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                         <h1 class="title">Frequent Pattern Mining</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.</p>

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

 <ul id="markdown-toc">
   <li><a href="#fp-growth" id="markdown-toc-fp-growth">FP-Growth</a></li>
   <li><a href="#prefixspan" id="markdown-toc-prefixspan">PrefixSpan</a></li>
 </ul>

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

 <p>The FP-growth algorithm is described in the paper
 <a href="http://dx.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>spark.mllib</code>, we implemented a parallel version of FP-growth called PFP,
 as described in <a href="http://dx.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 is more scalable than a single-machine implementation.
 We refer users to the papers for more details.</p>

 <p><code>spark.ml</code>&#8217;s FP-growth implementation takes the following (hyper-)parameters:</p>

 <ul>
   <li><code>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>minConfidence</code>: minimum confidence for generating Association Rule. Confidence is an indication of how often an
 association rule has been found to be true. For example, if in the transactions itemset <code>X</code> appears 4 times, <code>X</code>
 and <code>Y</code> co-occur only 2 times, the confidence for the rule <code>X =&gt; Y</code> is then 2/4 = 0.5. The parameter will not
 affect the mining for frequent itemsets, but specify the minimum confidence for generating association rules
 from frequent itemsets.</li>
   <li><code>numPartitions</code>: the number of partitions used to distribute the work. By default the param is not set, and
 number of partitions of the input dataset is used.</li>
 </ul>

 <p>The <code>FPGrowthModel</code> provides:</p>

 <ul>
   <li><code>freqItemsets</code>: frequent itemsets in the format of DataFrame(&#8220;items&#8221;[Array], &#8220;freq&#8221;[Long])</li>
   <li><code>associationRules</code>: association rules generated with confidence above <code>minConfidence</code>, in the format of
 DataFrame(&#8220;antecedent&#8221;[Array], &#8220;consequent&#8221;[Array], &#8220;confidence&#8221;[Double]).</li>
   <li><code>transform</code>: For each transaction in <code>itemsCol</code>, the <code>transform</code> method will compare its items against the antecedents
 of each association rule. If the record contains all the antecedents of a specific association rule, the rule
 will be considered as applicable and its consequents will be added to the prediction result. The transform
 method will summarize the consequents from all the applicable rules as prediction. The prediction column has
 the same data type as <code>itemsCol</code> and does not contain existing items in the <code>itemsCol</code>.</li>
 </ul>

 <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.fpm.FPGrowth">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.fpm.FPGrowth</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">createDataset</span><span class="o">(</span><span class="nc">Seq</span><span class="o">(</span>
   <span class="s">&quot;1 2 5&quot;</span><span class="o">,</span>
   <span class="s">&quot;1 2 3 5&quot;</span><span class="o">,</span>
   <span class="s">&quot;1 2&quot;</span><span class="o">)</span>
 <span class="o">).</span><span class="n">map</span><span class="o">(</span><span class="n">t</span> <span class="k">=&gt;</span> <span class="n">t</span><span class="o">.</span><span class="n">split</span><span class="o">(</span><span class="s">&quot; &quot;</span><span class="o">)).</span><span class="n">toDF</span><span class="o">(</span><span class="s">&quot;items&quot;</span><span class="o">)</span>

 <span class="k">val</span> <span class="n">fpgrowth</span> <span class="k">=</span> <span class="k">new</span> <span class="nc">FPGrowth</span><span class="o">().</span><span class="n">setItemsCol</span><span class="o">(</span><span class="s">&quot;items&quot;</span><span class="o">).</span><span class="n">setMinSupport</span><span class="o">(</span><span class="mf">0.5</span><span class="o">).</span><span class="n">setMinConfidence</span><span class="o">(</span><span class="mf">0.6</span><span class="o">)</span>
 <span class="k">val</span> <span class="n">model</span> <span class="k">=</span> <span class="n">fpgrowth</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">// Display frequent itemsets.</span>
 <span class="n">model</span><span class="o">.</span><span class="n">freqItemsets</span><span class="o">.</span><span class="n">show</span><span class="o">()</span>

 <span class="c1">// Display generated association rules.</span>
 <span class="n">model</span><span class="o">.</span><span class="n">associationRules</span><span class="o">.</span><span class="n">show</span><span class="o">()</span>

 <span class="c1">// transform examines the input items against all the association rules and summarize the</span>
 <span class="c1">// consequents as prediction</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">show</span><span class="o">()</span>
 </pre></div>
     <div><small>Find full example code at "examples/src/main/scala/org/apache/spark/examples/ml/FPGrowthExample.scala" in the Spark repo.</small></div>
   </div>

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

     <div class="highlight"><pre><span></span><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.ml.fpm.FPGrowth</span><span class="o">;</span>
 <span class="kn">import</span> <span class="nn">org.apache.spark.ml.fpm.FPGrowthModel</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.RowFactory</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="kn">import</span> <span class="nn">org.apache.spark.sql.types.*</span><span class="o">;</span>

 <span class="n">List</span><span class="o">&lt;</span><span class="n">Row</span><span class="o">&gt;</span> <span class="n">data</span> <span class="o">=</span> <span class="n">Arrays</span><span class="o">.</span><span class="na">asList</span><span class="o">(</span>
   <span class="n">RowFactory</span><span class="o">.</span><span class="na">create</span><span class="o">(</span><span class="n">Arrays</span><span class="o">.</span><span class="na">asList</span><span class="o">(</span><span class="s">&quot;1 2 5&quot;</span><span class="o">.</span><span class="na">split</span><span class="o">(</span><span class="s">&quot; &quot;</span><span class="o">))),</span>
   <span class="n">RowFactory</span><span class="o">.</span><span class="na">create</span><span class="o">(</span><span class="n">Arrays</span><span class="o">.</span><span class="na">asList</span><span class="o">(</span><span class="s">&quot;1 2 3 5&quot;</span><span class="o">.</span><span class="na">split</span><span class="o">(</span><span class="s">&quot; &quot;</span><span class="o">))),</span>
   <span class="n">RowFactory</span><span class="o">.</span><span class="na">create</span><span class="o">(</span><span class="n">Arrays</span><span class="o">.</span><span class="na">asList</span><span class="o">(</span><span class="s">&quot;1 2&quot;</span><span class="o">.</span><span class="na">split</span><span class="o">(</span><span class="s">&quot; &quot;</span><span class="o">)))</span>
 <span class="o">);</span>
 <span class="n">StructType</span> <span class="n">schema</span> <span class="o">=</span> <span class="k">new</span> <span class="n">StructType</span><span class="o">(</span><span class="k">new</span> <span class="n">StructField</span><span class="o">[]{</span> <span class="k">new</span> <span class="n">StructField</span><span class="o">(</span>
   <span class="s">&quot;items&quot;</span><span class="o">,</span> <span class="k">new</span> <span class="n">ArrayType</span><span class="o">(</span><span class="n">DataTypes</span><span class="o">.</span><span class="na">StringType</span><span class="o">,</span> <span class="kc">true</span><span class="o">),</span> <span class="kc">false</span><span class="o">,</span> <span class="n">Metadata</span><span class="o">.</span><span class="na">empty</span><span class="o">())</span>
 <span class="o">});</span>
 <span class="n">Dataset</span><span class="o">&lt;</span><span class="n">Row</span><span class="o">&gt;</span> <span class="n">itemsDF</span> <span class="o">=</span> <span class="n">spark</span><span class="o">.</span><span class="na">createDataFrame</span><span class="o">(</span><span class="n">data</span><span class="o">,</span> <span class="n">schema</span><span class="o">);</span>

 <span class="n">FPGrowthModel</span> <span class="n">model</span> <span class="o">=</span> <span class="k">new</span> <span class="n">FPGrowth</span><span class="o">()</span>
   <span class="o">.</span><span class="na">setItemsCol</span><span class="o">(</span><span class="s">&quot;items&quot;</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">setMinConfidence</span><span class="o">(</span><span class="mf">0.6</span><span class="o">)</span>
   <span class="o">.</span><span class="na">fit</span><span class="o">(</span><span class="n">itemsDF</span><span class="o">);</span>

 <span class="c1">// Display frequent itemsets.</span>
 <span class="n">model</span><span class="o">.</span><span class="na">freqItemsets</span><span class="o">().</span><span class="na">show</span><span class="o">();</span>

 <span class="c1">// Display generated association rules.</span>
 <span class="n">model</span><span class="o">.</span><span class="na">associationRules</span><span class="o">().</span><span class="na">show</span><span class="o">();</span>

 <span class="c1">// transform examines the input items against all the association rules and summarize the</span>
 <span class="c1">// consequents as prediction</span>
 <span class="n">model</span><span class="o">.</span><span class="na">transform</span><span class="o">(</span><span class="n">itemsDF</span><span class="o">).</span><span class="na">show</span><span class="o">();</span>
 </pre></div>
     <div><small>Find full example code at "examples/src/main/java/org/apache/spark/examples/ml/JavaFPGrowthExample.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.fpm.FPGrowth">Python API docs</a> for more details.</p>

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

 <span class="n">df</span> <span class="o">=</span> <span class="n">spark</span><span class="o">.</span><span class="n">createDataFrame</span><span class="p">([</span>
     <span class="p">(</span><span class="mi">0</span><span class="p">,</span> <span class="p">[</span><span class="mi">1</span><span class="p">,</span> <span class="mi">2</span><span class="p">,</span> <span class="mi">5</span><span class="p">]),</span>
     <span class="p">(</span><span class="mi">1</span><span class="p">,</span> <span class="p">[</span><span class="mi">1</span><span class="p">,</span> <span class="mi">2</span><span class="p">,</span> <span class="mi">3</span><span class="p">,</span> <span class="mi">5</span><span class="p">]),</span>
     <span class="p">(</span><span class="mi">2</span><span class="p">,</span> <span class="p">[</span><span class="mi">1</span><span class="p">,</span> <span class="mi">2</span><span class="p">])</span>
 <span class="p">],</span> <span class="p">[</span><span class="s2">&quot;id&quot;</span><span class="p">,</span> <span class="s2">&quot;items&quot;</span><span class="p">])</span>

 <span class="n">fpGrowth</span> <span class="o">=</span> <span class="n">FPGrowth</span><span class="p">(</span><span class="n">itemsCol</span><span class="o">=</span><span class="s2">&quot;items&quot;</span><span class="p">,</span> <span class="n">minSupport</span><span class="o">=</span><span class="mf">0.5</span><span class="p">,</span> <span class="n">minConfidence</span><span class="o">=</span><span class="mf">0.6</span><span class="p">)</span>
 <span class="n">model</span> <span class="o">=</span> <span class="n">fpGrowth</span><span class="o">.</span><span class="n">fit</span><span class="p">(</span><span class="n">df</span><span class="p">)</span>

 <span class="c1"># Display frequent itemsets.</span>
 <span class="n">model</span><span class="o">.</span><span class="n">freqItemsets</span><span class="o">.</span><span class="n">show</span><span class="p">()</span>

 <span class="c1"># Display generated association rules.</span>
 <span class="n">model</span><span class="o">.</span><span class="n">associationRules</span><span class="o">.</span><span class="n">show</span><span class="p">()</span>

 <span class="c1"># transform examines the input items against all the association rules and summarize the</span>
 <span class="c1"># consequents as prediction</span>
 <span class="n">model</span><span class="o">.</span><span class="n">transform</span><span class="p">(</span><span class="n">df</span><span class="p">)</span><span class="o">.</span><span class="n">show</span><span class="p">()</span>
 </pre></div>
     <div><small>Find full example code at "examples/src/main/python/ml/fpgrowth_example.py" in the Spark repo.</small></div>
   </div>

 <div data-lang="r">

     <p>Refer to the <a href="api/R/spark.fpGrowth.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> selectExpr<span class="p">(</span>createDataFrame<span class="p">(</span><span class="kt">data.frame</span><span class="p">(</span>rawItems <span class="o">=</span> <span class="kt">c</span><span class="p">(</span>
   <span class="s">&quot;1,2,5&quot;</span><span class="p">,</span> <span class="s">&quot;1,2,3,5&quot;</span><span class="p">,</span> <span class="s">&quot;1,2&quot;</span>
 <span class="p">))),</span> <span class="s">&quot;split(rawItems, &#39;,&#39;) AS items&quot;</span><span class="p">)</span>

 fpm <span class="o">&lt;-</span> spark.fpGrowth<span class="p">(</span>df<span class="p">,</span> itemsCol<span class="o">=</span><span class="s">&quot;items&quot;</span><span class="p">,</span> minSupport<span class="o">=</span><span class="m">0.5</span><span class="p">,</span> minConfidence<span class="o">=</span><span class="m">0.6</span><span class="p">)</span>

 <span class="c1"># Extracting frequent itemsets</span>

 spark.freqItemsets<span class="p">(</span>fpm<span class="p">)</span>

 <span class="c1"># Extracting association rules</span>

 spark.associationRules<span class="p">(</span>fpm<span class="p">)</span>

 <span class="c1"># Predict uses association rules to and combines possible consequents</span>

 predict<span class="p">(</span>fpm<span class="p">,</span> df<span class="p">)</span>
 </pre></div>
     <div><small>Find full example code at "examples/src/main/r/ml/fpm.R" 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="http://dx.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>spark.ml</code>&#8217;s PrefixSpan implementation takes the following parameters:</p>

 <ul>
   <li><code>minSupport</code>: the minimum support required to be considered a frequent
 sequential pattern.</li>
   <li><code>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>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>
   <li><code>sequenceCol</code>: the name of the sequence column in dataset (default &#8220;sequence&#8221;), rows with
 nulls in this column are ignored.</li>
 </ul>

 <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.fpm.PrefixSpan">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.fpm.PrefixSpan</span>

 <span class="k">val</span> <span class="n">smallTestData</span> <span class="k">=</span> <span class="nc">Seq</span><span class="o">(</span>
   <span class="nc">Seq</span><span class="o">(</span><span class="nc">Seq</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">Seq</span><span class="o">(</span><span class="mi">3</span><span class="o">)),</span>
   <span class="nc">Seq</span><span class="o">(</span><span class="nc">Seq</span><span class="o">(</span><span class="mi">1</span><span class="o">),</span> <span class="nc">Seq</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">Seq</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">Seq</span><span class="o">(</span><span class="nc">Seq</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">Seq</span><span class="o">(</span><span class="mi">5</span><span class="o">)),</span>
   <span class="nc">Seq</span><span class="o">(</span><span class="nc">Seq</span><span class="o">(</span><span class="mi">6</span><span class="o">)))</span>

 <span class="k">val</span> <span class="n">df</span> <span class="k">=</span> <span class="n">smallTestData</span><span class="o">.</span><span class="n">toDF</span><span class="o">(</span><span class="s">&quot;sequence&quot;</span><span class="o">)</span>
 <span class="k">val</span> <span class="n">result</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="n">setMinSupport</span><span class="o">(</span><span class="mf">0.5</span><span class="o">)</span>
   <span class="o">.</span><span class="n">setMaxPatternLength</span><span class="o">(</span><span class="mi">5</span><span class="o">)</span>
   <span class="o">.</span><span class="n">setMaxLocalProjDBSize</span><span class="o">(</span><span class="mi">32000000</span><span class="o">)</span>
   <span class="o">.</span><span class="n">findFrequentSequentialPatterns</span><span class="o">(</span><span class="n">df</span><span class="o">)</span>
   <span class="o">.</span><span class="n">show</span><span class="o">()</span>
 </pre></div>
     <div><small>Find full example code at "examples/src/main/scala/org/apache/spark/examples/ml/PrefixSpanExample.scala" in the Spark repo.</small></div>
   </div>

 <div data-lang="java">
     <p>Refer to the <a href="api/java/org/apache/spark/ml/fpm/PrefixSpan.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.fpm.PrefixSpan</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.RowFactory</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="kn">import</span> <span class="nn">org.apache.spark.sql.types.*</span><span class="o">;</span>

 <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="n">List</span><span class="o">&lt;</span><span class="n">Row</span><span class="o">&gt;</span> <span class="n">data</span> <span class="o">=</span> <span class="n">Arrays</span><span class="o">.</span><span class="na">asList</span><span class="o">(</span>
   <span class="n">RowFactory</span><span class="o">.</span><span class="na">create</span><span class="o">(</span><span class="n">Arrays</span><span class="o">.</span><span class="na">asList</span><span class="o">(</span><span class="n">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="n">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="n">RowFactory</span><span class="o">.</span><span class="na">create</span><span class="o">(</span><span class="n">Arrays</span><span class="o">.</span><span class="na">asList</span><span class="o">(</span><span class="n">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="n">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="n">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="n">RowFactory</span><span class="o">.</span><span class="na">create</span><span class="o">(</span><span class="n">Arrays</span><span class="o">.</span><span class="na">asList</span><span class="o">(</span><span class="n">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="n">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="n">RowFactory</span><span class="o">.</span><span class="na">create</span><span class="o">(</span><span class="n">Arrays</span><span class="o">.</span><span class="na">asList</span><span class="o">(</span><span class="n">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="n">StructType</span> <span class="n">schema</span> <span class="o">=</span> <span class="k">new</span> <span class="n">StructType</span><span class="o">(</span><span class="k">new</span> <span class="n">StructField</span><span class="o">[]{</span> <span class="k">new</span> <span class="n">StructField</span><span class="o">(</span>
   <span class="s">&quot;sequence&quot;</span><span class="o">,</span> <span class="k">new</span> <span class="n">ArrayType</span><span class="o">(</span><span class="k">new</span> <span class="n">ArrayType</span><span class="o">(</span><span class="n">DataTypes</span><span class="o">.</span><span class="na">IntegerType</span><span class="o">,</span> <span class="kc">true</span><span class="o">),</span> <span class="kc">true</span><span class="o">),</span>
   <span class="kc">false</span><span class="o">,</span> <span class="n">Metadata</span><span class="o">.</span><span class="na">empty</span><span class="o">())</span>
 <span class="o">});</span>
 <span class="n">Dataset</span><span class="o">&lt;</span><span class="n">Row</span><span class="o">&gt;</span> <span class="n">sequenceDF</span> <span class="o">=</span> <span class="n">spark</span><span class="o">.</span><span class="na">createDataFrame</span><span class="o">(</span><span class="n">data</span><span class="o">,</span> <span class="n">schema</span><span class="o">);</span>

 <span class="n">PrefixSpan</span> <span class="n">prefixSpan</span> <span class="o">=</span> <span class="k">new</span> <span class="n">PrefixSpan</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="na">setMaxPatternLength</span><span class="o">(</span><span class="mi">5</span><span class="o">);</span>

 <span class="c1">// Finding frequent sequential patterns</span>
 <span class="n">prefixSpan</span><span class="o">.</span><span class="na">findFrequentSequentialPatterns</span><span class="o">(</span><span class="n">sequenceDF</span><span class="o">).</span><span class="na">show</span><span class="o">();</span>
 </pre></div>
     <div><small>Find full example code at "examples/src/main/java/org/apache/spark/examples/ml/JavaPrefixSpanExample.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.fpm.PrefixSpan">Python API docs</a> for more details.</p>

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

 <span class="n">df</span> <span class="o">=</span> <span class="n">sc</span><span class="o">.</span><span class="n">parallelize</span><span class="p">([</span><span class="n">Row</span><span class="p">(</span><span class="n">sequence</span><span class="o">=</span><span class="p">[[</span><span class="mi">1</span><span class="p">,</span> <span class="mi">2</span><span class="p">],</span> <span class="p">[</span><span class="mi">3</span><span class="p">]]),</span>
                      <span class="n">Row</span><span class="p">(</span><span class="n">sequence</span><span class="o">=</span><span class="p">[[</span><span class="mi">1</span><span class="p">],</span> <span class="p">[</span><span class="mi">3</span><span class="p">,</span> <span class="mi">2</span><span class="p">],</span> <span class="p">[</span><span class="mi">1</span><span class="p">,</span> <span class="mi">2</span><span class="p">]]),</span>
                      <span class="n">Row</span><span class="p">(</span><span class="n">sequence</span><span class="o">=</span><span class="p">[[</span><span class="mi">1</span><span class="p">,</span> <span class="mi">2</span><span class="p">],</span> <span class="p">[</span><span class="mi">5</span><span class="p">]]),</span>
                      <span class="n">Row</span><span class="p">(</span><span class="n">sequence</span><span class="o">=</span><span class="p">[[</span><span class="mi">6</span><span class="p">]])])</span><span class="o">.</span><span class="n">toDF</span><span class="p">()</span>

 <span class="n">prefixSpan</span> <span class="o">=</span> <span class="n">PrefixSpan</span><span class="p">(</span><span class="n">minSupport</span><span class="o">=</span><span class="mf">0.5</span><span class="p">,</span> <span class="n">maxPatternLength</span><span class="o">=</span><span class="mi">5</span><span class="p">,</span>
                         <span class="n">maxLocalProjDBSize</span><span class="o">=</span><span class="mi">32000000</span><span class="p">)</span>

 <span class="c1"># Find frequent sequential patterns.</span>
 <span class="n">prefixSpan</span><span class="o">.</span><span class="n">findFrequentSequentialPatterns</span><span class="p">(</span><span class="n">df</span><span class="p">)</span><span class="o">.</span><span class="n">show</span><span class="p">()</span>
 </pre></div>
     <div><small>Find full example code at "examples/src/main/python/ml/prefixspan_example.py" in the Spark repo.</small></div>
   </div>

 </div>


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