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+ <h1 class="title">Machine Learning Library (MLlib)</h1>
+
+ <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>
+
+<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>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">&quot;mllib/data/sample_svm_data.txt&quot;</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">=&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="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">=&gt;</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</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">=&gt;</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">=&gt;</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">&quot;trainError = &quot;</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>
+
+<p>Both of the code snippets above can be executed in <code>spark-shell</code> to generate a
+classifier for the provided dataset.</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, arguably
+the most commonly used clustering approach that clusters the data points into
+<em>k</em> 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 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://research.yahoo.com/pub/2433">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>
+
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