span> <span class="o">+</span>
       <span class="s">s&quot;mu=</span><span class="si">${</span><span class="n">model</span><span class="o">.</span><span class="n">gaussians</span><span class="o">(</span><span class="n">i</span><span class="o">).</span><span class="n">mean</span><span class="si">}</span><span class="s">\nsigma=\n</span><span class="si">${</span><span class="n">model</span><span class="o">.</span><span class="n">gaussians</span><span class="o">(</span><span class="n">i</span><span class="o">).</span><span class="n">cov</span><span class="si">}</span><span class="s">\n&quot;</span><span class="o">)</span>
 <span class="o">}</span>
 </pre></div>
     <div><small>Find full example code at "examples/src/main/scala/org/apache/spark/examples/ml/GaussianMixtureExample.scala" in the Spark repo.</small></div>
   </div>

 <div data-lang="java">
     <p>Refer to the <a href="api/java/org/apache/spark/ml/clustering/GaussianMixture.html">Java API docs</a> for more details.</p>

     <div class="highlight"><pre><span></span><span class="kn">import</span> <span class="nn">org.apache.spark.ml.clustering.GaussianMixture</span><span class="o">;</span>
 <span class="kn">import</span> <span class="nn">org.apache.spark.ml.clustering.GaussianMixtureModel</span><span class="o">;</span>
 <span class="kn">import</span> <span class="nn">org.apache.spark.sql.Dataset</span><span class="o">;</span>
 <span class="kn">import</span> <span class="nn">org.apache.spark.sql.Row</span><span class="o">;</span>

 <span class="c1">// Loads data</span>
 <span class="n">Dataset</span><span class="o">&lt;</span><span class="n">Row</span><span class="o">&gt;</span> <span class="n">dataset</span> <span class="o">=</span> <span class="n">spark</span><span class="o">.</span><span class="na">read</span><span class="o">().</span><span class="na">format</span><span class="o">(</span><span class="s">&quot;libsvm&quot;</span><span class="o">).</span><span class="na">load</span><span class="o">(</span><span class="s">&quot;data/mllib/sample_kmeans_data.txt&quot;</span><span class="o">);</span>

 <span class="c1">// Trains a GaussianMixture model</span>
 <span class="n">GaussianMixture</span> <span class="n">gmm</span> <span class="o">=</span> <span class="k">new</span> <span class="n">GaussianMixture</span><span class="o">()</span>
   <span class="o">.</span><span class="na">setK</span><span class="o">(</span><span class="mi">2</span><span class="o">);</span>
 <span class="n">GaussianMixtureModel</span> <span class="n">model</span> <span class="o">=</span> <span class="n">gmm</span><span class="o">.</span><span class="na">fit</span><span class="o">(</span><span class="n">dataset</span><span class="o">);</span>

 <span class="c1">// Output the parameters of the mixture model</span>
 <span class="k">for</span> <span class="o">(</span><span class="kt">int</span> <span class="n">i</span> <span class="o">=</span> <span class="mi">0</span><span class="o">;</span> <span class="n">i</span> <span class="o">&lt;</span> <span class="n">model</span><span class="o">.</span><span class="na">getK</span><span class="o">();</span> <span class="n">i</span><span class="o">++)</span> <span class="o">{</span>
   <span class="n">System</span><span class="o">.</span><span class="na">out</span><span class="o">.</span><span class="na">printf</span><span class="o">(</span><span class="s">&quot;Gaussian %d:\nweight=%f\nmu=%s\nsigma=\n%s\n\n&quot;</span><span class="o">,</span>
           <span class="n">i</span><span class="o">,</span> <span class="n">model</span><span class="o">.</span><span class="na">weights</span><span class="o">()[</span><span class="n">i</span><span class="o">],</span> <span class="n">model</span><span class="o">.</span><span class="na">gaussians</span><span class="o">()[</span><span class="n">i</span><span class="o">].</span><span class="na">mean</span><span class="o">(),</span> <span class="n">model</span><span class="o">.</span><span class="na">gaussians</span><span class="o">()[</span><span class="n">i</span><span class="o">].</span><span class="na">cov</span><span class="o">());</span>
 <span class="o">}</span>
 </pre></div>
     <div><small>Find full example code at "examples/src/main/java/org/apache/spark/examples/ml/JavaGaussianMixtureExample.java" in the Spark repo.</small></div>
   </div>

 <div data-lang="python">
     <p>Refer to the <a href="api/python/pyspark.ml.html#pyspark.ml.clustering.GaussianMixture">Python API docs</a> for more details.</p>

     <div class="highlight"><pre><span></span><span class="kn">from</span> <span class="nn">pyspark.ml.clustering</span> <span class="kn">import</span> <span class="n">GaussianMixture</span>

 <span class="c1"># loads data</span>
 <span class="n">dataset</span> <span class="o">=</span> <span class="n">spark</span><span class="o">.</span><span class="n">read</span><span class="o">.</span><span class="n">format</span><span class="p">(</span><span class="s2">&quot;libsvm&quot;</span><span class="p">)</span><span class="o">.</span><span class="n">load</span><span class="p">(</span><span class="s2">&quot;data/mllib/sample_kmeans_data.txt&quot;</span><span class="p">)</span>

 <span class="n">gmm</span> <span class="o">=</span> <span class="n">GaussianMixture</span><span class="p">()</span><span class="o">.</span><span class="n">setK</span><span class="p">(</span><span class="mi">2</span><span class="p">)</span><span class="o">.</span><span class="n">setSeed</span><span class="p">(</span><span class="mi">538009335</span><span class="p">)</span>
 <span class="n">model</span> <span class="o">=</span> <span class="n">gmm</span><span class="o">.</span><span class="n">fit</span><span class="p">(</span><span class="n">dataset</span><span class="p">)</span>

 <span class="k">print</span><span class="p">(</span><span class="s2">&quot;Gaussians shown as a DataFrame: &quot;</span><span class="p">)</span>
 <span class="n">model</span><span class="o">.</span><span class="n">gaussiansDF</span><span class="o">.</span><span class="n">show</span><span class="p">(</span><span class="n">truncate</span><span class="o">=</span><span class="bp">False</span><span class="p">)</span>
 </pre></div>
     <div><small>Find full example code at "examples/src/main/python/ml/gaussian_mixture_example.py" in the Spark repo.</small></div>
   </div>

 <div data-lang="r">

     <p>Refer to the <a href="api/R/spark.gaussianMixture.html">R API docs</a> for more details.</p>

     <div class="highlight"><pre><span></span><span class="c1"># Load training data</span>
 df <span class="o">&lt;-</span> read.df<span class="p">(</span><span class="s">&quot;data/mllib/sample_kmeans_data.txt&quot;</span><span class="p">,</span> <span class="kn">source</span> <span class="o">=</span> <span class="s">&quot;libsvm&quot;</span><span class="p">)</span>
 training <span class="o">&lt;-</span> df
 test <span class="o">&lt;-</span> df

 <span class="c1"># Fit a gaussian mixture clustering model with spark.gaussianMixture</span>
 model <span class="o">&lt;-</span> spark.gaussianMixture<span class="p">(</span>training<span class="p">,</span> <span class="o">~</span> features<span class="p">,</span> k <span class="o">=</span> <span class="m">2</span><span class="p">)</span>

 <span class="c1"># Model summary</span>
 <span class="kp">summary</span><span class="p">(</span>model<span class="p">)</span>

 <span class="c1"># Prediction</span>
 predictions <span class="o">&lt;-</span> predict<span class="p">(</span>model<span class="p">,</span> test<span class="p">)</span>
 <span class="kp">head</span><span class="p">(</span>predictions<span class="p">)</span>
 </pre></div>
     <div><small>Find full example code at "examples/src/main/r/ml/gaussianMixture.R" in the Spark repo.</small></div>
   </div>

 </div>


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