SPARK-5019 [MLlib] - GaussianMixtureModel exposes instances of MultivariateGauss...

This PR modifies GaussianMixtureModel to expose instances of MutlivariateGaussian rather than separate mean and covariance arrays.

Author: Travis Galoppo <tjg2107@columbia.edu>

Closes #4088 from tgaloppo/spark-5019 and squashes the following commits:

3ef6c7f [Travis Galoppo] In GaussianMixtureModel: Changed name of weight, gaussian to weights, gaussians.  Other sources modified accordingly.
091e8da [Travis Galoppo] SPARK-5019 - GaussianMixtureModel exposes instances of MultivariateGaussian rather than mean/covariance matrices

examples/src/main/scala/org/apache/spark/examples/mllib/DenseGmmEM.scala

@@ -54,7 +54,7 @@ object DenseGmmEM {
     
     for (i <- 0 until clusters.k) {
       println("weight=%f\nmu=%s\nsigma=\n%s\n" format 
-        (clusters.weight(i), clusters.mu(i), clusters.sigma(i)))
+        (clusters.weights(i), clusters.gaussians(i).mu, clusters.gaussians(i).sigma))
     }
     
     println("Cluster labels (first <= 100):")

mllib/src/main/scala/org/apache/spark/mllib/clustering/GaussianMixtureEM.scala

@@ -134,9 +134,7 @@ class GaussianMixtureEM private (
     // diagonal covariance matrices using component variances
     // derived from the samples    
     val (weights, gaussians) = initialModel match {
-      case Some(gmm) => (gmm.weight, gmm.mu.zip(gmm.sigma).map { case(mu, sigma) => 
-        new MultivariateGaussian(mu, sigma) 
-      })
+      case Some(gmm) => (gmm.weights, gmm.gaussians)
       
       case None => {
         val samples = breezeData.takeSample(withReplacement = true, k * nSamples, seed)
@@ -176,10 +174,7 @@ class GaussianMixtureEM private (
       iter += 1
     } 
     
-    // Need to convert the breeze matrices to MLlib matrices
-    val means = Array.tabulate(k) { i => gaussians(i).mu }
-    val sigmas = Array.tabulate(k) { i => gaussians(i).sigma }
-    new GaussianMixtureModel(weights, means, sigmas)
+    new GaussianMixtureModel(weights, gaussians)
   }
     
   /** Average of dense breeze vectors */

mllib/src/main/scala/org/apache/spark/mllib/clustering/GaussianMixtureModel.scala

@@ -20,7 +20,7 @@ package org.apache.spark.mllib.clustering
 import breeze.linalg.{DenseVector => BreezeVector}
 
 import org.apache.spark.rdd.RDD
-import org.apache.spark.mllib.linalg.{Matrix, Vector}
+import org.apache.spark.mllib.linalg.Vector
 import org.apache.spark.mllib.stat.distribution.MultivariateGaussian
 import org.apache.spark.mllib.util.MLUtils
 
@@ -36,12 +36,13 @@ import org.apache.spark.mllib.util.MLUtils
  *              covariance matrix for Gaussian i
  */
 class GaussianMixtureModel(
-  val weight: Array[Double], 
-  val mu: Array[Vector], 
-  val sigma: Array[Matrix]) extends Serializable {
+  val weights: Array[Double], 
+  val gaussians: Array[MultivariateGaussian]) extends Serializable {
+  
+  require(weights.length == gaussians.length, "Length of weight and Gaussian arrays must match")
   
   /** Number of gaussians in mixture */
-  def k: Int = weight.length
+  def k: Int = weights.length
 
   /** Maps given points to their cluster indices. */
   def predict(points: RDD[Vector]): RDD[Int] = {
@@ -55,14 +56,10 @@ class GaussianMixtureModel(
    */
   def predictSoft(points: RDD[Vector]): RDD[Array[Double]] = {
     val sc = points.sparkContext
-    val dists = sc.broadcast {
-      (0 until k).map { i => 
-        new MultivariateGaussian(mu(i).toBreeze.toDenseVector, sigma(i).toBreeze.toDenseMatrix)
-      }.toArray
-    }
-    val weights = sc.broadcast(weight)
+    val bcDists = sc.broadcast(gaussians)
+    val bcWeights = sc.broadcast(weights)
     points.map { x => 
-      computeSoftAssignments(x.toBreeze.toDenseVector, dists.value, weights.value, k)
+      computeSoftAssignments(x.toBreeze.toDenseVector, bcDists.value, bcWeights.value, k)
     }
   }
   

mllib/src/test/scala/org/apache/spark/mllib/clustering/GMMExpectationMaximizationSuite.scala

@@ -20,6 +20,7 @@ package org.apache.spark.mllib.clustering
 import org.scalatest.FunSuite
 
 import org.apache.spark.mllib.linalg.{Vectors, Matrices}
+import org.apache.spark.mllib.stat.distribution.MultivariateGaussian
 import org.apache.spark.mllib.util.MLlibTestSparkContext
 import org.apache.spark.mllib.util.TestingUtils._
 
@@ -39,9 +40,9 @@ class GMMExpectationMaximizationSuite extends FunSuite with MLlibTestSparkContex
     val seeds = Array(314589, 29032897, 50181, 494821, 4660)
     seeds.foreach { seed =>
       val gmm = new GaussianMixtureEM().setK(1).setSeed(seed).run(data)
-      assert(gmm.weight(0) ~== Ew absTol 1E-5)
-      assert(gmm.mu(0) ~== Emu absTol 1E-5)
-      assert(gmm.sigma(0) ~== Esigma absTol 1E-5)
+      assert(gmm.weights(0) ~== Ew absTol 1E-5)
+      assert(gmm.gaussians(0).mu ~== Emu absTol 1E-5)
+      assert(gmm.gaussians(0).sigma ~== Esigma absTol 1E-5)
     }
   }
   
@@ -57,8 +58,10 @@ class GMMExpectationMaximizationSuite extends FunSuite with MLlibTestSparkContex
     // we set an initial gaussian to induce expected results
     val initialGmm = new GaussianMixtureModel(
       Array(0.5, 0.5),
-      Array(Vectors.dense(-1.0), Vectors.dense(1.0)),
-      Array(Matrices.dense(1, 1, Array(1.0)), Matrices.dense(1, 1, Array(1.0)))
+      Array(
+        new MultivariateGaussian(Vectors.dense(-1.0), Matrices.dense(1, 1, Array(1.0))),
+        new MultivariateGaussian(Vectors.dense(1.0), Matrices.dense(1, 1, Array(1.0)))
+      )
     )
     
     val Ew = Array(1.0 / 3.0, 2.0 / 3.0)
@@ -70,11 +73,11 @@ class GMMExpectationMaximizationSuite extends FunSuite with MLlibTestSparkContex
       .setInitialModel(initialGmm)
       .run(data)
       
-    assert(gmm.weight(0) ~== Ew(0) absTol 1E-3)
-    assert(gmm.weight(1) ~== Ew(1) absTol 1E-3)
-    assert(gmm.mu(0) ~== Emu(0) absTol 1E-3)
-    assert(gmm.mu(1) ~== Emu(1) absTol 1E-3)
-    assert(gmm.sigma(0) ~== Esigma(0) absTol 1E-3)
-    assert(gmm.sigma(1) ~== Esigma(1) absTol 1E-3)
+    assert(gmm.weights(0) ~== Ew(0) absTol 1E-3)
+    assert(gmm.weights(1) ~== Ew(1) absTol 1E-3)
+    assert(gmm.gaussians(0).mu ~== Emu(0) absTol 1E-3)
+    assert(gmm.gaussians(1).mu ~== Emu(1) absTol 1E-3)
+    assert(gmm.gaussians(0).sigma ~== Esigma(0) absTol 1E-3)
+    assert(gmm.gaussians(1).sigma ~== Esigma(1) absTol 1E-3)
   }
 }