Github user jkbradley commented on a diff in the pull request: https://github.com/apache/spark/pull/3022#discussion_r22016178 --- Diff: mllib/src/main/scala/org/apache/spark/mllib/clustering/GaussianMixtureModelEM.scala --- @@ -0,0 +1,284 @@ +/* + * 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, Matrix, 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] + + private type ExpectationSum = ( + Array[Double], // log-likelihood in index 0 + Array[Double], // array of weights + Array[DenseDoubleVector], // array of means + Array[DenseDoubleMatrix]) // array of cov matrices + + // create a zero'd ExpectationSum instance + private def zeroExpectationSum(k: Int, d: Int): ExpectationSum = { + (Array(0.0), + new Array[Double](k), + (0 until k).map(_ => BreezeVector.zeros[Double](d)).toArray, + (0 until k).map(_ => BreezeMatrix.zeros[Double](d,d)).toArray) + } + + // add two ExpectationSum objects (allowed to use modify m1) + // (U, U) => U for aggregation + private def addExpectationSums(m1: ExpectationSum, m2: ExpectationSum): ExpectationSum = { + m1._1(0) += m2._1(0) + for (i <- 0 until m1._2.length) { + m1._2(i) += m2._2(i) + m1._3(i) += m2._3(i) + m1._4(i) += m2._4(i) + } + m1 + } + + // compute cluster contributions for each input point + // (U, T) => U for aggregation + private def computeExpectation(weights: Array[Double], dists: Array[MultivariateGaussian]) + (model: ExpectationSum, x: DenseDoubleVector): ExpectationSum = { + val k = model._2.length + val p = (0 until k).map(i => eps + weights(i) * dists(i).pdf(x)).toArray --- End diff -- It is more common to write: ``` val p = weights.zip(dists).map { case (weight, dist) => eps + weight * dist.pdf(x) } ```
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