Spark 1.3.0 docs

author: Patrick Wendell <pwendell@apache.org> 2015-03-13 02:30:55 +0000
committer: Patrick Wendell <pwendell@apache.org> 2015-03-13 02:30:55 +0000
commit: aaf670598f15d47784d8b91b34dd614d0f8162af (patch)
tree: d86a329b056b3e9e9e79591d5b5bc3ee1781386b /site/docs/1.3.0/mllib-isotonic-regression.html
parent: 0d484ac791630a4f0ca7e82002113d94c931a1e7 (diff)
download: spark-website-aaf670598f15d47784d8b91b34dd614d0f8162af.tar.gz
spark-website-aaf670598f15d47784d8b91b34dd614d0f8162af.tar.bz2
spark-website-aaf670598f15d47784d8b91b34dd614d0f8162af.zip
1 files changed, 299 insertions, 0 deletions
diff --git a/site/docs/1.3.0/mllib-isotonic-regression.html b/site/docs/1.3.0/mllib-isotonic-regression.html
new file mode 100644
index 000000000..ca5c76713
--- /dev/null
+++ b/site/docs/1.3.0/mllib-isotonic-regression.html
@@ -0,0 +1,299 @@
+<!DOCTYPE html>
+<!--[if lt IE 7]>      <html class="no-js lt-ie9 lt-ie8 lt-ie7"> <![endif]-->
+<!--[if IE 7]>         <html class="no-js lt-ie9 lt-ie8"> <![endif]-->
+<!--[if IE 8]>         <html class="no-js lt-ie9"> <![endif]-->
+<!--[if gt IE 8]><!--> <html class="no-js"> <!--<![endif]-->
+    <head>
+        <meta charset="utf-8">
+        <meta http-equiv="X-UA-Compatible" content="IE=edge,chrome=1">
+        <title>Naive Bayes - MLlib - Spark 1.3.0 Documentation</title>
+        
+
+        
+
+        <link rel="stylesheet" href="css/bootstrap.min.css">
+        <style>
+            body {
+                padding-top: 60px;
+                padding-bottom: 40px;
+            }
+        </style>
+        <meta name="viewport" content="width=device-width">
+        <link rel="stylesheet" href="css/bootstrap-responsive.min.css">
+        <link rel="stylesheet" href="css/main.css">
+
+        <script src="js/vendor/modernizr-2.6.1-respond-1.1.0.min.js"></script>
+
+        <link rel="stylesheet" href="css/pygments-default.css">
+
+        
+
+    </head>
+    <body>
+        <!--[if lt IE 7]>
+            <p class="chromeframe">You are using an outdated browser. <a href="http://browsehappy.com/">Upgrade your browser today</a> or <a href="http://www.google.com/chromeframe/?redirect=true">install Google Chrome Frame</a> to better experience this site.</p>
+        <![endif]-->
+
+        <!-- This code is taken from http://twitter.github.com/bootstrap/examples/hero.html -->
+
+        <div class="navbar navbar-fixed-top" id="topbar">
+            <div class="navbar-inner">
+                <div class="container">
+                    <div class="brand"><a href="index.html">
+                      <img src="img/spark-logo-hd.png" style="height:50px;"/></a><span class="version">1.3.0</span>
+                    </div>
+                    <ul class="nav">
+                        <!--TODO(andyk): Add class="active" attribute to li some how.-->
+                        <li><a href="index.html">Overview</a></li>
+
+                        <li class="dropdown">
+                            <a href="#" class="dropdown-toggle" data-toggle="dropdown">Programming Guides<b class="caret"></b></a>
+                            <ul class="dropdown-menu">
+                                <li><a href="quick-start.html">Quick Start</a></li>
+                                <li><a href="programming-guide.html">Spark Programming Guide</a></li>
+                                <li class="divider"></li>
+                                <li><a href="streaming-programming-guide.html">Spark Streaming</a></li>
+                                <li><a href="sql-programming-guide.html">DataFrames and SQL</a></li>
+                                <li><a href="mllib-guide.html">MLlib (Machine Learning)</a></li>
+                                <li><a href="graphx-programming-guide.html">GraphX (Graph Processing)</a></li>
+                                <li><a href="bagel-programming-guide.html">Bagel (Pregel on Spark)</a></li>
+                            </ul>
+                        </li>
+
+                        <li class="dropdown">
+                            <a href="#" class="dropdown-toggle" data-toggle="dropdown">API Docs<b class="caret"></b></a>
+                            <ul class="dropdown-menu">
+                                <li><a href="api/scala/index.html#org.apache.spark.package">Scala</a></li>
+                                <li><a href="api/java/index.html">Java</a></li>
+                                <li><a href="api/python/index.html">Python</a></li>
+                            </ul>
+                        </li>
+
+                        <li class="dropdown">
+                            <a href="#" class="dropdown-toggle" data-toggle="dropdown">Deploying<b class="caret"></b></a>
+                            <ul class="dropdown-menu">
+                                <li><a href="cluster-overview.html">Overview</a></li>
+                                <li><a href="submitting-applications.html">Submitting Applications</a></li>
+                                <li class="divider"></li>
+                                <li><a href="spark-standalone.html">Spark Standalone</a></li>
+                                <li><a href="running-on-mesos.html">Mesos</a></li>
+                                <li><a href="running-on-yarn.html">YARN</a></li>
+                                <li class="divider"></li>
+                                <li><a href="ec2-scripts.html">Amazon EC2</a></li>
+                            </ul>
+                        </li>
+
+                        <li class="dropdown">
+                            <a href="api.html" class="dropdown-toggle" data-toggle="dropdown">More<b class="caret"></b></a>
+                            <ul class="dropdown-menu">
+                                <li><a href="configuration.html">Configuration</a></li>
+                                <li><a href="monitoring.html">Monitoring</a></li>
+                                <li><a href="tuning.html">Tuning Guide</a></li>
+                                <li><a href="job-scheduling.html">Job Scheduling</a></li>
+                                <li><a href="security.html">Security</a></li>
+                                <li><a href="hardware-provisioning.html">Hardware Provisioning</a></li>
+                                <li><a href="hadoop-third-party-distributions.html">3<sup>rd</sup>-Party Hadoop Distros</a></li>
+                                <li class="divider"></li>
+                                <li><a href="building-spark.html">Building Spark</a></li>
+                                <li><a href="https://cwiki.apache.org/confluence/display/SPARK/Contributing+to+Spark">Contributing to Spark</a></li>
+                                <li><a href="https://cwiki.apache.org/confluence/display/SPARK/Supplemental+Spark+Projects">Supplemental Projects</a></li>
+                            </ul>
+                        </li>
+                    </ul>
+                    <!--<p class="navbar-text pull-right"><span class="version-text">v1.3.0</span></p>-->
+                </div>
+            </div>
+        </div>
+
+        <div class="container" id="content">
+          
+            <h1 class="title"><a href="mllib-guide.html">MLlib</a> - Regression</h1>
+          
+
+          <h2 id="isotonic-regression">Isotonic regression</h2>
+<p><a href="http://en.wikipedia.org/wiki/Isotonic_regression">Isotonic regression</a>
+belongs to the family of regression algorithms. Formally isotonic regression is a problem where
+given a finite set of real numbers <code>$Y = {y_1, y_2, ..., y_n}$</code> representing observed responses
+and <code>$X = {x_1, x_2, ..., x_n}$</code> the unknown response values to be fitted
+finding a function that minimises</p>
+
+<p><code>\begin{equation}
+  f(x) = \sum_{i=1}^n w_i (y_i - x_i)^2
+\end{equation}</code></p>
+
+<p>with respect to complete order subject to
+<code>$x_1\le x_2\le ...\le x_n$</code> where <code>$w_i$</code> are positive weights.
+The resulting function is called isotonic regression and it is unique.
+It can be viewed as least squares problem under order restriction.
+Essentially isotonic regression is a
+<a href="http://en.wikipedia.org/wiki/Monotonic_function">monotonic function</a>
+best fitting the original data points.</p>
+
+<p>MLlib supports a
+<a href="http://doi.org/10.1198/TECH.2010.10111">pool adjacent violators algorithm</a>
+which uses an approach to
+<a href="http://doi.org/10.1007/978-3-642-99789-1_10">parallelizing isotonic regression</a>.
+The training input is a RDD of tuples of three double values that represent
+label, feature and weight in this order. Additionally IsotonicRegression algorithm has one
+optional parameter called $isotonic$ defaulting to true.
+This argument specifies if the isotonic regression is
+isotonic (monotonically increasing) or antitonic (monotonically decreasing).</p>
+
+<p>Training returns an IsotonicRegressionModel that can be used to predict
+labels for both known and unknown features. The result of isotonic regression
+is treated as piecewise linear function. The rules for prediction therefore are:</p>
+
+<ul>
+  <li>If the prediction input exactly matches a training feature
+then associated prediction is returned. In case there are multiple predictions with the same
+feature then one of them is returned. Which one is undefined
+(same as java.util.Arrays.binarySearch).</li>
+  <li>If the prediction input is lower or higher than all training features
+then prediction with lowest or highest feature is returned respectively.
+In case there are multiple predictions with the same feature
+then the lowest or highest is returned respectively.</li>
+  <li>If the prediction input falls between two training features then prediction is treated
+as piecewise linear function and interpolated value is calculated from the
+predictions of the two closest features. In case there are multiple values
+with the same feature then the same rules as in previous point are used.</li>
+</ul>
+
+<h3 id="examples">Examples</h3>
+
+<div class="codetabs">
+<div data-lang="scala">
+    <p>Data are read from a file where each line has a format label,feature
+i.e. 4710.28,500.00. The data are split to training and testing set.
+Model is created using the training set and a mean squared error is calculated from the predicted
+labels and real labels in the test set.</p>
+
+    <div class="highlight"><pre><code class="language-scala" data-lang="scala"><span class="k">import</span> <span class="nn">org.apache.spark.mllib.regression.IsotonicRegression</span>
+
+<span class="k">val</span> <span class="n">data</span> <span class="k">=</span> <span class="n">sc</span><span class="o">.</span><span class="n">textFile</span><span class="o">(</span><span class="s">&quot;data/mllib/sample_isotonic_regression_data.txt&quot;</span><span class="o">)</span>
+
+<span class="c1">// Create label, feature, weight tuples from input data with weight set to default value 1.0.</span>
+<span class="k">val</span> <span class="n">parsedData</span> <span class="k">=</span> <span class="n">data</span><span class="o">.</span><span class="n">map</span> <span class="o">{</span> <span class="n">line</span> <span class="k">=&gt;</span>
+  <span class="k">val</span> <span class="n">parts</span> <span class="k">=</span> <span class="n">line</span><span class="o">.</span><span class="n">split</span><span class="o">(</span><span class="sc">&#39;,&#39;</span><span class="o">).</span><span class="n">map</span><span class="o">(</span><span class="k">_</span><span class="o">.</span><span class="n">toDouble</span><span class="o">)</span>
+  <span class="o">(</span><span class="n">parts</span><span class="o">(</span><span class="mi">0</span><span class="o">),</span> <span class="n">parts</span><span class="o">(</span><span class="mi">1</span><span class="o">),</span> <span class="mf">1.0</span><span class="o">)</span>
+<span class="o">}</span>
+
+<span class="c1">// Split data into training (60%) and test (40%) sets.</span>
+<span class="k">val</span> <span class="n">splits</span> <span class="k">=</span> <span class="n">parsedData</span><span class="o">.</span><span class="n">randomSplit</span><span class="o">(</span><span class="nc">Array</span><span class="o">(</span><span class="mf">0.6</span><span class="o">,</span> <span class="mf">0.4</span><span class="o">),</span> <span class="n">seed</span> <span class="k">=</span> <span class="mi">11L</span><span class="o">)</span>
+<span class="k">val</span> <span class="n">training</span> <span class="k">=</span> <span class="n">splits</span><span class="o">(</span><span class="mi">0</span><span class="o">)</span>
+<span class="k">val</span> <span class="n">test</span> <span class="k">=</span> <span class="n">splits</span><span class="o">(</span><span class="mi">1</span><span class="o">)</span>
+
+<span class="c1">// Create isotonic regression model from training data.</span>
+<span class="c1">// Isotonic parameter defaults to true so it is only shown for demonstration</span>
+<span class="k">val</span> <span class="n">model</span> <span class="k">=</span> <span class="k">new</span> <span class="nc">IsotonicRegression</span><span class="o">().</span><span class="n">setIsotonic</span><span class="o">(</span><span class="kc">true</span><span class="o">).</span><span class="n">run</span><span class="o">(</span><span class="n">training</span><span class="o">)</span>
+
+<span class="c1">// Create tuples of predicted and real labels.</span>
+<span class="k">val</span> <span class="n">predictionAndLabel</span> <span class="k">=</span> <span class="n">test</span><span class="o">.</span><span class="n">map</span> <span class="o">{</span> <span class="n">point</span> <span class="k">=&gt;</span>
+  <span class="k">val</span> <span class="n">predictedLabel</span> <span class="k">=</span> <span class="n">model</span><span class="o">.</span><span class="n">predict</span><span class="o">(</span><span class="n">point</span><span class="o">.</span><span class="n">_2</span><span class="o">)</span>
+  <span class="o">(</span><span class="n">predictedLabel</span><span class="o">,</span> <span class="n">point</span><span class="o">.</span><span class="n">_1</span><span class="o">)</span>
+<span class="o">}</span>
+
+<span class="c1">// Calculate mean squared error between predicted and real labels.</span>
+<span class="k">val</span> <span class="n">meanSquaredError</span> <span class="k">=</span> <span class="n">predictionAndLabel</span><span class="o">.</span><span class="n">map</span><span class="o">{</span><span class="k">case</span><span class="o">(</span><span class="n">p</span><span class="o">,</span> <span class="n">l</span><span class="o">)</span> <span class="k">=&gt;</span> <span class="n">math</span><span class="o">.</span><span class="n">pow</span><span class="o">((</span><span class="n">p</span> <span class="o">-</span> <span class="n">l</span><span class="o">),</span> <span class="mi">2</span><span class="o">)}.</span><span class="n">mean</span><span class="o">()</span>
+<span class="n">println</span><span class="o">(</span><span class="s">&quot;Mean Squared Error = &quot;</span> <span class="o">+</span> <span class="n">meanSquaredError</span><span class="o">)</span></code></pre></div>
+
+  </div>
+
+<div data-lang="java">
+    <p>Data are read from a file where each line has a format label,feature
+i.e. 4710.28,500.00. The data are split to training and testing set.
+Model is created using the training set and a mean squared error is calculated from the predicted
+labels and real labels in the test set.</p>
+
+    <div class="highlight"><pre><code class="language-java" data-lang="java"><span class="kn">import</span> <span class="nn">org.apache.spark.SparkConf</span><span class="o">;</span>
+<span class="kn">import</span> <span class="nn">org.apache.spark.api.java.JavaDoubleRDD</span><span class="o">;</span>
+<span class="kn">import</span> <span class="nn">org.apache.spark.api.java.JavaPairRDD</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.api.java.function.Function</span><span class="o">;</span>
+<span class="kn">import</span> <span class="nn">org.apache.spark.api.java.function.PairFunction</span><span class="o">;</span>
+<span class="kn">import</span> <span class="nn">org.apache.spark.mllib.regression.IsotonicRegressionModel</span><span class="o">;</span>
+<span class="kn">import</span> <span class="nn">scala.Tuple2</span><span class="o">;</span>
+<span class="kn">import</span> <span class="nn">scala.Tuple3</span><span class="o">;</span>
+
+<span class="n">JavaRDD</span><span class="o">&lt;</span><span class="n">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">&quot;data/mllib/sample_isotonic_regression_data.txt&quot;</span><span class="o">);</span>
+
+<span class="c1">// Create label, feature, weight tuples from input data with weight set to default value 1.0.</span>
+<span class="n">JavaRDD</span><span class="o">&lt;</span><span class="n">Tuple3</span><span class="o">&lt;</span><span class="n">Double</span><span class="o">,</span> <span class="n">Double</span><span class="o">,</span> <span class="n">Double</span><span class="o">&gt;&gt;</span> <span class="n">parsedData</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="k">new</span> <span class="n">Function</span><span class="o">&lt;</span><span class="n">String</span><span class="o">,</span> <span class="n">Tuple3</span><span class="o">&lt;</span><span class="n">Double</span><span class="o">,</span> <span class="n">Double</span><span class="o">,</span> <span class="n">Double</span><span class="o">&gt;&gt;()</span> <span class="o">{</span>
+    <span class="kd">public</span> <span class="n">Tuple3</span><span class="o">&lt;</span><span class="n">Double</span><span class="o">,</span> <span class="n">Double</span><span class="o">,</span> <span class="n">Double</span><span class="o">&gt;</span> <span class="nf">call</span><span class="o">(</span><span class="n">String</span> <span class="n">line</span><span class="o">)</span> <span class="o">{</span>
+      <span class="n">String</span><span class="o">[]</span> <span class="n">parts</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">&quot;,&quot;</span><span class="o">);</span>
+      <span class="k">return</span> <span class="k">new</span> <span class="n">Tuple3</span><span class="o">&lt;&gt;(</span><span class="k">new</span> <span class="nf">Double</span><span class="o">(</span><span class="n">parts</span><span class="o">[</span><span class="mi">0</span><span class="o">]),</span> <span class="k">new</span> <span class="nf">Double</span><span class="o">(</span><span class="n">parts</span><span class="o">[</span><span class="mi">1</span><span class="o">]),</span> <span class="mf">1.0</span><span class="o">);</span>
+    <span class="o">}</span>
+  <span class="o">}</span>
+<span class="o">);</span>
+
+<span class="c1">// Split data into training (60%) and test (40%) sets.</span>
+<span class="n">JavaRDD</span><span class="o">&lt;</span><span class="n">Tuple3</span><span class="o">&lt;</span><span class="n">Double</span><span class="o">,</span> <span class="n">Double</span><span class="o">,</span> <span class="n">Double</span><span class="o">&gt;&gt;[]</span> <span class="n">splits</span> <span class="o">=</span> <span class="n">parsedData</span><span class="o">.</span><span class="na">randomSplit</span><span class="o">(</span><span class="k">new</span> <span class="kt">double</span><span class="o">[]</span> <span class="o">{</span><span class="mf">0.6</span><span class="o">,</span> <span class="mf">0.4</span><span class="o">},</span> <span class="mi">11L</span><span class="o">);</span>
+<span class="n">JavaRDD</span><span class="o">&lt;</span><span class="n">Tuple3</span><span class="o">&lt;</span><span class="n">Double</span><span class="o">,</span> <span class="n">Double</span><span class="o">,</span> <span class="n">Double</span><span class="o">&gt;&gt;</span> <span class="n">training</span> <span class="o">=</span> <span class="n">splits</span><span class="o">[</span><span class="mi">0</span><span class="o">];</span>
+<span class="n">JavaRDD</span><span class="o">&lt;</span><span class="n">Tuple3</span><span class="o">&lt;</span><span class="n">Double</span><span class="o">,</span> <span class="n">Double</span><span class="o">,</span> <span class="n">Double</span><span class="o">&gt;&gt;</span> <span class="n">test</span> <span class="o">=</span> <span class="n">splits</span><span class="o">[</span><span class="mi">1</span><span class="o">];</span>
+
+<span class="c1">// Create isotonic regression model from training data.</span>
+<span class="c1">// Isotonic parameter defaults to true so it is only shown for demonstration</span>
+<span class="n">IsotonicRegressionModel</span> <span class="n">model</span> <span class="o">=</span> <span class="k">new</span> <span class="nf">IsotonicRegression</span><span class="o">().</span><span class="na">setIsotonic</span><span class="o">(</span><span class="kc">true</span><span class="o">).</span><span class="na">run</span><span class="o">(</span><span class="n">training</span><span class="o">);</span>
+
+<span class="c1">// Create tuples of predicted and real labels.</span>
+<span class="n">JavaPairRDD</span><span class="o">&lt;</span><span class="n">Double</span><span class="o">,</span> <span class="n">Double</span><span class="o">&gt;</span> <span class="n">predictionAndLabel</span> <span class="o">=</span> <span class="n">test</span><span class="o">.</span><span class="na">mapToPair</span><span class="o">(</span>
+  <span class="k">new</span> <span class="n">PairFunction</span><span class="o">&lt;</span><span class="n">Tuple3</span><span class="o">&lt;</span><span class="n">Double</span><span class="o">,</span> <span class="n">Double</span><span class="o">,</span> <span class="n">Double</span><span class="o">&gt;,</span> <span class="n">Double</span><span class="o">,</span> <span class="n">Double</span><span class="o">&gt;()</span> <span class="o">{</span>
+    <span class="nd">@Override</span> <span class="kd">public</span> <span class="n">Tuple2</span><span class="o">&lt;</span><span class="n">Double</span><span class="o">,</span> <span class="n">Double</span><span class="o">&gt;</span> <span class="nf">call</span><span class="o">(</span><span class="n">Tuple3</span><span class="o">&lt;</span><span class="n">Double</span><span class="o">,</span> <span class="n">Double</span><span class="o">,</span> <span class="n">Double</span><span class="o">&gt;</span> <span class="n">point</span><span class="o">)</span> <span class="o">{</span>
+      <span class="n">Double</span> <span class="n">predictedLabel</span> <span class="o">=</span> <span class="n">model</span><span class="o">.</span><span class="na">predict</span><span class="o">(</span><span class="n">point</span><span class="o">.</span><span class="na">_2</span><span class="o">());</span>
+      <span class="k">return</span> <span class="k">new</span> <span class="n">Tuple2</span><span class="o">&lt;</span><span class="n">Double</span><span class="o">,</span> <span class="n">Double</span><span class="o">&gt;(</span><span class="n">predictedLabel</span><span class="o">,</span> <span class="n">point</span><span class="o">.</span><span class="na">_1</span><span class="o">());</span>
+    <span class="o">}</span>
+  <span class="o">}</span>
+<span class="o">);</span>
+
+<span class="c1">// Calculate mean squared error between predicted and real labels.</span>
+<span class="n">Double</span> <span class="n">meanSquaredError</span> <span class="o">=</span> <span class="k">new</span> <span class="nf">JavaDoubleRDD</span><span class="o">(</span><span class="n">predictionAndLabel</span><span class="o">.</span><span class="na">map</span><span class="o">(</span>
+  <span class="k">new</span> <span class="n">Function</span><span class="o">&lt;</span><span class="n">Tuple2</span><span class="o">&lt;</span><span class="n">Double</span><span class="o">,</span> <span class="n">Double</span><span class="o">&gt;,</span> <span class="n">Object</span><span class="o">&gt;()</span> <span class="o">{</span>
+    <span class="nd">@Override</span> <span class="kd">public</span> <span class="n">Object</span> <span class="nf">call</span><span class="o">(</span><span class="n">Tuple2</span><span class="o">&lt;</span><span class="n">Double</span><span class="o">,</span> <span class="n">Double</span><span class="o">&gt;</span> <span class="n">pl</span><span class="o">)</span> <span class="o">{</span>
+      <span class="k">return</span> <span class="n">Math</span><span class="o">.</span><span class="na">pow</span><span class="o">(</span><span class="n">pl</span><span class="o">.</span><span class="na">_1</span><span class="o">()</span> <span class="o">-</span> <span class="n">pl</span><span class="o">.</span><span class="na">_2</span><span class="o">(),</span> <span class="mi">2</span><span class="o">);</span>
+    <span class="o">}</span>
+  <span class="o">}</span>
+<span class="o">).</span><span class="na">rdd</span><span class="o">()).</span><span class="na">mean</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;Mean Squared Error = &quot;</span> <span class="o">+</span> <span class="n">meanSquaredError</span><span class="o">);</span></code></pre></div>
+
+  </div>
+</div>
+
+
+        </div> <!-- /container -->
+
+        <script src="js/vendor/jquery-1.8.0.min.js"></script>
+        <script src="js/vendor/bootstrap.min.js"></script>
+        <script src="js/main.js"></script>
+
+        <!-- MathJax Section -->
+        <script type="text/x-mathjax-config">
+            MathJax.Hub.Config({
+                TeX: { equationNumbers: { autoNumber: "AMS" } }
+            });
+        </script>
+        <script>
+            // Note that we load MathJax this way to work with local file (file://), HTTP and HTTPS.
+            // We could use "//cdn.mathjax...", but that won't support "file://".
+            (function(d, script) {
+                script = d.createElement('script');
+                script.type = 'text/javascript';
+                script.async = true;
+                script.onload = function(){
+                    MathJax.Hub.Config({
+                        tex2jax: {
+                            inlineMath: [ ["$", "$"], ["\\\\(","\\\\)"] ],
+                            displayMath: [ ["$$","$$"], ["\\[", "\\]"] ],
+                            processEscapes: true,
+                            skipTags: ['script', 'noscript', 'style', 'textarea', 'pre']
+                        }
+                    });
+                };
+                script.src = ('https:' == document.location.protocol ? 'https://' : 'http://') +
+                    'cdn.mathjax.org/mathjax/latest/MathJax.js?config=TeX-AMS-MML_HTMLorMML';
+                d.getElementsByTagName('head')[0].appendChild(script);
+            }(document));
+        </script>
+    </body>
+</html>
author	Patrick Wendell <pwendell@apache.org>	2015-03-13 02:30:55 +0000
committer	Patrick Wendell <pwendell@apache.org>	2015-03-13 02:30:55 +0000
commit	aaf670598f15d47784d8b91b34dd614d0f8162af (patch)
tree	d86a329b056b3e9e9e79591d5b5bc3ee1781386b /site/docs/1.3.0/mllib-isotonic-regression.html
parent	0d484ac791630a4f0ca7e82002113d94c931a1e7 (diff)
download	spark-website-aaf670598f15d47784d8b91b34dd614d0f8162af.tar.gz spark-website-aaf670598f15d47784d8b91b34dd614d0f8162af.tar.bz2 spark-website-aaf670598f15d47784d8b91b34dd614d0f8162af.zip