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From: jkbradley <git@git.apache.org>
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Subject: [GitHub] spark pull request: SPARK-4156 [MLLIB] EM algorithm for GMMs
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Message-Id: <20141215220106.576739C848F@tyr.zones.apache.org>
Date: Mon, 15 Dec 2014 22:01:06 +0000 (UTC)

Github user jkbradley commented on a diff in the pull request:

    https://github.com/apache/spark/pull/3022#discussion_r21860754
  
    --- Diff: mllib/src/main/scala/org/apache/spark/mllib/clustering/GaussianMixtureModelEM.scala ---
    @@ -0,0 +1,234 @@
    +/*
    + * Licensed to the Apache Software Foundation (ASF) under one or more
    + * contributor license agreements.  See the NOTICE file distributed with
    + * this work for additional information regarding copyright ownership.
    + * The ASF licenses this file to You under the Apache License, Version 2.0
    + * (the "License"); you may not use this file except in compliance with
    + * the License.  You may obtain a copy of the License at
    + *
    + *    http://www.apache.org/licenses/LICENSE-2.0
    + *
    + * Unless required by applicable law or agreed to in writing, software
    + * distributed under the License is distributed on an "AS IS" BASIS,
    + * WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied.
    + * See the License for the specific language governing permissions and
    + * limitations under the License.
    + */
    +
    +package org.apache.spark.mllib.clustering
    +
    +import breeze.linalg.{DenseVector => BreezeVector, DenseMatrix => BreezeMatrix}
    +import breeze.linalg.Transpose
    +
    +import org.apache.spark.rdd.RDD
    +import org.apache.spark.mllib.linalg.{Matrices, Vector, Vectors}
    +import org.apache.spark.mllib.stat.impl.MultivariateGaussian
    +import org.apache.spark.{Accumulator, AccumulatorParam, SparkContext}
    +import org.apache.spark.SparkContext.DoubleAccumulatorParam
    +
    +/**
    + * This class performs expectation maximization for multivariate Gaussian
    + * Mixture Models (GMMs).  A GMM represents a composite distribution of
    + * independent Gaussian distributions with associated "mixing" weights
    + * specifying each's contribution to the composite.
    + *
    + * Given a set of sample points, this class will maximize the log-likelihood 
    + * for a mixture of k Gaussians, iterating until the log-likelihood changes by 
    + * less than convergenceTol, or until it has reached the max number of iterations.
    + * While this process is generally guaranteed to converge, it is not guaranteed
    + * to find a global optimum.  
    + * 
    + * @param k The number of independent Gaussians in the mixture model
    + * @param convergenceTol The maximum change in log-likelihood at which convergence
    + * is considered to have occurred.
    + * @param maxIterations The maximum number of iterations to perform
    + */
    +class GaussianMixtureModelEM private (
    +    private var k: Int, 
    +    private var convergenceTol: Double, 
    +    private var maxIterations: Int) extends Serializable {
    +      
    +  // Type aliases for convenience
    +  private type DenseDoubleVector = BreezeVector[Double]
    +  private type DenseDoubleMatrix = BreezeMatrix[Double]
    +  
    +  // number of samples per cluster to use when initializing Gaussians
    +  private val nSamples = 5
    +  
    +  /** A default instance, 2 Gaussians, 100 iterations, 0.01 log-likelihood threshold */
    +  def this() = this(2, 0.01, 100)
    +  
    +  /** Set the number of Gaussians in the mixture model.  Default: 2 */
    +  def setK(k: Int): this.type = {
    +    this.k = k
    +    this
    +  }
    +  
    +  /** Return the number of Gaussians in the mixture model */
    +  def getK: Int = k
    +  
    +  /** Set the maximum number of iterations to run. Default: 100 */
    +  def setMaxIterations(maxIterations: Int): this.type = {
    +    this.maxIterations = maxIterations
    +    this
    +  }
    +  
    +  /** Return the maximum number of iterations to run */
    +  def getMaxIterations: Int = maxIterations
    +  
    +  /**
    +   * Set the largest change in log-likelihood at which convergence is 
    +   * considered to have occurred.
    +   */
    +  def setConvergenceTol(convergenceTol: Double): this.type = {
    +    this.convergenceTol = convergenceTol
    +    this
    +  }
    +  
    +  /** Return the largest change in log-likelihood at which convergence is
    +   *  considered to have occurred.
    +   */
    +  def getConvergenceTol: Double = convergenceTol
    +  
    +  /** Machine precision value used to ensure matrix conditioning */
    +  private val eps = math.pow(2.0, -52)
    +  
    +  /** Perform expectation maximization */
    +  def run(data: RDD[Vector]): GaussianMixtureModel = {
    +    val ctx = data.sparkContext
    +    
    +    // we will operate on the data as breeze data
    +    val breezeData = data.map( u => u.toBreeze.toDenseVector ).cache()
    +    
    +    // Get length of the input vectors
    +    val d = breezeData.first.length 
    +    
    +    // For each Gaussian, we will initialize the mean as the average
    +    // of some random samples from the data
    +    val samples = breezeData.takeSample(true, k * nSamples, scala.util.Random.nextInt)
    +    
    +    // gaussians will be array of (weight, mean, covariance) tuples
    +    // we start with uniform weights, a random mean from the data, and
    +    // diagonal covariance matrices using component variances
    +    // derived from the samples 
    +    var gaussians = (0 until k).map{ i => (1.0 / k, 
    --- End diff --
    
    I would format as:
    ```
    var gaussians = (0 until k).map{ i =>
      (1.0 / k, 
        vectorMean(samples.slice(i * nSamples, (i + 1) * nSamples)),
        initCovariance(samples.slice(i * nSamples, (i + 1) * nSamples)))
    }.toArray
    ```
    (indentation + ending the first line with "=>")


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