Github user mengxr commented on a diff in the pull request:
https://github.com/apache/spark/pull/3022#discussion_r22092954
--- Diff:
mllib/src/main/scala/org/apache/spark/mllib/clustering/GaussianMixtureModelEM.scala
---
@@ -0,0 +1,248 @@
+/*
+ * 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 scala.collection.mutable.IndexedSeqView
+
+/**
+ * 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 VectorArrayView = IndexedSeqView[DenseDoubleVector,
Array[DenseDoubleVector]]
+
+ 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)
+ var i = 0
+ while (i < m1._2.length) {
+ m1._2(i) += m2._2(i)
+ m1._3(i) += m2._3(i)
+ m1._4(i) += m2._4(i)
+ i = i + 1
+ }
+ m1
+ }
+
+ // compute cluster contributions for each input point
+ // (U, T) => U for aggregation
+ private def computeExpectation(
+ weights: Array[Double],
+ dists: Array[MultivariateGaussian])
+ (sums: ExpectationSum, x: DenseDoubleVector): ExpectationSum = {
+ val k = sums._2.length
+ val p = weights.zip(dists).map { case (weight, dist) => eps + weight *
dist.pdf(x) }
+ val pSum = p.sum
+ sums._1(0) += math.log(pSum)
+ val xxt = x * new Transpose(x)
+ var i = 0
+ while (i < k) {
+ p(i) /= pSum
+ sums._2(i) += p(i)
+ sums._3(i) += x * p(i)
+ sums._4(i) += xxt * p(i)
+ i = i + 1
+ }
+ sums
+ }
+
+ // number of samples per cluster to use when initializing Gaussians
+ private val nSamples = 5
+
+ // an initializing GMM can be provided rather than using the
+ // default random starting point
+ private var initialGmm: Option[GaussianMixtureModel] = None
+
+ /** A default instance, 2 Gaussians, 100 iterations, 0.01 log-likelihood
threshold */
+ def this() = this(2, 0.01, 100)
+
+ /** Set the initial GMM starting point, bypassing the random
initialization.
+ * You must call setK() prior to calling this method, and the condition
+ * (gmm.k == this.k) must be met; failure will result in an
IllegalArgumentException
+ */
+ def setInitialGmm(gmm: GaussianMixtureModel): this.type = {
+ if (gmm.k == k) {
+ initialGmm = Some(gmm)
+ } else {
+ throw new IllegalArgumentException("initialing GMM has mismatched
cluster count (gmm.k != k)")
+ }
+ this
+ }
+
+ /** Return the user supplied initial GMM, if supplied */
+ def getInitialGmm: Option[GaussianMixtureModel] = initialGmm
+
+ /** 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 sc = 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
+
+ // Determine initial weights and corresponding Gaussians.
+ // If the user supplied an initial GMM, we use those values, otherwise
+ // we start with uniform weights, a random mean from the data, and
+ // diagonal covariance matrices using component variances
+ // derived from the samples
+ val (weights, gaussians) = initialGmm match {
+ case Some(gmm) => (gmm.weight, gmm.mu.zip(gmm.sigma).map{ case(mu,
sigma) =>
+ new MultivariateGaussian(mu.toBreeze.toDenseVector,
sigma.toBreeze.toDenseMatrix)
+ }.toArray)
+
+ case None => {
+ val samples = breezeData.takeSample(true, k * nSamples,
scala.util.Random.nextInt)
+ (Array.fill[Double](k)(1.0 / k), (0 until k).map{ i =>
+ val slice = samples.view(i * nSamples, (i + 1) * nSamples)
+ new MultivariateGaussian(vectorMean(slice),
initCovariance(slice))
+ }.toArray)
+ }
+ }
+
+ var llh = Double.MinValue // current log-likelihood
+ var llhp = 0.0 // previous log-likelihood
+
+ var iter = 0
+ do {
+ // create and broadcast curried cluster contribution function
+ val compute = sc.broadcast(computeExpectation(weights, gaussians)_)
+
+ // aggregate the cluster contribution for all sample points
+ val (logLikelihood, wSums, muSums, sigmaSums) =
+ breezeData.aggregate(zeroExpectationSum(k, d))(compute.value,
addExpectationSums)
+
+ // Create new distributions based on the partial assignments
+ // (often referred to as the "M" step in literature)
+ val sumWeights = wSums.sum
+ for (i <- 0 until k) {
--- End diff --
Use `while` instead of `for`.
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