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             <h1 class="title">Machine Learning Library (MLlib)</h1>


           <p>MLlib is a Spark implementation of some common machine learning algorithms and utilities,
 including classification, regression, clustering, collaborative
 filtering, dimensionality reduction, as well as underlying optimization primitives:</p>

 <ul>
   <li><a href="mllib-basics.html">Basics</a>
     <ul>
       <li>data types </li>
       <li>summary statistics</li>
     </ul>
   </li>
   <li>Classification and regression
     <ul>
       <li><a href="mllib-linear-methods.html#linear-support-vector-machine-svm">linear support vector machine (SVM)</a></li>
       <li><a href="mllib-linear-methods.html#logistic-regression">logistic regression</a></li>
       <li><a href="mllib-linear-methods.html#linear-least-squares-lasso-and-ridge-regression">linear least squares, Lasso, and ridge regression</a></li>
       <li><a href="mllib-decision-tree.html">decision tree</a></li>
       <li><a href="mllib-naive-bayes.html">naive Bayes</a></li>
     </ul>
   </li>
   <li><a href="mllib-collaborative-filtering.html">Collaborative filtering</a>
     <ul>
       <li>alternating least squares (ALS)</li>
     </ul>
   </li>
   <li><a href="mllib-clustering.html">Clustering</a>
     <ul>
       <li>k-means</li>
     </ul>
   </li>
   <li><a href="mllib-dimensionality-reduction.html">Dimensionality reduction</a>
     <ul>
       <li>singular value decomposition (SVD)</li>
       <li>principal component analysis (PCA)</li>
     </ul>
   </li>
   <li><a href="mllib-optimization.html">Optimization</a>
     <ul>
       <li>stochastic gradient descent</li>
       <li>limited-memory BFGS (L-BFGS)</li>
     </ul>
   </li>
 </ul>

 <p>MLlib is a new component under active development.
 The APIs marked <code>Experimental</code>/<code>DeveloperApi</code> may change in future releases,
 and we will provide migration guide between releases.</p>

 <h1 id="dependencies">Dependencies</h1>

 <p>MLlib uses linear algebra packages <a href="http://www.scalanlp.org/">Breeze</a>, which depends on
 <a href="https://github.com/fommil/netlib-java">netlib-java</a>, and
 <a href="https://github.com/mikiobraun/jblas">jblas</a>.
 <code>netlib-java</code> and <code>jblas</code> depend on native Fortran routines.
 You need to install the
 <a href="https://github.com/mikiobraun/jblas/wiki/Missing-Libraries">gfortran runtime library</a> if it is not
 already present on your nodes. MLlib will throw a linking error if it cannot detect these libraries
 automatically.  Due to license issues, we do not include <code>netlib-java</code>&#8217;s native libraries in MLlib&#8217;s
 dependency set. If no native library is available at runtime, you will see a warning message.  To
 use native libraries from <code>netlib-java</code>, please include artifact
 <code>com.github.fommil.netlib:all:1.1.2</code> as a dependency of your project or build your own (see
 <a href="https://github.com/fommil/netlib-java/blob/master/README.md#machine-optimised-system-libraries">instructions</a>).</p>

 <p>To use MLlib in Python, you will need <a href="http://www.numpy.org">NumPy</a> version 1.4 or newer.</p>

 <hr />

 <h1 id="migration-guide">Migration Guide</h1>

 <h2 id="from-09-to-10">From 0.9 to 1.0</h2>

 <p>In MLlib v1.0, we support both dense and sparse input in a unified way, which introduces a few
 breaking changes.  If your data is sparse, please store it in a sparse format instead of dense to
 take advantage of sparsity in both storage and computation.</p>

 <div class="codetabs">
 <div data-lang="scala">

     <p>We used to represent a feature vector by <code>Array[Double]</code>, which is replaced by
 <a href="api/scala/index.html#org.apache.spark.mllib.linalg.Vector"><code>Vector</code></a> in v1.0. Algorithms that used
 to accept <code>RDD[Array[Double]]</code> now take
 <code>RDD[Vector]</code>. <a href="api/scala/index.html#org.apache.spark.mllib.regression.LabeledPoint"><code>LabeledPoint</code></a>
 is now a wrapper of <code>(Double, Vector)</code> instead of <code>(Double, Array[Double])</code>. Converting
 <code>Array[Double]</code> to <code>Vector</code> is straightforward:</p>

     <div class="highlight"><pre><code class="scala"><span class="k">import</span> <span class="nn">org.apache.spark.mllib.linalg.</span><span class="o">{</span><span class="nc">Vector</span><span class="o">,</span> <span class="nc">Vectors</span><span class="o">}</span>

 <span class="k">val</span> <span class="n">array</span><span class="k">:</span> <span class="kt">Array</span><span class="o">[</span><span class="kt">Double</span><span class="o">]</span> <span class="k">=</span> <span class="o">...</span> <span class="c1">// a double array</span>
 <span class="k">val</span> <span class="n">vector</span><span class="k">:</span> <span class="kt">Vector</span> <span class="o">=</span> <span class="nc">Vectors</span><span class="o">.</span><span class="n">dense</span><span class="o">(</span><span class="n">array</span><span class="o">)</span> <span class="c1">// a dense vector</span>
 </code></pre></div>

     <p><a href="api/scala/index.html#org.apache.spark.mllib.linalg.Vectors$"><code>Vectors</code></a> provides factory methods to create sparse vectors.</p>

     <p><em>Note</em>. Scala imports <code>scala.collection.immutable.Vector</code> by default, so you have to import <code>org.apache.spark.mllib.linalg.Vector</code> explicitly to use MLlib&#8217;s <code>Vector</code>.</p>

   </div>

 <div data-lang="java">

     <p>We used to represent a feature vector by <code>double[]</code>, which is replaced by
 <a href="api/java/index.html?org/apache/spark/mllib/linalg/Vector.html"><code>Vector</code></a> in v1.0. Algorithms that used
 to accept <code>RDD&lt;double[]&gt;</code> now take
 <code>RDD&lt;Vector&gt;</code>. <a href="api/java/index.html?org/apache/spark/mllib/regression/LabeledPoint.html"><code>LabeledPoint</code></a>
 is now a wrapper of <code>(double, Vector)</code> instead of <code>(double, double[])</code>. Converting <code>double[]</code> to
 <code>Vector</code> is straightforward:</p>

     <div class="highlight"><pre><code class="java"><span class="kn">import</span> <span class="nn">org.apache.spark.mllib.linalg.Vector</span><span class="o">;</span>
 <span class="kn">import</span> <span class="nn">org.apache.spark.mllib.linalg.Vectors</span><span class="o">;</span>

 <span class="kt">double</span><span class="o">[]</span> <span class="n">array</span> <span class="o">=</span> <span class="o">...</span> <span class="c1">// a double array</span>
 <span class="n">Vector</span> <span class="n">vector</span> <span class="o">=</span> <span class="n">Vectors</span><span class="o">.</span><span class="na">dense</span><span class="o">(</span><span class="n">array</span><span class="o">);</span> <span class="c1">// a dense vector</span>
 </code></pre></div>

     <p><a href="api/scala/index.html#org.apache.spark.mllib.linalg.Vectors$"><code>Vectors</code></a> provides factory methods to
 create sparse vectors.</p>

   </div>

 <div data-lang="python">

     <p>We used to represent a labeled feature vector in a NumPy array, where the first entry corresponds to
 the label and the rest are features.  This representation is replaced by class
 <a href="api/python/pyspark.mllib.regression.LabeledPoint-class.html"><code>LabeledPoint</code></a>, which takes both
 dense and sparse feature vectors.</p>

     <div class="highlight"><pre><code class="python"><span class="kn">from</span> <span class="nn">pyspark.mllib.linalg</span> <span class="kn">import</span> <span class="n">SparseVector</span>
 <span class="kn">from</span> <span class="nn">pyspark.mllib.regression</span> <span class="kn">import</span> <span class="n">LabeledPoint</span>

 <span class="c"># Create a labeled point with a positive label and a dense feature vector.</span>
 <span class="n">pos</span> <span class="o">=</span> <span class="n">LabeledPoint</span><span class="p">(</span><span class="mf">1.0</span><span class="p">,</span> <span class="p">[</span><span class="mf">1.0</span><span class="p">,</span> <span class="mf">0.0</span><span class="p">,</span> <span class="mf">3.0</span><span class="p">])</span>

 <span class="c"># Create a labeled point with a negative label and a sparse feature vector.</span>
 <span class="n">neg</span> <span class="o">=</span> <span class="n">LabeledPoint</span><span class="p">(</span><span class="mf">0.0</span><span class="p">,</span> <span class="n">SparseVector</span><span class="p">(</span><span class="mi">3</span><span class="p">,</span> <span class="p">[</span><span class="mi">0</span><span class="p">,</span> <span class="mi">2</span><span class="p">],</span> <span class="p">[</span><span class="mf">1.0</span><span class="p">,</span> <span class="mf">3.0</span><span class="p">]))</span>
 </code></pre></div>

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	<h1 class="title">Machine Learning Library (MLlib)</h1>


	<p>MLlib is a Spark implementation of some common machine learning algorithms and utilities,
	including classification, regression, clustering, collaborative
	filtering, dimensionality reduction, as well as underlying optimization primitives:</p>

	<ul>
	<li><a href="mllib-basics.html">Basics</a>
	<ul>
	<li>data types </li>
	<li>summary statistics</li>
	</ul>
	</li>
	<li>Classification and regression
	<ul>
	<li><a href="mllib-linear-methods.html#linear-support-vector-machine-svm">linear support vector machine (SVM)</a></li>
	<li><a href="mllib-linear-methods.html#logistic-regression">logistic regression</a></li>
	<li><a href="mllib-linear-methods.html#linear-least-squares-lasso-and-ridge-regression">linear least squares, Lasso, and ridge regression</a></li>
	<li><a href="mllib-decision-tree.html">decision tree</a></li>
	<li><a href="mllib-naive-bayes.html">naive Bayes</a></li>
	</ul>
	</li>
	<li><a href="mllib-collaborative-filtering.html">Collaborative filtering</a>
	<ul>
	<li>alternating least squares (ALS)</li>
	</ul>
	</li>
	<li><a href="mllib-clustering.html">Clustering</a>
	<ul>
	<li>k-means</li>
	</ul>
	</li>
	<li><a href="mllib-dimensionality-reduction.html">Dimensionality reduction</a>
	<ul>
	<li>singular value decomposition (SVD)</li>
	<li>principal component analysis (PCA)</li>
	</ul>
	</li>
	<li><a href="mllib-optimization.html">Optimization</a>
	<ul>
	<li>stochastic gradient descent</li>
	<li>limited-memory BFGS (L-BFGS)</li>
	</ul>
	</li>
	</ul>

	<p>MLlib is a new component under active development.
	The APIs marked <code>Experimental</code>/<code>DeveloperApi</code> may change in future releases,
	and we will provide migration guide between releases.</p>

	<h1 id="dependencies">Dependencies</h1>

	<p>MLlib uses linear algebra packages <a href="http://www.scalanlp.org/">Breeze</a>, which depends on
	<a href="https://github.com/fommil/netlib-java">netlib-java</a>, and
	<a href="https://github.com/mikiobraun/jblas">jblas</a>.
	<code>netlib-java</code> and <code>jblas</code> depend on native Fortran routines.
	You need to install the
	<a href="https://github.com/mikiobraun/jblas/wiki/Missing-Libraries">gfortran runtime library</a> if it is not
	already present on your nodes. MLlib will throw a linking error if it cannot detect these libraries
	automatically. Due to license issues, we do not include <code>netlib-java</code>’s native libraries in MLlib’s
	dependency set. If no native library is available at runtime, you will see a warning message. To
	use native libraries from <code>netlib-java</code>, please include artifact
	<code>com.github.fommil.netlib:all:1.1.2</code> as a dependency of your project or build your own (see
	<a href="https://github.com/fommil/netlib-java/blob/master/README.md#machine-optimised-system-libraries">instructions</a>).</p>

	<p>To use MLlib in Python, you will need <a href="http://www.numpy.org">NumPy</a> version 1.4 or newer.</p>

	<hr />

	<h1 id="migration-guide">Migration Guide</h1>

	<h2 id="from-09-to-10">From 0.9 to 1.0</h2>

	<p>In MLlib v1.0, we support both dense and sparse input in a unified way, which introduces a few
	breaking changes. If your data is sparse, please store it in a sparse format instead of dense to
	take advantage of sparsity in both storage and computation.</p>

	<div class="codetabs">
	<div data-lang="scala">

	<p>We used to represent a feature vector by <code>Array[Double]</code>, which is replaced by
	<a href="api/scala/index.html#org.apache.spark.mllib.linalg.Vector"><code>Vector</code></a> in v1.0. Algorithms that used
	to accept <code>RDD[Array[Double]]</code> now take
	<code>RDD[Vector]</code>. <a href="api/scala/index.html#org.apache.spark.mllib.regression.LabeledPoint"><code>LabeledPoint</code></a>
	is now a wrapper of <code>(Double, Vector)</code> instead of <code>(Double, Array[Double])</code>. Converting
	<code>Array[Double]</code> to <code>Vector</code> is straightforward:</p>

	<div class="highlight"><pre><code class="scala"><span class="k">import</span> <span class="nn">org.apache.spark.mllib.linalg.</span><span class="o">{</span><span class="nc">Vector</span><span class="o">,</span> <span class="nc">Vectors</span><span class="o">}</span>

	<span class="k">val</span> <span class="n">array</span><span class="k">:</span> <span class="kt">Array</span><span class="o">[</span><span class="kt">Double</span><span class="o">]</span> <span class="k">=</span> <span class="o">...</span> <span class="c1">// a double array</span>
	<span class="k">val</span> <span class="n">vector</span><span class="k">:</span> <span class="kt">Vector</span> <span class="o">=</span> <span class="nc">Vectors</span><span class="o">.</span><span class="n">dense</span><span class="o">(</span><span class="n">array</span><span class="o">)</span> <span class="c1">// a dense vector</span>
	</code></pre></div>

	<p><a href="api/scala/index.html#org.apache.spark.mllib.linalg.Vectors$"><code>Vectors</code></a> provides factory methods to create sparse vectors.</p>

	<p><em>Note</em>. Scala imports <code>scala.collection.immutable.Vector</code> by default, so you have to import <code>org.apache.spark.mllib.linalg.Vector</code> explicitly to use MLlib’s <code>Vector</code>.</p>

	</div>

	<div data-lang="java">

	<p>We used to represent a feature vector by <code>double[]</code>, which is replaced by
	<a href="api/java/index.html?org/apache/spark/mllib/linalg/Vector.html"><code>Vector</code></a> in v1.0. Algorithms that used
	to accept <code>RDD<double[]></code> now take
	<code>RDD<Vector></code>. <a href="api/java/index.html?org/apache/spark/mllib/regression/LabeledPoint.html"><code>LabeledPoint</code></a>
	is now a wrapper of <code>(double, Vector)</code> instead of <code>(double, double[])</code>. Converting <code>double[]</code> to
	<code>Vector</code> is straightforward:</p>

	<div class="highlight"><pre><code class="java"><span class="kn">import</span> <span class="nn">org.apache.spark.mllib.linalg.Vector</span><span class="o">;</span>
	<span class="kn">import</span> <span class="nn">org.apache.spark.mllib.linalg.Vectors</span><span class="o">;</span>

	<span class="kt">double</span><span class="o">[]</span> <span class="n">array</span> <span class="o">=</span> <span class="o">...</span> <span class="c1">// a double array</span>
	<span class="n">Vector</span> <span class="n">vector</span> <span class="o">=</span> <span class="n">Vectors</span><span class="o">.</span><span class="na">dense</span><span class="o">(</span><span class="n">array</span><span class="o">);</span> <span class="c1">// a dense vector</span>
	</code></pre></div>

	<p><a href="api/scala/index.html#org.apache.spark.mllib.linalg.Vectors$"><code>Vectors</code></a> provides factory methods to
	create sparse vectors.</p>

	</div>

	<div data-lang="python">

	<p>We used to represent a labeled feature vector in a NumPy array, where the first entry corresponds to
	the label and the rest are features. This representation is replaced by class
	<a href="api/python/pyspark.mllib.regression.LabeledPoint-class.html"><code>LabeledPoint</code></a>, which takes both
	dense and sparse feature vectors.</p>

	<div class="highlight"><pre><code class="python"><span class="kn">from</span> <span class="nn">pyspark.mllib.linalg</span> <span class="kn">import</span> <span class="n">SparseVector</span>
	<span class="kn">from</span> <span class="nn">pyspark.mllib.regression</span> <span class="kn">import</span> <span class="n">LabeledPoint</span>

	<span class="c"># Create a labeled point with a positive label and a dense feature vector.</span>
	<span class="n">pos</span> <span class="o">=</span> <span class="n">LabeledPoint</span><span class="p">(</span><span class="mf">1.0</span><span class="p">,</span> <span class="p">[</span><span class="mf">1.0</span><span class="p">,</span> <span class="mf">0.0</span><span class="p">,</span> <span class="mf">3.0</span><span class="p">])</span>

	<span class="c"># Create a labeled point with a negative label and a sparse feature vector.</span>
	<span class="n">neg</span> <span class="o">=</span> <span class="n">LabeledPoint</span><span class="p">(</span><span class="mf">0.0</span><span class="p">,</span> <span class="n">SparseVector</span><span class="p">(</span><span class="mi">3</span><span class="p">,</span> <span class="p">[</span><span class="mi">0</span><span class="p">,</span> <span class="mi">2</span><span class="p">],</span> <span class="p">[</span><span class="mf">1.0</span><span class="p">,</span> <span class="mf">3.0</span><span class="p">]))</span>
	</code></pre></div>

	</div>
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