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                         <h1 class="title">Frequent Pattern Mining - RDD-based API</h1>


                     <p>Mining frequent items, itemsets, subsequences, or other substructures is usually among the
 first steps to analyze a large-scale dataset, which has been an active research topic in
 data mining for years.
 We refer users to Wikipedia&#8217;s <a href="http://en.wikipedia.org/wiki/Association_rule_learning">association rule learning</a>
 for more information.
 <code class="language-plaintext highlighter-rouge">spark.mllib</code> provides a parallel implementation of FP-growth,
 a popular algorithm to mining frequent itemsets.</p>

 <h2 id="fp-growth">FP-growth</h2>

 <p>The FP-growth algorithm is described in the paper
 <a href="https://doi.org/10.1145/335191.335372">Han et al., Mining frequent patterns without candidate generation</a>,
 where &#8220;FP&#8221; stands for frequent pattern.
 Given a dataset of transactions, the first step of FP-growth is to calculate item frequencies and identify frequent items.
 Different from <a href="http://en.wikipedia.org/wiki/Apriori_algorithm">Apriori-like</a> algorithms designed for the same purpose,
 the second step of FP-growth uses a suffix tree (FP-tree) structure to encode transactions without generating candidate sets
 explicitly, which are usually expensive to generate.
 After the second step, the frequent itemsets can be extracted from the FP-tree.
 In <code class="language-plaintext highlighter-rouge">spark.mllib</code>, we implemented a parallel version of FP-growth called PFP,
 as described in <a href="https://doi.org/10.1145/1454008.1454027">Li et al., PFP: Parallel FP-growth for query recommendation</a>.
 PFP distributes the work of growing FP-trees based on the suffixes of transactions,
 and hence more scalable than a single-machine implementation.
 We refer users to the papers for more details.</p>

 <p><code class="language-plaintext highlighter-rouge">spark.mllib</code>&#8217;s FP-growth implementation takes the following (hyper-)parameters:</p>

 <ul>
   <li><code class="language-plaintext highlighter-rouge">minSupport</code>: the minimum support for an itemset to be identified as frequent.
 For example, if an item appears 3 out of 5 transactions, it has a support of 3/5=0.6.</li>
   <li><code class="language-plaintext highlighter-rouge">numPartitions</code>: the number of partitions used to distribute the work.</li>
 </ul>

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

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

     <p><a href="api/scala/org/apache/spark/mllib/fpm/FPGrowth.html"><code class="language-plaintext highlighter-rouge">FPGrowth</code></a> implements the
 FP-growth algorithm.
 It takes an <code class="language-plaintext highlighter-rouge">RDD</code> of transactions, where each transaction is an <code class="language-plaintext highlighter-rouge">Array</code> of items of a generic type.
 Calling <code class="language-plaintext highlighter-rouge">FPGrowth.run</code> with transactions returns an
 <a href="api/scala/org/apache/spark/mllib/fpm/FPGrowthModel.html"><code class="language-plaintext highlighter-rouge">FPGrowthModel</code></a>
 that stores the frequent itemsets with their frequencies.  The following
 example illustrates how to mine frequent itemsets and association rules
 (see <a href="mllib-frequent-pattern-mining.html#association-rules">Association
 Rules</a> for
 details) from <code class="language-plaintext highlighter-rouge">transactions</code>.</p>

     <p>Refer to the <a href="api/scala/org/apache/spark/mllib/fpm/FPGrowth.html"><code class="language-plaintext highlighter-rouge">FPGrowth</code> Scala docs</a> for details on the API.</p>

     <div class="highlight"><pre class="codehilite"><code><span class="k">import</span> <span class="nn">org.apache.spark.mllib.fpm.FPGrowth</span>
 <span class="k">import</span> <span class="nn">org.apache.spark.rdd.RDD</span>

 <span class="k">val</span> <span class="nv">data</span> <span class="k">=</span> <span class="nv">sc</span><span class="o">.</span><span class="py">textFile</span><span class="o">(</span><span class="s">"data/mllib/sample_fpgrowth.txt"</span><span class="o">)</span>

 <span class="k">val</span> <span class="nv">transactions</span><span class="k">:</span> <span class="kt">RDD</span><span class="o">[</span><span class="kt">Array</span><span class="o">[</span><span class="kt">String</span><span class="o">]]</span> <span class="k">=</span> <span class="nv">data</span><span class="o">.</span><span class="py">map</span><span class="o">(</span><span class="n">s</span> <span class="k">=&gt;</span> <span class="nv">s</span><span class="o">.</span><span class="py">trim</span><span class="o">.</span><span class="py">split</span><span class="o">(</span><span class="sc">' '</span><span class="o">))</span>

 <span class="k">val</span> <span class="nv">fpg</span> <span class="k">=</span> <span class="k">new</span> <span class="nc">FPGrowth</span><span class="o">()</span>
   <span class="o">.</span><span class="py">setMinSupport</span><span class="o">(</span><span class="mf">0.2</span><span class="o">)</span>
   <span class="o">.</span><span class="py">setNumPartitions</span><span class="o">(</span><span class="mi">10</span><span class="o">)</span>
 <span class="k">val</span> <span class="nv">model</span> <span class="k">=</span> <span class="nv">fpg</span><span class="o">.</span><span class="py">run</span><span class="o">(</span><span class="n">transactions</span><span class="o">)</span>

 <span class="nv">model</span><span class="o">.</span><span class="py">freqItemsets</span><span class="o">.</span><span class="py">collect</span><span class="o">().</span><span class="py">foreach</span> <span class="o">{</span> <span class="n">itemset</span> <span class="k">=&gt;</span>
   <span class="nf">println</span><span class="o">(</span><span class="n">s</span><span class="s">"${itemset.items.mkString("</span><span class="o">[</span><span class="err">"</span>, <span class="err">"</span>,<span class="err">"</span>, <span class="err">"</span><span class="o">]</span><span class="s">")},${itemset.freq}"</span><span class="o">)</span>
 <span class="o">}</span>

 <span class="k">val</span> <span class="nv">minConfidence</span> <span class="k">=</span> <span class="mf">0.8</span>
 <span class="nv">model</span><span class="o">.</span><span class="py">generateAssociationRules</span><span class="o">(</span><span class="n">minConfidence</span><span class="o">).</span><span class="py">collect</span><span class="o">().</span><span class="py">foreach</span> <span class="o">{</span> <span class="n">rule</span> <span class="k">=&gt;</span>
   <span class="nf">println</span><span class="o">(</span><span class="n">s</span><span class="s">"${rule.antecedent.mkString("</span><span class="o">[</span><span class="err">"</span>, <span class="err">"</span>,<span class="err">"</span>, <span class="err">"</span><span class="o">]</span><span class="s">")}=&gt; "</span> <span class="o">+</span>
     <span class="n">s</span><span class="s">"${rule.consequent .mkString("</span><span class="o">[</span><span class="err">"</span>, <span class="err">"</span>,<span class="err">"</span>, <span class="err">"</span><span class="o">]</span><span class="s">")},${rule.confidence}"</span><span class="o">)</span>
 <span class="o">}</span></code></pre></div>
     <div><small>Find full example code at "examples/src/main/scala/org/apache/spark/examples/mllib/SimpleFPGrowth.scala" in the Spark repo.</small></div>

   </div>

 <div data-lang="java">

     <p><a href="api/java/org/apache/spark/mllib/fpm/FPGrowth.html"><code class="language-plaintext highlighter-rouge">FPGrowth</code></a> implements the
 FP-growth algorithm.
 It takes a <code class="language-plaintext highlighter-rouge">JavaRDD</code> of transactions, where each transaction is an <code class="language-plaintext highlighter-rouge">Iterable</code> of items of a generic type.
 Calling <code class="language-plaintext highlighter-rouge">FPGrowth.run</code> with transactions returns an
 <a href="api/java/org/apache/spark/mllib/fpm/FPGrowthModel.html"><code class="language-plaintext highlighter-rouge">FPGrowthModel</code></a>
 that stores the frequent itemsets with their frequencies.  The following
 example illustrates how to mine frequent itemsets and association rules
 (see <a href="mllib-frequent-pattern-mining.html#association-rules">Association
 Rules</a> for
 details) from <code class="language-plaintext highlighter-rouge">transactions</code>.</p>

     <p>Refer to the <a href="api/java/org/apache/spark/mllib/fpm/FPGrowth.html"><code class="language-plaintext highlighter-rouge">FPGrowth</code> Java docs</a> for details on the API.</p>

     <div class="highlight"><pre class="codehilite"><code><span class="kn">import</span> <span class="nn">java.util.Arrays</span><span class="o">;</span>
 <span class="kn">import</span> <span class="nn">java.util.List</span><span class="o">;</span>

 <span class="kn">import</span> <span class="nn">org.apache.spark.api.java.JavaRDD</span><span class="o">;</span>
 <span class="kn">import</span> <span class="nn">org.apache.spark.api.java.JavaSparkContext</span><span class="o">;</span>
 <span class="kn">import</span> <span class="nn">org.apache.spark.mllib.fpm.AssociationRules</span><span class="o">;</span>
 <span class="kn">import</span> <span class="nn">org.apache.spark.mllib.fpm.FPGrowth</span><span class="o">;</span>
 <span class="kn">import</span> <span class="nn">org.apache.spark.mllib.fpm.FPGrowthModel</span><span class="o">;</span>

 <span class="nc">JavaRDD</span><span class="o">&lt;</span><span class="nc">String</span><span class="o">&gt;</span> <span class="n">data</span> <span class="o">=</span> <span class="n">sc</span><span class="o">.</span><span class="na">textFile</span><span class="o">(</span><span class="s">"data/mllib/sample_fpgrowth.txt"</span><span class="o">);</span>

 <span class="nc">JavaRDD</span><span class="o">&lt;</span><span class="nc">List</span><span class="o">&lt;</span><span class="nc">String</span><span class="o">&gt;&gt;</span> <span class="n">transactions</span> <span class="o">=</span> <span class="n">data</span><span class="o">.</span><span class="na">map</span><span class="o">(</span><span class="n">line</span> <span class="o">-&gt;</span> <span class="nc">Arrays</span><span class="o">.</span><span class="na">asList</span><span class="o">(</span><span class="n">line</span><span class="o">.</span><span class="na">split</span><span class="o">(</span><span class="s">" "</span><span class="o">)));</span>

 <span class="nc">FPGrowth</span> <span class="n">fpg</span> <span class="o">=</span> <span class="k">new</span> <span class="nc">FPGrowth</span><span class="o">()</span>
   <span class="o">.</span><span class="na">setMinSupport</span><span class="o">(</span><span class="mf">0.2</span><span class="o">)</span>
   <span class="o">.</span><span class="na">setNumPartitions</span><span class="o">(</span><span class="mi">10</span><span class="o">);</span>
 <span class="nc">FPGrowthModel</span><span class="o">&lt;</span><span class="nc">String</span><span class="o">&gt;</span> <span class="n">model</span> <span class="o">=</span> <span class="n">fpg</span><span class="o">.</span><span class="na">run</span><span class="o">(</span><span class="n">transactions</span><span class="o">);</span>

 <span class="k">for</span> <span class="o">(</span><span class="nc">FPGrowth</span><span class="o">.</span><span class="na">FreqItemset</span><span class="o">&lt;</span><span class="nc">String</span><span class="o">&gt;</span> <span class="nl">itemset:</span> <span class="n">model</span><span class="o">.</span><span class="na">freqItemsets</span><span class="o">().</span><span class="na">toJavaRDD</span><span class="o">().</span><span class="na">collect</span><span class="o">())</span> <span class="o">{</span>
   <span class="nc">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">"["</span> <span class="o">+</span> <span class="n">itemset</span><span class="o">.</span><span class="na">javaItems</span><span class="o">()</span> <span class="o">+</span> <span class="s">"], "</span> <span class="o">+</span> <span class="n">itemset</span><span class="o">.</span><span class="na">freq</span><span class="o">());</span>
 <span class="o">}</span>

 <span class="kt">double</span> <span class="n">minConfidence</span> <span class="o">=</span> <span class="mf">0.8</span><span class="o">;</span>
 <span class="k">for</span> <span class="o">(</span><span class="nc">AssociationRules</span><span class="o">.</span><span class="na">Rule</span><span class="o">&lt;</span><span class="nc">String</span><span class="o">&gt;</span> <span class="n">rule</span>
   <span class="o">:</span> <span class="n">model</span><span class="o">.</span><span class="na">generateAssociationRules</span><span class="o">(</span><span class="n">minConfidence</span><span class="o">).</span><span class="na">toJavaRDD</span><span class="o">().</span><span class="na">collect</span><span class="o">())</span> <span class="o">{</span>
   <span class="nc">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">rule</span><span class="o">.</span><span class="na">javaAntecedent</span><span class="o">()</span> <span class="o">+</span> <span class="s">" =&gt; "</span> <span class="o">+</span> <span class="n">rule</span><span class="o">.</span><span class="na">javaConsequent</span><span class="o">()</span> <span class="o">+</span> <span class="s">", "</span> <span class="o">+</span> <span class="n">rule</span><span class="o">.</span><span class="na">confidence</span><span class="o">());</span>
 <span class="o">}</span></code></pre></div>
     <div><small>Find full example code at "examples/src/main/java/org/apache/spark/examples/mllib/JavaSimpleFPGrowth.java" in the Spark repo.</small></div>

   </div>

 <div data-lang="python">

     <p><a href="api/python/reference/api/pyspark.mllib.fpm.FPGrowth.html"><code class="language-plaintext highlighter-rouge">FPGrowth</code></a> implements the
 FP-growth algorithm.
 It takes an <code class="language-plaintext highlighter-rouge">RDD</code> of transactions, where each transaction is an <code class="language-plaintext highlighter-rouge">List</code> of items of a generic type.
 Calling <code class="language-plaintext highlighter-rouge">FPGrowth.train</code> with transactions returns an
 <a href="api/python/reference/api/pyspark.mllib.fpm.FPGrowthModel.html"><code class="language-plaintext highlighter-rouge">FPGrowthModel</code></a>
 that stores the frequent itemsets with their frequencies.</p>

     <p>Refer to the <a href="api/python/reference/api/pyspark.mllib.fpm.FPGrowth.html"><code class="language-plaintext highlighter-rouge">FPGrowth</code> Python docs</a> for more details on the API.</p>

     <div class="highlight"><pre class="codehilite"><code><span class="kn">from</span> <span class="nn">pyspark.mllib.fpm</span> <span class="kn">import</span> <span class="n">FPGrowth</span>

 <span class="n">data</span> <span class="o">=</span> <span class="n">sc</span><span class="p">.</span><span class="n">textFile</span><span class="p">(</span><span class="s">"data/mllib/sample_fpgrowth.txt"</span><span class="p">)</span>
 <span class="n">transactions</span> <span class="o">=</span> <span class="n">data</span><span class="p">.</span><span class="nb">map</span><span class="p">(</span><span class="k">lambda</span> <span class="n">line</span><span class="p">:</span> <span class="n">line</span><span class="p">.</span><span class="n">strip</span><span class="p">().</span><span class="n">split</span><span class="p">(</span><span class="s">' '</span><span class="p">))</span>
 <span class="n">model</span> <span class="o">=</span> <span class="n">FPGrowth</span><span class="p">.</span><span class="n">train</span><span class="p">(</span><span class="n">transactions</span><span class="p">,</span> <span class="n">minSupport</span><span class="o">=</span><span class="mf">0.2</span><span class="p">,</span> <span class="n">numPartitions</span><span class="o">=</span><span class="mi">10</span><span class="p">)</span>
 <span class="n">result</span> <span class="o">=</span> <span class="n">model</span><span class="p">.</span><span class="n">freqItemsets</span><span class="p">().</span><span class="n">collect</span><span class="p">()</span>
 <span class="k">for</span> <span class="n">fi</span> <span class="ow">in</span> <span class="n">result</span><span class="p">:</span>
     <span class="k">print</span><span class="p">(</span><span class="n">fi</span><span class="p">)</span></code></pre></div>
     <div><small>Find full example code at "examples/src/main/python/mllib/fpgrowth_example.py" in the Spark repo.</small></div>

   </div>

 </div>

 <h2 id="association-rules">Association Rules</h2>

 <div class="codetabs">
 <div data-lang="scala">
     <p><a href="api/scala/org/apache/spark/mllib/fpm/AssociationRules.html">AssociationRules</a>
 implements a parallel rule generation algorithm for constructing rules
 that have a single item as the consequent.</p>

     <p>Refer to the <a href="api/java/org/apache/spark/mllib/fpm/AssociationRules.html"><code class="language-plaintext highlighter-rouge">AssociationRules</code> Scala docs</a> for details on the API.</p>

     <div class="highlight"><pre class="codehilite"><code><span class="k">import</span> <span class="nn">org.apache.spark.mllib.fpm.AssociationRules</span>
 <span class="k">import</span> <span class="nn">org.apache.spark.mllib.fpm.FPGrowth.FreqItemset</span>

 <span class="k">val</span> <span class="nv">freqItemsets</span> <span class="k">=</span> <span class="nv">sc</span><span class="o">.</span><span class="py">parallelize</span><span class="o">(</span><span class="nc">Seq</span><span class="o">(</span>
   <span class="k">new</span> <span class="nc">FreqItemset</span><span class="o">(</span><span class="nc">Array</span><span class="o">(</span><span class="s">"a"</span><span class="o">),</span> <span class="mi">15L</span><span class="o">),</span>
   <span class="k">new</span> <span class="nc">FreqItemset</span><span class="o">(</span><span class="nc">Array</span><span class="o">(</span><span class="s">"b"</span><span class="o">),</span> <span class="mi">35L</span><span class="o">),</span>
   <span class="k">new</span> <span class="nc">FreqItemset</span><span class="o">(</span><span class="nc">Array</span><span class="o">(</span><span class="s">"a"</span><span class="o">,</span> <span class="s">"b"</span><span class="o">),</span> <span class="mi">12L</span><span class="o">)</span>
 <span class="o">))</span>

 <span class="k">val</span> <span class="nv">ar</span> <span class="k">=</span> <span class="k">new</span> <span class="nc">AssociationRules</span><span class="o">()</span>
   <span class="o">.</span><span class="py">setMinConfidence</span><span class="o">(</span><span class="mf">0.8</span><span class="o">)</span>
 <span class="k">val</span> <span class="nv">results</span> <span class="k">=</span> <span class="nv">ar</span><span class="o">.</span><span class="py">run</span><span class="o">(</span><span class="n">freqItemsets</span><span class="o">)</span>

 <span class="nv">results</span><span class="o">.</span><span class="py">collect</span><span class="o">().</span><span class="py">foreach</span> <span class="o">{</span> <span class="n">rule</span> <span class="k">=&gt;</span>
 <span class="nf">println</span><span class="o">(</span><span class="n">s</span><span class="s">"[${rule.antecedent.mkString("</span><span class="o">,</span><span class="s">")}=&gt;${rule.consequent.mkString("</span><span class="o">,</span><span class="s">")} ]"</span> <span class="o">+</span>
     <span class="n">s</span><span class="s">" ${rule.confidence}"</span><span class="o">)</span>
 <span class="o">}</span></code></pre></div>
     <div><small>Find full example code at "examples/src/main/scala/org/apache/spark/examples/mllib/AssociationRulesExample.scala" in the Spark repo.</small></div>

   </div>

 <div data-lang="java">
     <p><a href="api/java/org/apache/spark/mllib/fpm/AssociationRules.html">AssociationRules</a>
 implements a parallel rule generation algorithm for constructing rules
 that have a single item as the consequent.</p>

     <p>Refer to the <a href="api/java/org/apache/spark/mllib/fpm/AssociationRules.html"><code class="language-plaintext highlighter-rouge">AssociationRules</code> Java docs</a> for details on the API.</p>

     <div class="highlight"><pre class="codehilite"><code><span class="kn">import</span> <span class="nn">java.util.Arrays</span><span class="o">;</span>

 <span class="kn">import</span> <span class="nn">org.apache.spark.api.java.JavaRDD</span><span class="o">;</span>
 <span class="kn">import</span> <span class="nn">org.apache.spark.api.java.JavaSparkContext</span><span class="o">;</span>
 <span class="kn">import</span> <span class="nn">org.apache.spark.mllib.fpm.AssociationRules</span><span class="o">;</span>
 <span class="kn">import</span> <span class="nn">org.apache.spark.mllib.fpm.FPGrowth</span><span class="o">;</span>
 <span class="kn">import</span> <span class="nn">org.apache.spark.mllib.fpm.FPGrowth.FreqItemset</span><span class="o">;</span>

 <span class="nc">JavaRDD</span><span class="o">&lt;</span><span class="nc">FPGrowth</span><span class="o">.</span><span class="na">FreqItemset</span><span class="o">&lt;</span><span class="nc">String</span><span class="o">&gt;&gt;</span> <span class="n">freqItemsets</span> <span class="o">=</span> <span class="n">sc</span><span class="o">.</span><span class="na">parallelize</span><span class="o">(</span><span class="nc">Arrays</span><span class="o">.</span><span class="na">asList</span><span class="o">(</span>
   <span class="k">new</span> <span class="nc">FreqItemset</span><span class="o">&lt;&gt;(</span><span class="k">new</span> <span class="nc">String</span><span class="o">[]</span> <span class="o">{</span><span class="s">"a"</span><span class="o">},</span> <span class="mi">15L</span><span class="o">),</span>
   <span class="k">new</span> <span class="nc">FreqItemset</span><span class="o">&lt;&gt;(</span><span class="k">new</span> <span class="nc">String</span><span class="o">[]</span> <span class="o">{</span><span class="s">"b"</span><span class="o">},</span> <span class="mi">35L</span><span class="o">),</span>
   <span class="k">new</span> <span class="nc">FreqItemset</span><span class="o">&lt;&gt;(</span><span class="k">new</span> <span class="nc">String</span><span class="o">[]</span> <span class="o">{</span><span class="s">"a"</span><span class="o">,</span> <span class="s">"b"</span><span class="o">},</span> <span class="mi">12L</span><span class="o">)</span>
 <span class="o">));</span>

 <span class="nc">AssociationRules</span> <span class="n">arules</span> <span class="o">=</span> <span class="k">new</span> <span class="nc">AssociationRules</span><span class="o">()</span>
   <span class="o">.</span><span class="na">setMinConfidence</span><span class="o">(</span><span class="mf">0.8</span><span class="o">);</span>
 <span class="nc">JavaRDD</span><span class="o">&lt;</span><span class="nc">AssociationRules</span><span class="o">.</span><span class="na">Rule</span><span class="o">&lt;</span><span class="nc">String</span><span class="o">&gt;&gt;</span> <span class="n">results</span> <span class="o">=</span> <span class="n">arules</span><span class="o">.</span><span class="na">run</span><span class="o">(</span><span class="n">freqItemsets</span><span class="o">);</span>

 <span class="k">for</span> <span class="o">(</span><span class="nc">AssociationRules</span><span class="o">.</span><span class="na">Rule</span><span class="o">&lt;</span><span class="nc">String</span><span class="o">&gt;</span> <span class="n">rule</span> <span class="o">:</span> <span class="n">results</span><span class="o">.</span><span class="na">collect</span><span class="o">())</span> <span class="o">{</span>
   <span class="nc">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">rule</span><span class="o">.</span><span class="na">javaAntecedent</span><span class="o">()</span> <span class="o">+</span> <span class="s">" =&gt; "</span> <span class="o">+</span> <span class="n">rule</span><span class="o">.</span><span class="na">javaConsequent</span><span class="o">()</span> <span class="o">+</span> <span class="s">", "</span> <span class="o">+</span> <span class="n">rule</span><span class="o">.</span><span class="na">confidence</span><span class="o">());</span>
 <span class="o">}</span></code></pre></div>
     <div><small>Find full example code at "examples/src/main/java/org/apache/spark/examples/mllib/JavaAssociationRulesExample.java" in the Spark repo.</small></div>

   </div>
 </div>

 <h2 id="prefixspan">PrefixSpan</h2>

 <p>PrefixSpan is a sequential pattern mining algorithm described in
 <a href="https://doi.org/10.1109%2FTKDE.2004.77">Pei et al., Mining Sequential Patterns by Pattern-Growth: The
 PrefixSpan Approach</a>. We refer
 the reader to the referenced paper for formalizing the sequential
 pattern mining problem.</p>

 <p><code class="language-plaintext highlighter-rouge">spark.mllib</code>&#8217;s PrefixSpan implementation takes the following parameters:</p>

 <ul>
   <li><code class="language-plaintext highlighter-rouge">minSupport</code>: the minimum support required to be considered a frequent
 sequential pattern.</li>
   <li><code class="language-plaintext highlighter-rouge">maxPatternLength</code>: the maximum length of a frequent sequential
 pattern. Any frequent pattern exceeding this length will not be
 included in the results.</li>
   <li><code class="language-plaintext highlighter-rouge">maxLocalProjDBSize</code>: the maximum number of items allowed in a
 prefix-projected database before local iterative processing of the
 projected database begins. This parameter should be tuned with respect
 to the size of your executors.</li>
 </ul>

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

 <p>The following example illustrates PrefixSpan running on the sequences
 (using same notation as Pei et al):</p>

 <div class="language-plaintext highlighter-rouge"><div class="highlight"><pre class="highlight"><code>  &lt;(12)3&gt;
   &lt;1(32)(12)&gt;
   &lt;(12)5&gt;
   &lt;6&gt;
 </code></pre></div></div>

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

     <p><a href="api/scala/org/apache/spark/mllib/fpm/PrefixSpan.html"><code class="language-plaintext highlighter-rouge">PrefixSpan</code></a> implements the
 PrefixSpan algorithm.
 Calling <code class="language-plaintext highlighter-rouge">PrefixSpan.run</code> returns a
 <a href="api/scala/org/apache/spark/mllib/fpm/PrefixSpanModel.html"><code class="language-plaintext highlighter-rouge">PrefixSpanModel</code></a>
 that stores the frequent sequences with their frequencies.</p>

     <p>Refer to the <a href="api/scala/org/apache/spark/mllib/fpm/PrefixSpan.html"><code class="language-plaintext highlighter-rouge">PrefixSpan</code> Scala docs</a> and <a href="api/scala/org/apache/spark/mllib/fpm/PrefixSpanModel.html"><code class="language-plaintext highlighter-rouge">PrefixSpanModel</code> Scala docs</a> for details on the API.</p>

     <div class="highlight"><pre class="codehilite"><code><span class="k">import</span> <span class="nn">org.apache.spark.mllib.fpm.PrefixSpan</span>

 <span class="k">val</span> <span class="nv">sequences</span> <span class="k">=</span> <span class="nv">sc</span><span class="o">.</span><span class="py">parallelize</span><span class="o">(</span><span class="nc">Seq</span><span class="o">(</span>
   <span class="nc">Array</span><span class="o">(</span><span class="nc">Array</span><span class="o">(</span><span class="mi">1</span><span class="o">,</span> <span class="mi">2</span><span class="o">),</span> <span class="nc">Array</span><span class="o">(</span><span class="mi">3</span><span class="o">)),</span>
   <span class="nc">Array</span><span class="o">(</span><span class="nc">Array</span><span class="o">(</span><span class="mi">1</span><span class="o">),</span> <span class="nc">Array</span><span class="o">(</span><span class="mi">3</span><span class="o">,</span> <span class="mi">2</span><span class="o">),</span> <span class="nc">Array</span><span class="o">(</span><span class="mi">1</span><span class="o">,</span> <span class="mi">2</span><span class="o">)),</span>
   <span class="nc">Array</span><span class="o">(</span><span class="nc">Array</span><span class="o">(</span><span class="mi">1</span><span class="o">,</span> <span class="mi">2</span><span class="o">),</span> <span class="nc">Array</span><span class="o">(</span><span class="mi">5</span><span class="o">)),</span>
   <span class="nc">Array</span><span class="o">(</span><span class="nc">Array</span><span class="o">(</span><span class="mi">6</span><span class="o">))</span>
 <span class="o">),</span> <span class="mi">2</span><span class="o">).</span><span class="py">cache</span><span class="o">()</span>
 <span class="k">val</span> <span class="nv">prefixSpan</span> <span class="k">=</span> <span class="k">new</span> <span class="nc">PrefixSpan</span><span class="o">()</span>
   <span class="o">.</span><span class="py">setMinSupport</span><span class="o">(</span><span class="mf">0.5</span><span class="o">)</span>
   <span class="o">.</span><span class="py">setMaxPatternLength</span><span class="o">(</span><span class="mi">5</span><span class="o">)</span>
 <span class="k">val</span> <span class="nv">model</span> <span class="k">=</span> <span class="nv">prefixSpan</span><span class="o">.</span><span class="py">run</span><span class="o">(</span><span class="n">sequences</span><span class="o">)</span>
 <span class="nv">model</span><span class="o">.</span><span class="py">freqSequences</span><span class="o">.</span><span class="py">collect</span><span class="o">().</span><span class="py">foreach</span> <span class="o">{</span> <span class="n">freqSequence</span> <span class="k">=&gt;</span>
   <span class="nf">println</span><span class="o">(</span>
     <span class="n">s</span><span class="s">"${freqSequence.sequence.map(_.mkString("</span><span class="o">[</span><span class="err">"</span>, <span class="err">"</span>, <span class="err">"</span>, <span class="err">"</span><span class="o">]</span><span class="s">")).mkString("</span><span class="o">[</span><span class="err">"</span>, <span class="err">"</span>, <span class="err">"</span>, <span class="err">"</span><span class="o">]</span><span class="s">")},"</span> <span class="o">+</span>
       <span class="n">s</span><span class="s">" ${freqSequence.freq}"</span><span class="o">)</span>
 <span class="o">}</span></code></pre></div>
     <div><small>Find full example code at "examples/src/main/scala/org/apache/spark/examples/mllib/PrefixSpanExample.scala" in the Spark repo.</small></div>

   </div>

 <div data-lang="java">

     <p><a href="api/java/org/apache/spark/mllib/fpm/PrefixSpan.html"><code class="language-plaintext highlighter-rouge">PrefixSpan</code></a> implements the
 PrefixSpan algorithm.
 Calling <code class="language-plaintext highlighter-rouge">PrefixSpan.run</code> returns a
 <a href="api/java/org/apache/spark/mllib/fpm/PrefixSpanModel.html"><code class="language-plaintext highlighter-rouge">PrefixSpanModel</code></a>
 that stores the frequent sequences with their frequencies.</p>

     <p>Refer to the <a href="api/java/org/apache/spark/mllib/fpm/PrefixSpan.html"><code class="language-plaintext highlighter-rouge">PrefixSpan</code> Java docs</a> and <a href="api/java/org/apache/spark/mllib/fpm/PrefixSpanModel.html"><code class="language-plaintext highlighter-rouge">PrefixSpanModel</code> Java docs</a> for details on the API.</p>

     <div class="highlight"><pre class="codehilite"><code><span class="kn">import</span> <span class="nn">java.util.Arrays</span><span class="o">;</span>
 <span class="kn">import</span> <span class="nn">java.util.List</span><span class="o">;</span>

 <span class="kn">import</span> <span class="nn">org.apache.spark.mllib.fpm.PrefixSpan</span><span class="o">;</span>
 <span class="kn">import</span> <span class="nn">org.apache.spark.mllib.fpm.PrefixSpanModel</span><span class="o">;</span>

 <span class="nc">JavaRDD</span><span class="o">&lt;</span><span class="nc">List</span><span class="o">&lt;</span><span class="nc">List</span><span class="o">&lt;</span><span class="nc">Integer</span><span class="o">&gt;&gt;&gt;</span> <span class="n">sequences</span> <span class="o">=</span> <span class="n">sc</span><span class="o">.</span><span class="na">parallelize</span><span class="o">(</span><span class="nc">Arrays</span><span class="o">.</span><span class="na">asList</span><span class="o">(</span>
   <span class="nc">Arrays</span><span class="o">.</span><span class="na">asList</span><span class="o">(</span><span class="nc">Arrays</span><span class="o">.</span><span class="na">asList</span><span class="o">(</span><span class="mi">1</span><span class="o">,</span> <span class="mi">2</span><span class="o">),</span> <span class="nc">Arrays</span><span class="o">.</span><span class="na">asList</span><span class="o">(</span><span class="mi">3</span><span class="o">)),</span>
   <span class="nc">Arrays</span><span class="o">.</span><span class="na">asList</span><span class="o">(</span><span class="nc">Arrays</span><span class="o">.</span><span class="na">asList</span><span class="o">(</span><span class="mi">1</span><span class="o">),</span> <span class="nc">Arrays</span><span class="o">.</span><span class="na">asList</span><span class="o">(</span><span class="mi">3</span><span class="o">,</span> <span class="mi">2</span><span class="o">),</span> <span class="nc">Arrays</span><span class="o">.</span><span class="na">asList</span><span class="o">(</span><span class="mi">1</span><span class="o">,</span> <span class="mi">2</span><span class="o">)),</span>
   <span class="nc">Arrays</span><span class="o">.</span><span class="na">asList</span><span class="o">(</span><span class="nc">Arrays</span><span class="o">.</span><span class="na">asList</span><span class="o">(</span><span class="mi">1</span><span class="o">,</span> <span class="mi">2</span><span class="o">),</span> <span class="nc">Arrays</span><span class="o">.</span><span class="na">asList</span><span class="o">(</span><span class="mi">5</span><span class="o">)),</span>
   <span class="nc">Arrays</span><span class="o">.</span><span class="na">asList</span><span class="o">(</span><span class="nc">Arrays</span><span class="o">.</span><span class="na">asList</span><span class="o">(</span><span class="mi">6</span><span class="o">))</span>
 <span class="o">),</span> <span class="mi">2</span><span class="o">);</span>
 <span class="nc">PrefixSpan</span> <span class="n">prefixSpan</span> <span class="o">=</span> <span class="k">new</span> <span class="nc">PrefixSpan</span><span class="o">()</span>
   <span class="o">.</span><span class="na">setMinSupport</span><span class="o">(</span><span class="mf">0.5</span><span class="o">)</span>
   <span class="o">.</span><span class="na">setMaxPatternLength</span><span class="o">(</span><span class="mi">5</span><span class="o">);</span>
 <span class="nc">PrefixSpanModel</span><span class="o">&lt;</span><span class="nc">Integer</span><span class="o">&gt;</span> <span class="n">model</span> <span class="o">=</span> <span class="n">prefixSpan</span><span class="o">.</span><span class="na">run</span><span class="o">(</span><span class="n">sequences</span><span class="o">);</span>
 <span class="k">for</span> <span class="o">(</span><span class="nc">PrefixSpan</span><span class="o">.</span><span class="na">FreqSequence</span><span class="o">&lt;</span><span class="nc">Integer</span><span class="o">&gt;</span> <span class="nl">freqSeq:</span> <span class="n">model</span><span class="o">.</span><span class="na">freqSequences</span><span class="o">().</span><span class="na">toJavaRDD</span><span class="o">().</span><span class="na">collect</span><span class="o">())</span> <span class="o">{</span>
   <span class="nc">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">freqSeq</span><span class="o">.</span><span class="na">javaSequence</span><span class="o">()</span> <span class="o">+</span> <span class="s">", "</span> <span class="o">+</span> <span class="n">freqSeq</span><span class="o">.</span><span class="na">freq</span><span class="o">());</span>
 <span class="o">}</span></code></pre></div>
     <div><small>Find full example code at "examples/src/main/java/org/apache/spark/examples/mllib/JavaPrefixSpanExample.java" in the Spark repo.</small></div>

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