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<h1 class="title">Machine Learning Library (MLlib)</h1>
<ul id="markdown-toc">
<li><a href="#dependencies">Dependencies</a></li>
<li><a href="#binary-classification">Binary Classification</a></li>
<li><a href="#linear-regression">Linear Regression</a></li>
<li><a href="#clustering">Clustering</a></li>
<li><a href="#collaborative-filtering">Collaborative Filtering</a> <ul>
<li><a href="#explicit-vs-implicit-feedback">Explicit vs Implicit Feedback</a></li>
</ul>
</li>
<li><a href="#gradient-descent-primitive">Gradient Descent Primitive</a></li>
<li><a href="#using-mllib-in-scala">Using MLLib in Scala</a> <ul>
<li><a href="#binary-classification-1">Binary Classification</a></li>
<li><a href="#linear-regression-1">Linear Regression</a></li>
<li><a href="#clustering-1">Clustering</a></li>
<li><a href="#collaborative-filtering-1">Collaborative Filtering</a></li>
</ul>
</li>
<li><a href="#using-mllib-in-java">Using MLLib in Java</a></li>
<li><a href="#using-mllib-in-python">Using MLLib in Python</a> <ul>
<li><a href="#binary-classification-2">Binary Classification</a></li>
<li><a href="#linear-regression-2">Linear Regression</a></li>
<li><a href="#clustering-2">Clustering</a></li>
<li><a href="#collaborative-filtering-2">Collaborative Filtering</a></li>
</ul>
</li>
</ul>
<p>MLlib is a Spark implementation of some common machine learning (ML)
functionality, as well associated tests and data generators. MLlib
currently supports four common types of machine learning problem settings,
namely, binary classification, regression, clustering and collaborative
filtering, as well as an underlying gradient descent optimization primitive.
This guide will outline the functionality supported in MLlib and also provides
an example of invoking MLlib.</p>
<h1 id="dependencies">Dependencies</h1>
<p>MLlib uses the <a href="https://github.com/mikiobraun/jblas">jblas</a> linear algebra library, which itself
depends on native Fortran routines. You may need to install the
<a href="https://github.com/mikiobraun/jblas/wiki/Missing-Libraries">gfortran runtime library</a>
if it is not already present on your nodes. MLlib will throw a linking error if it cannot
detect these libraries automatically.</p>
<p>To use MLlib in Python, you will need <a href="http://www.numpy.org">NumPy</a> version 1.7 or newer
and Python 2.7.</p>
<h1 id="binary-classification">Binary Classification</h1>
<p>Binary classification is a supervised learning problem in which we want to
classify entities into one of two distinct categories or labels, e.g.,
predicting whether or not emails are spam. This problem involves executing a
learning <em>Algorithm</em> on a set of <em>labeled</em> examples, i.e., a set of entities
represented via (numerical) features along with underlying category labels.
The algorithm returns a trained <em>Model</em> that can predict the label for new
entities for which the underlying label is unknown. </p>
<p>MLlib currently supports two standard model families for binary classification,
namely <a href="http://en.wikipedia.org/wiki/Support_vector_machine">Linear Support Vector Machines
(SVMs)</a> and <a href="http://en.wikipedia.org/wiki/Logistic_regression">Logistic
Regression</a>, along with <a href="http://en.wikipedia.org/wiki/Regularization_(mathematics)">L1
and L2 regularized</a>
variants of each model family. The training algorithms all leverage an
underlying gradient descent primitive (described
<a href="#gradient-descent-primitive">below</a>), and take as input a regularization
parameter (<em>regParam</em>) along with various parameters associated with gradient
descent (<em>stepSize</em>, <em>numIterations</em>, <em>miniBatchFraction</em>). </p>
<p>Available algorithms for binary classification:</p>
<ul>
<li><a href="api/mllib/index.html#org.apache.spark.mllib.classification.SVMWithSGD">SVMWithSGD</a></li>
<li><a href="api/mllib/index.html#org.apache.spark.mllib.classification.LogisticRegressionWithSGD">LogisticRegressionWithSGD</a></li>
</ul>
<h1 id="linear-regression">Linear Regression</h1>
<p>Linear regression is another classical supervised learning setting. In this
problem, each entity is associated with a real-valued label (as opposed to a
binary label as in binary classification), and we want to predict labels as
closely as possible given numerical features representing entities. MLlib
supports linear regression as well as L1
(<a href="http://en.wikipedia.org/wiki/Lasso_(statistics)#Lasso_method">lasso</a>) and L2
(<a href="http://en.wikipedia.org/wiki/Ridge_regression">ridge</a>) regularized variants.
The regression algorithms in MLlib also leverage the underlying gradient
descent primitive (described <a href="#gradient-descent-primitive">below</a>), and have
the same parameters as the binary classification algorithms described above. </p>
<p>Available algorithms for linear regression: </p>
<ul>
<li><a href="api/mllib/index.html#org.apache.spark.mllib.regression.LinearRegressionWithSGD">LinearRegressionWithSGD</a></li>
<li><a href="api/mllib/index.html#org.apache.spark.mllib.regression.RidgeRegressionWithSGD">RidgeRegressionWithSGD</a></li>
<li><a href="api/mllib/index.html#org.apache.spark.mllib.regression.LassoWithSGD">LassoWithSGD</a></li>
</ul>
<h1 id="clustering">Clustering</h1>
<p>Clustering is an unsupervised learning problem whereby we aim to group subsets
of entities with one another based on some notion of similarity. Clustering is
often used for exploratory analysis and/or as a component of a hierarchical
supervised learning pipeline (in which distinct classifiers or regression
models are trained for each cluster). MLlib supports
<a href="http://en.wikipedia.org/wiki/K-means_clustering">k-means</a> clustering, one of
the most commonly used clustering algorithms that clusters the data points into
predfined number of clusters. The MLlib implementation includes a parallelized
variant of the <a href="http://en.wikipedia.org/wiki/K-means%2B%2B">k-means++</a> method
called <a href="http://theory.stanford.edu/~sergei/papers/vldb12-kmpar.pdf">kmeans||</a>.
The implementation in MLlib has the following parameters: </p>
<ul>
<li><em>k</em> is the number of desired clusters.</li>
<li><em>maxIterations</em> is the maximum number of iterations to run.</li>
<li><em>initializationMode</em> specifies either random initialization or
initialization via k-means||.</li>
<li><em>runs</em> is the number of times to run the k-means algorithm (k-means is not
guaranteed to find a globally optimal solution, and when run multiple times on
a given dataset, the algorithm returns the best clustering result).</li>
<li><em>initializiationSteps</em> determines the number of steps in the k-means|| algorithm.</li>
<li><em>epsilon</em> determines the distance threshold within which we consider k-means to have converged. </li>
</ul>
<p>Available algorithms for clustering: </p>
<ul>
<li><a href="api/mllib/index.html#org.apache.spark.mllib.clustering.KMeans">KMeans</a></li>
</ul>
<h1 id="collaborative-filtering">Collaborative Filtering</h1>
<p><a href="http://en.wikipedia.org/wiki/Recommender_system#Collaborative_filtering">Collaborative filtering</a>
is commonly used for recommender systems. These techniques aim to fill in the
missing entries of a user-item association matrix. MLlib currently supports
model-based collaborative filtering, in which users and products are described
by a small set of latent factors that can be used to predict missing entries.
In particular, we implement the <a href="http://www2.research.att.com/~volinsky/papers/ieeecomputer.pdf">alternating least squares
(ALS)</a>
algorithm to learn these latent factors. The implementation in MLlib has the
following parameters:</p>
<ul>
<li><em>numBlocks</em> is the number of blacks used to parallelize computation (set to -1 to auto-configure). </li>
<li><em>rank</em> is the number of latent factors in our model.</li>
<li><em>iterations</em> is the number of iterations to run.</li>
<li><em>lambda</em> specifies the regularization parameter in ALS.</li>
<li><em>implicitPrefs</em> specifies whether to use the <em>explicit feedback</em> ALS variant or one adapted for <em>implicit feedback</em> data</li>
<li><em>alpha</em> is a parameter applicable to the implicit feedback variant of ALS that governs the <em>baseline</em> confidence in preference observations</li>
</ul>
<h2 id="explicit-vs-implicit-feedback">Explicit vs Implicit Feedback</h2>
<p>The standard approach to matrix factorization based collaborative filtering treats
the entries in the user-item matrix as <em>explicit</em> preferences given by the user to the item.</p>
<p>It is common in many real-world use cases to only have access to <em>implicit feedback</em>
(e.g. views, clicks, purchases, likes, shares etc.). The approach used in MLlib to deal with
such data is taken from
<a href="http://www2.research.att.com/~yifanhu/PUB/cf.pdf">Collaborative Filtering for Implicit Feedback Datasets</a>.
Essentially instead of trying to model the matrix of ratings directly, this approach treats the data as
a combination of binary preferences and <em>confidence values</em>. The ratings are then related
to the level of confidence in observed user preferences, rather than explicit ratings given to items.
The model then tries to find latent factors that can be used to predict the expected preference of a user
for an item. </p>
<p>Available algorithms for collaborative filtering: </p>
<ul>
<li><a href="api/mllib/index.html#org.apache.spark.mllib.recommendation.ALS">ALS</a></li>
</ul>
<h1 id="gradient-descent-primitive">Gradient Descent Primitive</h1>
<p><a href="http://en.wikipedia.org/wiki/Gradient_descent">Gradient descent</a> (along with
stochastic variants thereof) are first-order optimization methods that are
well-suited for large-scale and distributed computation. Gradient descent
methods aim to find a local minimum of a function by iteratively taking steps
in the direction of the negative gradient of the function at the current point,
i.e., the current parameter value. Gradient descent is included as a low-level
primitive in MLlib, upon which various ML algorithms are developed, and has the
following parameters:</p>
<ul>
<li><em>gradient</em> is a class that computes the stochastic gradient of the function
being optimized, i.e., with respect to a single training example, at the
current parameter value. MLlib includes gradient classes for common loss
functions, e.g., hinge, logistic, least-squares. The gradient class takes as
input a training example, its label, and the current parameter value. </li>
<li><em>updater</em> is a class that updates weights in each iteration of gradient
descent. MLlib includes updaters for cases without regularization, as well as
L1 and L2 regularizers.</li>
<li><em>stepSize</em> is a scalar value denoting the initial step size for gradient
descent. All updaters in MLlib use a step size at the t-th step equal to
stepSize / sqrt(t). </li>
<li><em>numIterations</em> is the number of iterations to run.</li>
<li><em>regParam</em> is the regularization parameter when using L1 or L2 regularization.</li>
<li><em>miniBatchFraction</em> is the fraction of the data used to compute the gradient
at each iteration.</li>
</ul>
<p>Available algorithms for gradient descent:</p>
<ul>
<li><a href="api/mllib/index.html#org.apache.spark.mllib.optimization.GradientDescent">GradientDescent</a></li>
</ul>
<h1 id="using-mllib-in-scala">Using MLLib in Scala</h1>
<p>Following code snippets can be executed in <code>spark-shell</code>.</p>
<h2 id="binary-classification-1">Binary Classification</h2>
<p>The following code snippet illustrates how to load a sample dataset, execute a
training algorithm on this training data using a static method in the algorithm
object, and make predictions with the resulting model to compute the training
error.</p>
<div class="highlight"><pre><code class="scala"><span class="k">import</span> <span class="nn">org.apache.spark.SparkContext</span>
<span class="k">import</span> <span class="nn">org.apache.spark.mllib.classification.SVMWithSGD</span>
<span class="k">import</span> <span class="nn">org.apache.spark.mllib.regression.LabeledPoint</span>
<span class="c1">// Load and parse the data file</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">"mllib/data/sample_svm_data.txt"</span><span class="o">)</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">=></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">' '</span><span class="o">)</span>
<span class="nc">LabeledPoint</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">toDouble</span><span class="o">,</span> <span class="n">parts</span><span class="o">.</span><span class="n">tail</span><span class="o">.</span><span class="n">map</span><span class="o">(</span><span class="n">x</span> <span class="k">=></span> <span class="n">x</span><span class="o">.</span><span class="n">toDouble</span><span class="o">).</span><span class="n">toArray</span><span class="o">)</span>
<span class="o">}</span>
<span class="c1">// Run training algorithm to build the model</span>
<span class="k">val</span> <span class="n">numIterations</span> <span class="k">=</span> <span class="mi">20</span>
<span class="k">val</span> <span class="n">model</span> <span class="k">=</span> <span class="nc">SVMWithSGD</span><span class="o">.</span><span class="n">train</span><span class="o">(</span><span class="n">parsedData</span><span class="o">,</span> <span class="n">numIterations</span><span class="o">)</span>
<span class="c1">// Evaluate model on training examples and compute training error</span>
<span class="k">val</span> <span class="n">labelAndPreds</span> <span class="k">=</span> <span class="n">parsedData</span><span class="o">.</span><span class="n">map</span> <span class="o">{</span> <span class="n">point</span> <span class="k">=></span>
<span class="k">val</span> <span class="n">prediction</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">features</span><span class="o">)</span>
<span class="o">(</span><span class="n">point</span><span class="o">.</span><span class="n">label</span><span class="o">,</span> <span class="n">prediction</span><span class="o">)</span>
<span class="o">}</span>
<span class="k">val</span> <span class="n">trainErr</span> <span class="k">=</span> <span class="n">labelAndPreds</span><span class="o">.</span><span class="n">filter</span><span class="o">(</span><span class="n">r</span> <span class="k">=></span> <span class="n">r</span><span class="o">.</span><span class="n">_1</span> <span class="o">!=</span> <span class="n">r</span><span class="o">.</span><span class="n">_2</span><span class="o">).</span><span class="n">count</span><span class="o">.</span><span class="n">toDouble</span> <span class="o">/</span> <span class="n">parsedData</span><span class="o">.</span><span class="n">count</span>
<span class="n">println</span><span class="o">(</span><span class="s">"Training Error = "</span> <span class="o">+</span> <span class="n">trainErr</span><span class="o">)</span>
</code></pre></div>
<p>The <code>SVMWithSGD.train()</code> method by default performs L2 regularization with the
regularization parameter set to 1.0. If we want to configure this algorithm, we
can customize <code>SVMWithSGD</code> further by creating a new object directly and
calling setter methods. All other MLlib algorithms support customization in
this way as well. For example, the following code produces an L1 regularized
variant of SVMs with regularization parameter set to 0.1, and runs the training
algorithm for 200 iterations.</p>
<div class="highlight"><pre><code class="scala"><span class="k">import</span> <span class="nn">org.apache.spark.mllib.optimization.L1Updater</span>
<span class="k">val</span> <span class="n">svmAlg</span> <span class="k">=</span> <span class="k">new</span> <span class="nc">SVMWithSGD</span><span class="o">()</span>
<span class="n">svmAlg</span><span class="o">.</span><span class="n">optimizer</span><span class="o">.</span><span class="n">setNumIterations</span><span class="o">(</span><span class="mi">200</span><span class="o">)</span>
<span class="o">.</span><span class="n">setRegParam</span><span class="o">(</span><span class="mf">0.1</span><span class="o">)</span>
<span class="o">.</span><span class="n">setUpdater</span><span class="o">(</span><span class="k">new</span> <span class="n">L1Updater</span><span class="o">)</span>
<span class="k">val</span> <span class="n">modelL1</span> <span class="k">=</span> <span class="n">svmAlg</span><span class="o">.</span><span class="n">run</span><span class="o">(</span><span class="n">parsedData</span><span class="o">)</span>
</code></pre></div>
<h2 id="linear-regression-1">Linear Regression</h2>
<p>The following example demonstrate how to load training data, parse it as an RDD of LabeledPoint. The
example then uses LinearRegressionWithSGD to build a simple linear model to predict label values. We
compute the Mean Squared Error at the end to evaluate
<a href="http://en.wikipedia.org/wiki/Goodness_of_fit">goodness of fit</a></p>
<div class="highlight"><pre><code class="scala"><span class="k">import</span> <span class="nn">org.apache.spark.mllib.regression.LinearRegressionWithSGD</span>
<span class="k">import</span> <span class="nn">org.apache.spark.mllib.regression.LabeledPoint</span>
<span class="c1">// Load and parse the data</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">"mllib/data/ridge-data/lpsa.data"</span><span class="o">)</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">=></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">','</span><span class="o">)</span>
<span class="nc">LabeledPoint</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">toDouble</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="n">split</span><span class="o">(</span><span class="sc">' '</span><span class="o">).</span><span class="n">map</span><span class="o">(</span><span class="n">x</span> <span class="k">=></span> <span class="n">x</span><span class="o">.</span><span class="n">toDouble</span><span class="o">).</span><span class="n">toArray</span><span class="o">)</span>
<span class="o">}</span>
<span class="c1">// Building the model</span>
<span class="k">val</span> <span class="n">numIterations</span> <span class="k">=</span> <span class="mi">20</span>
<span class="k">val</span> <span class="n">model</span> <span class="k">=</span> <span class="nc">LinearRegressionWithSGD</span><span class="o">.</span><span class="n">train</span><span class="o">(</span><span class="n">parsedData</span><span class="o">,</span> <span class="n">numIterations</span><span class="o">)</span>
<span class="c1">// Evaluate model on training examples and compute training error</span>
<span class="k">val</span> <span class="n">valuesAndPreds</span> <span class="k">=</span> <span class="n">parsedData</span><span class="o">.</span><span class="n">map</span> <span class="o">{</span> <span class="n">point</span> <span class="k">=></span>
<span class="k">val</span> <span class="n">prediction</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">features</span><span class="o">)</span>
<span class="o">(</span><span class="n">point</span><span class="o">.</span><span class="n">label</span><span class="o">,</span> <span class="n">prediction</span><span class="o">)</span>
<span class="o">}</span>
<span class="k">val</span> <span class="nc">MSE</span> <span class="k">=</span> <span class="n">valuesAndPreds</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">v</span><span class="o">,</span> <span class="n">p</span><span class="o">)</span> <span class="k">=></span> <span class="n">math</span><span class="o">.</span><span class="n">pow</span><span class="o">((</span><span class="n">v</span> <span class="o">-</span> <span class="n">p</span><span class="o">),</span> <span class="mi">2</span><span class="o">)}.</span><span class="n">reduce</span><span class="o">(</span><span class="k">_</span> <span class="o">+</span> <span class="k">_</span><span class="o">)/</span><span class="n">valuesAndPreds</span><span class="o">.</span><span class="n">count</span>
<span class="n">println</span><span class="o">(</span><span class="s">"training Mean Squared Error = "</span> <span class="o">+</span> <span class="nc">MSE</span><span class="o">)</span>
</code></pre></div>
<p>Similarly you can use RidgeRegressionWithSGD and LassoWithSGD and compare training
<a href="http://en.wikipedia.org/wiki/Mean_squared_error">Mean Squared Errors</a>.</p>
<h2 id="clustering-1">Clustering</h2>
<p>In the following example after loading and parsing data, we use the KMeans object to cluster the data
into two clusters. The number of desired clusters is passed to the algorithm. We then compute Within
Set Sum of Squared Error (WSSSE). You can reduce this error measure by increasing <em>k</em>. In fact the
optimal <em>k</em> is usually one where there is an “elbow” in the WSSSE graph.</p>
<div class="highlight"><pre><code class="scala"><span class="k">import</span> <span class="nn">org.apache.spark.mllib.clustering.KMeans</span>
<span class="c1">// Load and parse the data</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">"kmeans_data.txt"</span><span class="o">)</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="k">_</span><span class="o">.</span><span class="n">split</span><span class="o">(</span><span class="sc">' '</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="c1">// Cluster the data into two classes using KMeans</span>
<span class="k">val</span> <span class="n">numIterations</span> <span class="k">=</span> <span class="mi">20</span>
<span class="k">val</span> <span class="n">numClusters</span> <span class="k">=</span> <span class="mi">2</span>
<span class="k">val</span> <span class="n">clusters</span> <span class="k">=</span> <span class="nc">KMeans</span><span class="o">.</span><span class="n">train</span><span class="o">(</span><span class="n">parsedData</span><span class="o">,</span> <span class="n">numClusters</span><span class="o">,</span> <span class="n">numIterations</span><span class="o">)</span>
<span class="c1">// Evaluate clustering by computing Within Set Sum of Squared Errors</span>
<span class="k">val</span> <span class="nc">WSSSE</span> <span class="k">=</span> <span class="n">clusters</span><span class="o">.</span><span class="n">computeCost</span><span class="o">(</span><span class="n">parsedData</span><span class="o">)</span>
<span class="n">println</span><span class="o">(</span><span class="s">"Within Set Sum of Squared Errors = "</span> <span class="o">+</span> <span class="nc">WSSSE</span><span class="o">)</span>
</code></pre></div>
<h2 id="collaborative-filtering-1">Collaborative Filtering</h2>
<p>In the following example we load rating data. Each row consists of a user, a product and a rating.
We use the default ALS.train() method which assumes ratings are explicit. We evaluate the recommendation
model by measuring the Mean Squared Error of rating prediction.</p>
<div class="highlight"><pre><code class="scala"><span class="k">import</span> <span class="nn">org.apache.spark.mllib.recommendation.ALS</span>
<span class="k">import</span> <span class="nn">org.apache.spark.mllib.recommendation.Rating</span>
<span class="c1">// Load and parse the data</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">"mllib/data/als/test.data"</span><span class="o">)</span>
<span class="k">val</span> <span class="n">ratings</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="k">_</span><span class="o">.</span><span class="n">split</span><span class="o">(</span><span class="sc">','</span><span class="o">)</span> <span class="k">match</span> <span class="o">{</span>
<span class="k">case</span> <span class="nc">Array</span><span class="o">(</span><span class="n">user</span><span class="o">,</span> <span class="n">item</span><span class="o">,</span> <span class="n">rate</span><span class="o">)</span> <span class="k">=></span> <span class="nc">Rating</span><span class="o">(</span><span class="n">user</span><span class="o">.</span><span class="n">toInt</span><span class="o">,</span> <span class="n">item</span><span class="o">.</span><span class="n">toInt</span><span class="o">,</span> <span class="n">rate</span><span class="o">.</span><span class="n">toDouble</span><span class="o">)</span>
<span class="o">})</span>
<span class="c1">// Build the recommendation model using ALS</span>
<span class="k">val</span> <span class="n">numIterations</span> <span class="k">=</span> <span class="mi">20</span>
<span class="k">val</span> <span class="n">model</span> <span class="k">=</span> <span class="nc">ALS</span><span class="o">.</span><span class="n">train</span><span class="o">(</span><span class="n">ratings</span><span class="o">,</span> <span class="mi">1</span><span class="o">,</span> <span class="mi">20</span><span class="o">,</span> <span class="mf">0.01</span><span class="o">)</span>
<span class="c1">// Evaluate the model on rating data</span>
<span class="k">val</span> <span class="n">usersProducts</span> <span class="k">=</span> <span class="n">ratings</span><span class="o">.</span><span class="n">map</span><span class="o">{</span> <span class="k">case</span> <span class="nc">Rating</span><span class="o">(</span><span class="n">user</span><span class="o">,</span> <span class="n">product</span><span class="o">,</span> <span class="n">rate</span><span class="o">)</span> <span class="k">=></span> <span class="o">(</span><span class="n">user</span><span class="o">,</span> <span class="n">product</span><span class="o">)}</span>
<span class="k">val</span> <span class="n">predictions</span> <span class="k">=</span> <span class="n">model</span><span class="o">.</span><span class="n">predict</span><span class="o">(</span><span class="n">usersProducts</span><span class="o">).</span><span class="n">map</span><span class="o">{</span>
<span class="k">case</span> <span class="nc">Rating</span><span class="o">(</span><span class="n">user</span><span class="o">,</span> <span class="n">product</span><span class="o">,</span> <span class="n">rate</span><span class="o">)</span> <span class="k">=></span> <span class="o">((</span><span class="n">user</span><span class="o">,</span> <span class="n">product</span><span class="o">),</span> <span class="n">rate</span><span class="o">)</span>
<span class="o">}</span>
<span class="k">val</span> <span class="n">ratesAndPreds</span> <span class="k">=</span> <span class="n">ratings</span><span class="o">.</span><span class="n">map</span><span class="o">{</span>
<span class="k">case</span> <span class="nc">Rating</span><span class="o">(</span><span class="n">user</span><span class="o">,</span> <span class="n">product</span><span class="o">,</span> <span class="n">rate</span><span class="o">)</span> <span class="k">=></span> <span class="o">((</span><span class="n">user</span><span class="o">,</span> <span class="n">product</span><span class="o">),</span> <span class="n">rate</span><span class="o">)</span>
<span class="o">}.</span><span class="n">join</span><span class="o">(</span><span class="n">predictions</span><span class="o">)</span>
<span class="k">val</span> <span class="nc">MSE</span> <span class="k">=</span> <span class="n">ratesAndPreds</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">user</span><span class="o">,</span> <span class="n">product</span><span class="o">),</span> <span class="o">(</span><span class="n">r1</span><span class="o">,</span> <span class="n">r2</span><span class="o">))</span> <span class="k">=></span> <span class="n">math</span><span class="o">.</span><span class="n">pow</span><span class="o">((</span><span class="n">r1</span><span class="o">-</span> <span class="n">r2</span><span class="o">),</span> <span class="mi">2</span><span class="o">)</span>
<span class="o">}.</span><span class="n">reduce</span><span class="o">(</span><span class="k">_</span> <span class="o">+</span> <span class="k">_</span><span class="o">)/</span><span class="n">ratesAndPreds</span><span class="o">.</span><span class="n">count</span>
<span class="n">println</span><span class="o">(</span><span class="s">"Mean Squared Error = "</span> <span class="o">+</span> <span class="nc">MSE</span><span class="o">)</span>
</code></pre></div>
<p>If the rating matrix is derived from other source of information (i.e., it is inferred from
other signals), you can use the trainImplicit method to get better results.</p>
<div class="highlight"><pre><code class="scala"><span class="k">val</span> <span class="n">model</span> <span class="k">=</span> <span class="nc">ALS</span><span class="o">.</span><span class="n">trainImplicit</span><span class="o">(</span><span class="n">ratings</span><span class="o">,</span> <span class="mi">1</span><span class="o">,</span> <span class="mi">20</span><span class="o">,</span> <span class="mf">0.01</span><span class="o">)</span>
</code></pre></div>
<h1 id="using-mllib-in-java">Using MLLib in Java</h1>
<p>All of MLlib’s methods use Java-friendly types, so you can import and call them there the same
way you do in Scala. The only caveat is that the methods take Scala RDD objects, while the
Spark Java API uses a separate <code>JavaRDD</code> class. You can convert a Java RDD to a Scala one by
calling <code>.rdd()</code> on your <code>JavaRDD</code> object.</p>
<h1 id="using-mllib-in-python">Using MLLib in Python</h1>
<p>Following examples can be tested in the PySpark shell.</p>
<h2 id="binary-classification-2">Binary Classification</h2>
<p>The following example shows how to load a sample dataset, build Logistic Regression model,
and make predictions with the resulting model to compute the training error.</p>
<div class="highlight"><pre><code class="python"><span class="kn">from</span> <span class="nn">pyspark.mllib.classification</span> <span class="kn">import</span> <span class="n">LogisticRegressionWithSGD</span>
<span class="kn">from</span> <span class="nn">numpy</span> <span class="kn">import</span> <span class="n">array</span>
<span class="c"># Load and parse the data</span>
<span class="n">data</span> <span class="o">=</span> <span class="n">sc</span><span class="o">.</span><span class="n">textFile</span><span class="p">(</span><span class="s">"mllib/data/sample_svm_data.txt"</span><span class="p">)</span>
<span class="n">parsedData</span> <span class="o">=</span> <span class="n">data</span><span class="o">.</span><span class="n">map</span><span class="p">(</span><span class="k">lambda</span> <span class="n">line</span><span class="p">:</span> <span class="n">array</span><span class="p">([</span><span class="nb">float</span><span class="p">(</span><span class="n">x</span><span class="p">)</span> <span class="k">for</span> <span class="n">x</span> <span class="ow">in</span> <span class="n">line</span><span class="o">.</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">LogisticRegressionWithSGD</span><span class="o">.</span><span class="n">train</span><span class="p">(</span><span class="n">parsedData</span><span class="p">)</span>
<span class="c"># Build the model</span>
<span class="n">labelsAndPreds</span> <span class="o">=</span> <span class="n">parsedData</span><span class="o">.</span><span class="n">map</span><span class="p">(</span><span class="k">lambda</span> <span class="n">point</span><span class="p">:</span> <span class="p">(</span><span class="nb">int</span><span class="p">(</span><span class="n">point</span><span class="o">.</span><span class="n">item</span><span class="p">(</span><span class="mi">0</span><span class="p">)),</span>
<span class="n">model</span><span class="o">.</span><span class="n">predict</span><span class="p">(</span><span class="n">point</span><span class="o">.</span><span class="n">take</span><span class="p">(</span><span class="nb">range</span><span class="p">(</span><span class="mi">1</span><span class="p">,</span> <span class="n">point</span><span class="o">.</span><span class="n">size</span><span class="p">)))))</span>
<span class="c"># Evaluating the model on training data</span>
<span class="n">trainErr</span> <span class="o">=</span> <span class="n">labelsAndPreds</span><span class="o">.</span><span class="n">filter</span><span class="p">(</span><span class="k">lambda</span> <span class="p">(</span><span class="n">v</span><span class="p">,</span> <span class="n">p</span><span class="p">):</span> <span class="n">v</span> <span class="o">!=</span> <span class="n">p</span><span class="p">)</span><span class="o">.</span><span class="n">count</span><span class="p">()</span> <span class="o">/</span> <span class="nb">float</span><span class="p">(</span><span class="n">parsedData</span><span class="o">.</span><span class="n">count</span><span class="p">())</span>
<span class="k">print</span><span class="p">(</span><span class="s">"Training Error = "</span> <span class="o">+</span> <span class="nb">str</span><span class="p">(</span><span class="n">trainErr</span><span class="p">))</span>
</code></pre></div>
<h2 id="linear-regression-2">Linear Regression</h2>
<p>The following example demonstrate how to load training data, parse it as an RDD of LabeledPoint. The
example then uses LinearRegressionWithSGD to build a simple linear model to predict label values. We
compute the Mean Squared Error at the end to evaluate
<a href="http://en.wikipedia.org/wiki/Goodness_of_fit">goodness of fit</a></p>
<div class="highlight"><pre><code class="python"><span class="kn">from</span> <span class="nn">pyspark.mllib.regression</span> <span class="kn">import</span> <span class="n">LinearRegressionWithSGD</span>
<span class="kn">from</span> <span class="nn">numpy</span> <span class="kn">import</span> <span class="n">array</span>
<span class="c"># Load and parse the data</span>
<span class="n">data</span> <span class="o">=</span> <span class="n">sc</span><span class="o">.</span><span class="n">textFile</span><span class="p">(</span><span class="s">"mllib/data/ridge-data/lpsa.data"</span><span class="p">)</span>
<span class="n">parsedData</span> <span class="o">=</span> <span class="n">data</span><span class="o">.</span><span class="n">map</span><span class="p">(</span><span class="k">lambda</span> <span class="n">line</span><span class="p">:</span> <span class="n">array</span><span class="p">([</span><span class="nb">float</span><span class="p">(</span><span class="n">x</span><span class="p">)</span> <span class="k">for</span> <span class="n">x</span> <span class="ow">in</span> <span class="n">line</span><span class="o">.</span><span class="n">replace</span><span class="p">(</span><span class="s">','</span><span class="p">,</span> <span class="s">' '</span><span class="p">)</span><span class="o">.</span><span class="n">split</span><span class="p">(</span><span class="s">' '</span><span class="p">)]))</span>
<span class="c"># Build the model</span>
<span class="n">model</span> <span class="o">=</span> <span class="n">LinearRegressionWithSGD</span><span class="o">.</span><span class="n">train</span><span class="p">(</span><span class="n">parsedData</span><span class="p">)</span>
<span class="c"># Evaluate the model on training data</span>
<span class="n">valuesAndPreds</span> <span class="o">=</span> <span class="n">parsedData</span><span class="o">.</span><span class="n">map</span><span class="p">(</span><span class="k">lambda</span> <span class="n">point</span><span class="p">:</span> <span class="p">(</span><span class="n">point</span><span class="o">.</span><span class="n">item</span><span class="p">(</span><span class="mi">0</span><span class="p">),</span>
<span class="n">model</span><span class="o">.</span><span class="n">predict</span><span class="p">(</span><span class="n">point</span><span class="o">.</span><span class="n">take</span><span class="p">(</span><span class="nb">range</span><span class="p">(</span><span class="mi">1</span><span class="p">,</span> <span class="n">point</span><span class="o">.</span><span class="n">size</span><span class="p">)))))</span>
<span class="n">MSE</span> <span class="o">=</span> <span class="n">valuesAndPreds</span><span class="o">.</span><span class="n">map</span><span class="p">(</span><span class="k">lambda</span> <span class="p">(</span><span class="n">v</span><span class="p">,</span> <span class="n">p</span><span class="p">):</span> <span class="p">(</span><span class="n">v</span> <span class="o">-</span> <span class="n">p</span><span class="p">)</span><span class="o">**</span><span class="mi">2</span><span class="p">)</span><span class="o">.</span><span class="n">reduce</span><span class="p">(</span><span class="k">lambda</span> <span class="n">x</span><span class="p">,</span> <span class="n">y</span><span class="p">:</span> <span class="n">x</span> <span class="o">+</span> <span class="n">y</span><span class="p">)</span><span class="o">/</span><span class="n">valuesAndPreds</span><span class="o">.</span><span class="n">count</span><span class="p">()</span>
<span class="k">print</span><span class="p">(</span><span class="s">"Mean Squared Error = "</span> <span class="o">+</span> <span class="nb">str</span><span class="p">(</span><span class="n">MSE</span><span class="p">))</span>
</code></pre></div>
<h2 id="clustering-2">Clustering</h2>
<p>In the following example after loading and parsing data, we use the KMeans object to cluster the data
into two clusters. The number of desired clusters is passed to the algorithm. We then compute Within
Set Sum of Squared Error (WSSSE). You can reduce this error measure by increasing <em>k</em>. In fact the
optimal <em>k</em> is usually one where there is an “elbow” in the WSSSE graph.</p>
<div class="highlight"><pre><code class="python"><span class="kn">from</span> <span class="nn">pyspark.mllib.clustering</span> <span class="kn">import</span> <span class="n">KMeans</span>
<span class="kn">from</span> <span class="nn">numpy</span> <span class="kn">import</span> <span class="n">array</span>
<span class="kn">from</span> <span class="nn">math</span> <span class="kn">import</span> <span class="n">sqrt</span>
<span class="c"># Load and parse the data</span>
<span class="n">data</span> <span class="o">=</span> <span class="n">sc</span><span class="o">.</span><span class="n">textFile</span><span class="p">(</span><span class="s">"kmeans_data.txt"</span><span class="p">)</span>
<span class="n">parsedData</span> <span class="o">=</span> <span class="n">data</span><span class="o">.</span><span class="n">map</span><span class="p">(</span><span class="k">lambda</span> <span class="n">line</span><span class="p">:</span> <span class="n">array</span><span class="p">([</span><span class="nb">float</span><span class="p">(</span><span class="n">x</span><span class="p">)</span> <span class="k">for</span> <span class="n">x</span> <span class="ow">in</span> <span class="n">line</span><span class="o">.</span><span class="n">split</span><span class="p">(</span><span class="s">' '</span><span class="p">)]))</span>
<span class="c"># Build the model (cluster the data)</span>
<span class="n">clusters</span> <span class="o">=</span> <span class="n">KMeans</span><span class="o">.</span><span class="n">train</span><span class="p">(</span><span class="n">parsedData</span><span class="p">,</span> <span class="mi">2</span><span class="p">,</span> <span class="n">maxIterations</span><span class="o">=</span><span class="mi">10</span><span class="p">,</span>
<span class="n">runs</span><span class="o">=</span><span class="mi">30</span><span class="p">,</span> <span class="n">initialization_mode</span><span class="o">=</span><span class="s">"random"</span><span class="p">)</span>
<span class="c"># Evaluate clustering by computing Within Set Sum of Squared Errors</span>
<span class="k">def</span> <span class="nf">error</span><span class="p">(</span><span class="n">point</span><span class="p">):</span>
<span class="n">center</span> <span class="o">=</span> <span class="n">clusters</span><span class="o">.</span><span class="n">centers</span><span class="p">[</span><span class="n">clusters</span><span class="o">.</span><span class="n">predict</span><span class="p">(</span><span class="n">point</span><span class="p">)]</span>
<span class="k">return</span> <span class="n">sqrt</span><span class="p">(</span><span class="nb">sum</span><span class="p">([</span><span class="n">x</span><span class="o">**</span><span class="mi">2</span> <span class="k">for</span> <span class="n">x</span> <span class="ow">in</span> <span class="p">(</span><span class="n">point</span> <span class="o">-</span> <span class="n">center</span><span class="p">)]))</span>
<span class="n">WSSSE</span> <span class="o">=</span> <span class="n">parsedData</span><span class="o">.</span><span class="n">map</span><span class="p">(</span><span class="k">lambda</span> <span class="n">point</span><span class="p">:</span> <span class="n">error</span><span class="p">(</span><span class="n">point</span><span class="p">))</span><span class="o">.</span><span class="n">reduce</span><span class="p">(</span><span class="k">lambda</span> <span class="n">x</span><span class="p">,</span> <span class="n">y</span><span class="p">:</span> <span class="n">x</span> <span class="o">+</span> <span class="n">y</span><span class="p">)</span>
<span class="k">print</span><span class="p">(</span><span class="s">"Within Set Sum of Squared Error = "</span> <span class="o">+</span> <span class="nb">str</span><span class="p">(</span><span class="n">WSSSE</span><span class="p">))</span>
</code></pre></div>
<p>Similarly you can use RidgeRegressionWithSGD and LassoWithSGD and compare training Mean Squared
Errors.</p>
<h2 id="collaborative-filtering-2">Collaborative Filtering</h2>
<p>In the following example we load rating data. Each row consists of a user, a product and a rating.
We use the default ALS.train() method which assumes ratings are explicit. We evaluate the
recommendation by measuring the Mean Squared Error of rating prediction.</p>
<div class="highlight"><pre><code class="python"><span class="kn">from</span> <span class="nn">pyspark.mllib.recommendation</span> <span class="kn">import</span> <span class="n">ALS</span>
<span class="kn">from</span> <span class="nn">numpy</span> <span class="kn">import</span> <span class="n">array</span>
<span class="c"># Load and parse the data</span>
<span class="n">data</span> <span class="o">=</span> <span class="n">sc</span><span class="o">.</span><span class="n">textFile</span><span class="p">(</span><span class="s">"mllib/data/als/test.data"</span><span class="p">)</span>
<span class="n">ratings</span> <span class="o">=</span> <span class="n">data</span><span class="o">.</span><span class="n">map</span><span class="p">(</span><span class="k">lambda</span> <span class="n">line</span><span class="p">:</span> <span class="n">array</span><span class="p">([</span><span class="nb">float</span><span class="p">(</span><span class="n">x</span><span class="p">)</span> <span class="k">for</span> <span class="n">x</span> <span class="ow">in</span> <span class="n">line</span><span class="o">.</span><span class="n">split</span><span class="p">(</span><span class="s">','</span><span class="p">)]))</span>
<span class="c"># Build the recommendation model using Alternating Least Squares</span>
<span class="n">model</span> <span class="o">=</span> <span class="n">ALS</span><span class="o">.</span><span class="n">train</span><span class="p">(</span><span class="n">ratings</span><span class="p">,</span> <span class="mi">1</span><span class="p">,</span> <span class="mi">20</span><span class="p">)</span>
<span class="c"># Evaluate the model on training data</span>
<span class="n">testdata</span> <span class="o">=</span> <span class="n">ratings</span><span class="o">.</span><span class="n">map</span><span class="p">(</span><span class="k">lambda</span> <span class="n">p</span><span class="p">:</span> <span class="p">(</span><span class="nb">int</span><span class="p">(</span><span class="n">p</span><span class="p">[</span><span class="mi">0</span><span class="p">]),</span> <span class="nb">int</span><span class="p">(</span><span class="n">p</span><span class="p">[</span><span class="mi">1</span><span class="p">])))</span>
<span class="n">predictions</span> <span class="o">=</span> <span class="n">model</span><span class="o">.</span><span class="n">predictAll</span><span class="p">(</span><span class="n">testdata</span><span class="p">)</span><span class="o">.</span><span class="n">map</span><span class="p">(</span><span class="k">lambda</span> <span class="n">r</span><span class="p">:</span> <span class="p">((</span><span class="n">r</span><span class="p">[</span><span class="mi">0</span><span class="p">],</span> <span class="n">r</span><span class="p">[</span><span class="mi">1</span><span class="p">]),</span> <span class="n">r</span><span class="p">[</span><span class="mi">2</span><span class="p">]))</span>
<span class="n">ratesAndPreds</span> <span class="o">=</span> <span class="n">ratings</span><span class="o">.</span><span class="n">map</span><span class="p">(</span><span class="k">lambda</span> <span class="n">r</span><span class="p">:</span> <span class="p">((</span><span class="n">r</span><span class="p">[</span><span class="mi">0</span><span class="p">],</span> <span class="n">r</span><span class="p">[</span><span class="mi">1</span><span class="p">]),</span> <span class="n">r</span><span class="p">[</span><span class="mi">2</span><span class="p">]))</span><span class="o">.</span><span class="n">join</span><span class="p">(</span><span class="n">predictions</span><span class="p">)</span>
<span class="n">MSE</span> <span class="o">=</span> <span class="n">ratesAndPreds</span><span class="o">.</span><span class="n">map</span><span class="p">(</span><span class="k">lambda</span> <span class="n">r</span><span class="p">:</span> <span class="p">(</span><span class="n">r</span><span class="p">[</span><span class="mi">1</span><span class="p">][</span><span class="mi">0</span><span class="p">]</span> <span class="o">-</span> <span class="n">r</span><span class="p">[</span><span class="mi">1</span><span class="p">][</span><span class="mi">1</span><span class="p">])</span><span class="o">**</span><span class="mi">2</span><span class="p">)</span><span class="o">.</span><span class="n">reduce</span><span class="p">(</span><span class="k">lambda</span> <span class="n">x</span><span class="p">,</span> <span class="n">y</span><span class="p">:</span> <span class="n">x</span> <span class="o">+</span> <span class="n">y</span><span class="p">)</span><span class="o">/</span><span class="n">ratesAndPreds</span><span class="o">.</span><span class="n">count</span><span class="p">()</span>
<span class="k">print</span><span class="p">(</span><span class="s">"Mean Squared Error = "</span> <span class="o">+</span> <span class="nb">str</span><span class="p">(</span><span class="n">MSE</span><span class="p">))</span>
</code></pre></div>
<p>If the rating matrix is derived from other source of information (i.e., it is inferred from other
signals), you can use the trainImplicit method to get better results.</p>
<div class="highlight"><pre><code class="python"><span class="c"># Build the recommendation model using Alternating Least Squares based on implicit ratings</span>
<span class="n">model</span> <span class="o">=</span> <span class="n">ALS</span><span class="o">.</span><span class="n">trainImplicit</span><span class="p">(</span><span class="n">ratings</span><span class="p">,</span> <span class="mi">1</span><span class="p">,</span> <span class="mi">20</span><span class="p">)</span>
</code></pre></div>
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