Github user javadba commented on a diff in the pull request:
https://github.com/apache/spark/pull/4254#discussion_r23807925
--- Diff:
mllib/src/main/scala/org/apache/spark/mllib/clustering/PowerIterationClustering.scala
---
@@ -0,0 +1,220 @@
+/*
+ * 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.{DenseMatrix => BDM, DenseVector => BDV}
+import org.apache.log4j.Logger
+import org.apache.spark.SparkContext
+import org.apache.spark.graphx._
+import org.apache.spark.mllib.linalg.{Vector, Vectors}
+import org.apache.spark.rdd.RDD
+
+import scala.language.existentials
+
+/**
+ * Implements the scalable graph clustering algorithm Power Iteration
Clustering (see
+ * www.icml2010.org/papers/387.pdf). From the abstract:
+ *
+ * The input data is first transformed to a normalized Affinity Matrix via
Gaussian pairwise
+ * distance calculations. Power iteration is then used to find a
dimensionality-reduced
+ * representation. The resulting pseudo-eigenvector provides effective
clustering - as
+ * performed by Parallel KMeans.
+ */
+object PowerIterationClustering {
+
+ private val logger = Logger.getLogger(getClass.getName())
+
+ type LabeledPoint = (VertexId, BDV[Double])
+ type Points = Seq[LabeledPoint]
+ type DGraph = Graph[Double, Double]
+ type IndexedVector[Double] = (Long, BDV[Double])
+
+ // Terminate iteration when norm changes by less than this value
+ val defaultMinNormChange: Double = 1e-11
+
+ // Default number of iterations for PIC loop
+ val defaultIterations: Int = 20
+
+ // Do not allow divide by zero: change to this value instead
+ val defaultDivideByZeroVal: Double = 1e-15
+
+ // Default number of runs by the KMeans.run() method
+ val defaultKMeansRuns = 10
+
+ /**
+ *
+ * Run a Power Iteration Clustering
+ *
+ * @param sc Spark Context
+ * @param G Affinity Matrix in a Sparse Graph structure
+ * @param nClusters Number of clusters to create
+ * @param nIterations Number of iterations of the PIC algorithm
+ * that calculates primary PseudoEigenvector and
Eigenvalue
+ * @param nRuns Number of runs for the KMeans clustering
+ * @return Tuple of (Seq[(Cluster Id,Cluster Center)],
+ * Seq[(VertexId, ClusterID Membership)]
+ */
+ def run(sc: SparkContext,
+ G: Graph[Double, Double],
+ nClusters: Int,
+ nIterations: Int = defaultIterations,
+ nRuns: Int = defaultKMeansRuns)
+ : (Seq[(Int, Vector)], Seq[((VertexId, Vector), Int)]) = {
+ val (gUpdated, lambda, vt) = getPrincipalEigen(sc, G, nIterations)
+ // TODO: avoid local collect and then sc.parallelize.
+ val localVt = vt.collect.sortBy(_._1)
+ val vectRdd = sc.parallelize(localVt.map(v => (v._1,
Vectors.dense(v._2))))
+ vectRdd.cache()
+ val model = KMeans.train(vectRdd.map {
+ _._2
+ }, nClusters, nRuns)
+ vectRdd.unpersist()
+ if (logger.isDebugEnabled) {
+ logger.debug(s"Eigenvalue = $lambda EigenVector:
${localVt.mkString(",")}")
+ }
+ val estimates = vectRdd.zip(model.predict(vectRdd.map(_._2)))
+ if (logger.isDebugEnabled) {
+ logger.debug(s"lambda=$lambda eigen=${localVt.mkString(",")}")
+ }
+ val ccs = (0 until
model.clusterCenters.length).zip(model.clusterCenters)
+ if (logger.isDebugEnabled) {
+ logger.debug(s"Kmeans model cluster centers: ${ccs.mkString(",")}")
+ }
+ val estCollected = estimates.collect.sortBy(_._1._1)
+ if (logger.isDebugEnabled) {
+ val clusters = estCollected.map(_._2)
+ val counts = estCollected.groupBy(_._2).mapValues {
+ _.length
+ }
+ logger.debug(s"Cluster counts: Counts: ${counts.mkString(",")}"
+ + s"\nCluster Estimates: ${estCollected.mkString(",")}")
+ }
+ (ccs, estCollected)
+ }
+
+
+ /**
+ * Create a Graph given an initial Vt0 and a set of Edges that
+ * represent the Normalized Affinity Matrix (W)
+ */
+ def createGraphFromEdges(sc: SparkContext,
+ edgesRdd: RDD[Edge[Double]],
+ nPoints: Int,
+ optInitialVt: Option[Seq[(VertexId, Double)]] =
None) = {
+
+ assert(nPoints > 0, "Must provide number of points from the original
dataset")
+ val G = if (optInitialVt.isDefined) {
+ val initialVt = optInitialVt.get
+ val vertsRdd = sc.parallelize(initialVt)
+ Graph(vertsRdd, edgesRdd)
+ } else {
+ Graph.fromEdges(edgesRdd, -1.0)
+ }
+ G
+
+ }
+
+ /**
+ * Calculate the dominant Eigenvalue and Eigenvector for a given sparse
graph
+ * using the PIC method
+ * @param sc
+ * @param G Input Graph representing the Normalized Affinity Matrix (W)
+ * @param nIterations Number of iterations of the PIC algorithm
+ * @param optMinNormChange Minimum norm acceleration for detecting
convergence
+ * - indicated as "epsilon" in the PIC paper
+ * @return
+ */
+ def getPrincipalEigen(sc: SparkContext,
+ G: DGraph,
+ nIterations: Int = defaultIterations,
+ optMinNormChange: Option[Double] = None
+ ): (DGraph, Double, VertexRDD[Double]) = {
+
+ var priorNorm = Double.MaxValue
+ var norm = Double.MaxValue
+ var priorNormVelocity = Double.MaxValue
+ var normVelocity = Double.MaxValue
+ var normAccel = Double.MaxValue
+ val DummyVertexId = -99L
+ var vnorm: Double = -1.0
+ var outG: DGraph = null
+ var prevG: DGraph = G
+ val epsilon = optMinNormChange
+ .getOrElse(1e-5 / G.vertices.count())
--- End diff --
Added the following - feel free to comment further
// The epsilon calculation is provided by the original paper
www.icml2010.org/papers/387.pdf as epsilon = 1e-5/(#points)
// However that seems quite small for large#points
// Instead we use epsilonPrime = Max(epsilon, 1e-10)
val epsilon = optMinNormChange
.getOrElse(math.max(1e-5 / G.vertices.count(), 1e-10))
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