Github user jkbradley commented on a diff in the pull request:
https://github.com/apache/spark/pull/15413#discussion_r94084918
--- Diff:
mllib/src/main/scala/org/apache/spark/ml/clustering/GaussianMixture.scala ---
@@ -356,13 +427,243 @@ class GaussianMixture @Since("2.0.0") (
override def transformSchema(schema: StructType): StructType = {
validateAndTransformSchema(schema)
}
+
+ /**
+ * Initialize weights and corresponding gaussian distributions at random.
+ *
+ * We start with uniform weights, a random mean from the data, and
diagonal covariance matrices
+ * using component variances derived from the samples.
+ *
+ * @param instances The training instances.
+ * @param numClusters The number of clusters.
+ * @param numFeatures The number of features of training instance.
+ * @return The initialized weights and corresponding gaussian
distributions. Note the
+ * covariance matrix of multivariate gaussian distribution is
symmetric and
+ * we only save the upper triangular part as a dense vector.
+ */
+ private def initRandom(
+ instances: RDD[Vector],
+ numClusters: Int,
+ numFeatures: Int): (Array[Double], Array[(DenseVector,
DenseVector)]) = {
+ val samples = instances.takeSample(withReplacement = true, numClusters
* numSamples, $(seed))
+ val weights: Array[Double] = Array.fill(numClusters)(1.0 / numClusters)
+ val gaussians: Array[(DenseVector, DenseVector)] =
Array.tabulate(numClusters) { i =>
+ val slice = samples.view(i * numSamples, (i + 1) * numSamples)
+ val mean = {
+ val v = new DenseVector(new Array[Double](numFeatures))
+ var i = 0
+ while (i < numSamples) {
+ BLAS.axpy(1.0, slice(i), v)
+ i += 1
+ }
+ BLAS.scal(1.0 / numSamples, v)
+ v
+ }
+ /*
+ Construct matrix where diagonal entries are element-wise
+ variance of input vectors (computes biased variance).
+ Since the covariance matrix of multivariate gaussian distribution
is symmetric,
+ only the upper triangular part of the matrix will be saved as a
dense vector
+ in order to reduce the shuffled data size.
+ */
+ val cov = {
+ val ss = new DenseVector(new Array[Double](numFeatures)).asBreeze
+ slice.foreach(xi => ss += (xi.asBreeze - mean.asBreeze) :^ 2.0)
+ val diagVec = Vectors.fromBreeze(ss)
+ BLAS.scal(1.0 / numSamples, diagVec)
+ val covVec = new DenseVector(Array.fill[Double](
+ numFeatures * (numFeatures + 1) / 2)(0.0))
+ diagVec.toArray.zipWithIndex.foreach { case (v: Double, i: Int) =>
+ covVec.values(i + i * (i + 1) / 2) = v
+ }
+ covVec
+ }
+ (mean, cov)
+ }
+ (weights, gaussians)
+ }
}
@Since("2.0.0")
object GaussianMixture extends DefaultParamsReadable[GaussianMixture] {
@Since("2.0.0")
override def load(path: String): GaussianMixture = super.load(path)
+
+ /**
+ * Heuristic to distribute the computation of the
[[MultivariateGaussian]]s, approximately when
+ * numFeatures > 25 except for when numClusters is very small.
+ *
+ * @param numClusters Number of clusters
+ * @param numFeatures Number of features
+ */
+ private[clustering] def shouldDistributeGaussians(
+ numClusters: Int,
+ numFeatures: Int): Boolean = {
+ ((numClusters - 1.0) / numClusters) * numFeatures > 25.0
+ }
+
+ /**
+ * Convert an n * (n + 1) / 2 dimension array representing the upper
triangular part of a matrix
+ * into an n * n array representing the full symmetric matrix.
+ *
+ * @param n The order of the n by n matrix.
+ * @param triangularValues The upper triangular part of the matrix
packed in an array
+ * (column major).
+ * @return An array which represents the symmetric matrix in column
major.
+ */
+ private[clustering] def unpackUpperTriangularMatrix(
+ n: Int,
+ triangularValues: Array[Double]): Array[Double] = {
+ val symmetricValues = new Array[Double](n * n)
+ var r = 0
+ var i = 0
+ while(i < n) {
+ var j = 0
+ while (j <= i) {
+ symmetricValues(i * n + j) = triangularValues(r)
+ symmetricValues(j * n + i) = triangularValues(r)
+ r += 1
+ j += 1
+ }
+ i += 1
+ }
+ symmetricValues
+ }
+
+ /**
+ * Update the weight, mean and covariance of gaussian distribution.
+ *
+ * @param mean The mean of the gaussian distribution.
+ * @param cov The covariance matrix of the gaussian distribution. Note
we only
+ * save the upper triangular part as a dense vector.
+ * @param weight The weight of the gaussian distribution.
+ * @param sumWeights The sum of weights of all clusters.
+ * @return The updated weight, mean and covariance.
+ */
+ private[clustering] def updateWeightsAndGaussians(
+ mean: DenseVector,
+ cov: DenseVector,
+ weight: Double,
+ sumWeights: Double): (Double, (DenseVector, DenseVector)) = {
+ BLAS.scal(1.0 / weight, mean)
+ BLAS.spr(-weight, mean, cov)
+ BLAS.scal(1.0 / weight, cov)
+ val newWeight = weight / sumWeights
+ val newGaussian = (mean, cov)
+ (newWeight, newGaussian)
+ }
+}
+
+/**
+ * ExpectationAggregator computes the partial expectation results.
+ *
+ * @param numFeatures The number of features.
+ * @param bcWeights The broadcast weights for each Gaussian distribution
in the mixture.
+ * @param bcGaussians The broadcast array of Multivariate Gaussian
(Normal) Distribution
+ * in the mixture. Note only upper triangular part of
the covariance
+ * matrix of each distribution is stored as dense
vector in order to
+ * reduce shuffled data size.
+ */
+private class ExpectationAggregator(
+ numFeatures: Int,
+ bcWeights: Broadcast[Array[Double]],
+ bcGaussians: Broadcast[Array[(DenseVector, DenseVector)]]) extends
Serializable {
+
+ private val k: Int = bcWeights.value.length
+ private var totalCnt: Long = 0L
+ private var newLogLikelihood: Double = 0.0
+ private val newWeights: Array[Double] = new Array[Double](k)
+ private val newMeans: Array[DenseVector] = Array.fill(k)(
+ new DenseVector(Array.fill[Double](numFeatures)(0.0)))
+ private val newCovs: Array[DenseVector] = Array.fill(k)(
+ new DenseVector(Array.fill[Double](numFeatures * (numFeatures + 1) /
2)(0.0)))
+
+ @transient private lazy val oldGaussians = {
+ bcGaussians.value.map { case (mean, covVec) =>
+ val cov = new DenseMatrix(numFeatures, numFeatures,
+ GaussianMixture.unpackUpperTriangularMatrix(numFeatures,
covVec.values))
+ new MultivariateGaussian(mean, cov)
+ }
+ }
+
+ def count: Long = totalCnt
+
+ def logLikelihood: Double = newLogLikelihood
+
+ def weights: Array[Double] = newWeights
+
+ def means: Array[DenseVector] = newMeans
+
+ def covs: Array[DenseVector] = newCovs
+
+ /**
+ * Add a new training instance to this ExpectationAggregator, update the
weights,
+ * means and covariances for each distributions, and update the log
likelihood.
+ *
+ * @param instance The instance of data point to be added.
+ * @return This ExpectationAggregator object.
+ */
+ def add(instance: Vector): this.type = {
+ val localWeights = bcWeights.value
+ val localOldGaussians = oldGaussians
+
+ val prob = new Array[Double](k)
+ var probSum = 0.0
+ var i = 0
+ while(i < k) {
--- End diff --
And in several other places
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