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From skonto <...@git.apache.org>
Subject [GitHub] flink pull request #757: [FLINK-2131][ml]: Initialization schemes for k-mean...
Date Fri, 30 Sep 2016 22:31:49 GMT
Github user skonto commented on a diff in the pull request:

    https://github.com/apache/flink/pull/757#discussion_r81429036
  
    --- Diff: flink-staging/flink-ml/src/main/scala/org/apache/flink/ml/clustering/KMeans.scala
---
    @@ -0,0 +1,614 @@
    +/*
    + * 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.flink.ml.clustering
    +
    +import org.apache.flink.api.common.functions.RichFilterFunction
    +import org.apache.flink.api.java.functions.FunctionAnnotation.ForwardedFields
    +import org.apache.flink.api.scala.{DataSet, _}
    +import org.apache.flink.configuration.Configuration
    +import org.apache.flink.ml._
    +import org.apache.flink.ml.common.FlinkMLTools.ModuloKeyPartitioner
    +import org.apache.flink.ml.common.{LabeledVector, _}
    +import org.apache.flink.ml.math.Breeze._
    +import org.apache.flink.ml.math.{BLAS, Vector}
    +import org.apache.flink.ml.metrics.distances.EuclideanDistanceMetric
    +import org.apache.flink.ml.pipeline._
    +
    +import scala.collection.JavaConverters._
    +import scala.util.Random
    +
    +
    +/**
    + * Implements the KMeans algorithm which calculates cluster centroids based on set of
training data
    + * points and a set of k initial centroids.
    + *
    + * [[KMeans]] is a [[Predictor]] which needs to be trained on a set of data points and
can then be
    + * used to assign new points to the learned cluster centroids.
    + *
    + * The KMeans algorithm works as described on Wikipedia
    + * (http://en.wikipedia.org/wiki/K-means_clustering):
    + *
    + * Given an initial set of k means m1(1),…,mk(1) (see below), the algorithm proceeds
by alternating
    + * between two steps:
    + *
    + * ===Assignment step:===
    + *
    + * Assign each observation to the cluster whose mean yields the least within-cluster
sum  of
    + * squares (WCSS). Since the sum of squares is the squared Euclidean distance, this is
intuitively
    + * the "nearest" mean. (Mathematically, this means partitioning the observations according
to the
    + * Voronoi diagram generated by the means).
    + *
    + * `S_i^(t) = { x_p : || x_p - m_i^(t) ||^2 ≤ || x_p - m_j^(t) ||^2 \forall j, 1 ≤
j ≤ k}`,
    + * where each `x_p`  is assigned to exactly one `S^{(t)}`, even if it could be assigned
to two or
    + * more of them.
    + *
    + * ===Update step:===
    + *
    + * Calculate the new means to be the centroids of the observations in the new clusters.
    + *
    + * `m^{(t+1)}_i = ( 1 / |S^{(t)}_i| ) \sum_{x_j \in S^{(t)}_i} x_j`
    + *
    + * Since the arithmetic mean is a least-squares estimator, this also minimizes the within-cluster
    + * sum of squares (WCSS) objective.
    + *
    + * @example
    + * {{{
    + *       val trainingDS: DataSet[Vector] = env.fromCollection(Clustering.trainingData)
    + *       val initialCentroids: DataSet[LabledVector] = env.fromCollection(Clustering.initCentroids)
    + *
    + *       val kmeans = KMeans()
    + *         .setInitialCentroids(initialCentroids)
    + *         .setNumIterations(10)
    + *
    + *       kmeans.fit(trainingDS)
    + *
    + *       // getting the computed centroids
    + *       val centroidsResult = kmeans.centroids.get.collect()
    + *
    + *       // get matching clusters for new points
    + *       val testDS: DataSet[Vector] = env.fromCollection(Clustering.testData)
    + *       val clusters: DataSet[LabeledVector] = kmeans.predict(testDS)
    + * }}}
    + *
    + * =Parameters=
    + *
    + * - [[org.apache.flink.ml.clustering.KMeans.NumIterations]]:
    + * Defines the number of iterations to recalculate the centroids of the clusters. As
it
    + * is a heuristic algorithm, there is no guarantee that it will converge to the global
optimum. The
    + * centroids of the clusters and the reassignment of the data points will be repeated
till the
    + * given number of iterations is reached.
    + * (Default value: '''10''')
    + *
    + * - [[org.apache.flink.ml.clustering.KMeans.InitialCentroids]]:
    + * Defines the initial k centroids of the k clusters. They are used as start off point
of the
    + * algorithm for clustering the data set. The centroids are recalculated as often as
set in
    + * [[org.apache.flink.ml.clustering.KMeans.NumIterations]]. The choice of the initial
centroids
    + * mainly affects the outcome of the algorithm.
    + *
    + * - [[org.apache.flink.ml.clustering.KMeans.InitialStrategy]]:
    + * Defines the initialization strategy to be used for initializing the KMeans algorithm
in case
    + * the initial centroids are not provided. Allowed values are "random", "kmeans++" and
"kmeans||".
    + * (Default Value: '''random''')
    + *
    + * - [[org.apache.flink.ml.clustering.KMeans.NumClusters]]:
    + * Defines the number of clusters required. This is essential to provide when only the
    + * initialization strategy is specified, not the initial centroids themselves.
    + * (Default Value: '''0''')
    + *
    + * - [[org.apache.flink.ml.clustering.KMeans.OversamplingFactor]]:
    + *  Defines the oversampling rate for the kmeans|| initialization.
    + * (Default Value: '''2k'''), where k is the number of clusters.
    + *
    + * - [[org.apache.flink.ml.clustering.KMeans.KMeansParRounds]]:
    + *  Defines the number of rounds for the kmeans|| initialization.
    + * (Default Value: '''5''')
    + *
    + */
    +class KMeans extends Predictor[KMeans] {
    +
    +  import KMeans._
    +
    +  /**
    +   * Stores the learned clusters after the fit operation
    +   */
    +  var centroids: Option[DataSet[Seq[LabeledVector]]] = None
    +
    +  /**
    +   * Sets the maximum number of iterations.
    +   *
    +   * @param numIterations The maximum number of iterations.
    +   * @return itself
    +   */
    +  def setNumIterations(numIterations: Int): KMeans = {
    +    parameters.add(NumIterations, numIterations)
    +    this
    +  }
    +
    +  /**
    +   * Sets the number of clusters.
    +   *
    +   * @param numClusters The number of clusters
    +   * @return itself
    +   */
    +  def setNumClusters(numClusters: Int): KMeans = {
    +    parameters.add(NumClusters, numClusters)
    +    this
    +  }
    +
    +  /**
    +   * Sets the initial centroids on which the algorithm will start computing. These points
should
    +   * depend on the data and will significantly influence the resulting centroids.
    +   * Note that this setting will override [[setInitializationStrategy())]] and the size
of
    +   * initialCentroids will override the value, if set, by [[setNumClusters()]]
    +   *
    +   * @param initialCentroids A set of labeled vectors.
    +   * @return itself
    +   */
    +  def setInitialCentroids(initialCentroids: Seq[LabeledVector]): KMeans = {
    +    parameters.add(InitialCentroids, initialCentroids)
    +    this
    +  }
    +
    +  /**
    +   * Automatically initialize the KMeans algorithm. Allowed options are "random", "kmeans++"
and
    +   * "kmeans||"
    +   *
    +   * @param initialStrategy
    +   * @return itself
    +   */
    +  def setInitializationStrategy(initialStrategy: String): KMeans = {
    +    require(Array("random", "kmeans++", "kmeans||").contains(initialStrategy), s"$initialStrategy"
+
    +      s" is not supported")
    +    parameters.add(InitialStrategy, initialStrategy)
    +    this
    +  }
    +
    +  /**
    +   * Oversampling factor to be used in case the initialization strategy is set to be
"kmeans||"
    +   *
    +   * @param oversamplingFactor Oversampling factor(\ell)
    +   * @return this
    +   */
    +  def setOversamplingFactor(oversamplingFactor: Double): KMeans = {
    +    require(oversamplingFactor > 0, "Oversampling factor must be positive.")
    +    parameters.add(OversamplingFactor, oversamplingFactor)
    +    this
    +  }
    +
    +  /**
    +   * Number of initialization rounds to be done when the initialization strategy is set
to be
    +   * "kmeans||"
    +   *
    +   * @param numRounds Number of rounds(r)
    +   * @return this
    +   */
    +  def setNumRounds(numRounds: Int): KMeans = {
    +    require(numRounds > 0, "Number of rounds must be positive")
    +    parameters.add(KMeansParRounds, numRounds)
    +    this
    +  }
    +
    +}
    +
    +/**
    + * Companion object of KMeans. Contains convenience functions, the parameter type definitions
    + * of the algorithm and the [[FitOperation]] & [[PredictOperation]].
    + */
    +object KMeans {
    +
    +  private val RANDOM_FRACTION = "random_sample_fraction"
    +  private val PARINIT_SET = "par_init_solution_set"
    +  private val PARINIT_COST = "par_init_solution_cost"
    +  private val PARINIT_SAMPLE = "par_init_oversample_factor"
    +
    +  /** Euclidean Distance Metric */
    +  val euclidean = EuclideanDistanceMetric()
    +
    +  case object NumIterations extends Parameter[Int] {
    +    val defaultValue = Some(10)
    +  }
    +
    +  case object InitialCentroids extends Parameter[Seq[LabeledVector]] {
    +    val defaultValue = None
    +  }
    +
    +  case object InitialStrategy extends Parameter[String]{
    +    val defaultValue = Some("kmeans||")
    +  }
    +
    +  case object NumClusters extends Parameter[Int] {
    +    val defaultValue = None
    +  }
    +
    +  case object OversamplingFactor extends Parameter[Double] {
    +    val defaultValue = None
    +  }
    +
    +  case object KMeansParRounds extends Parameter[Int] {
    +    val defaultValue = Some(5)
    +  }
    +
    +  // ========================================== Factory methods ====================================
    +
    +  def apply(): KMeans = {
    +    new KMeans()
    +  }
    +
    +  // ========================================== Operations =========================================
    +
    +  /** Provides the operation that makes the predictions for individual examples.
    +    * The label of the vector will be the index of the cluster the input vector belongs
to.
    +    *
    +    * @tparam T
    +    * @return A PredictOperation, through which it is possible to predict a value, given
a
    +    *         feature vector
    +    */
    +  implicit def predictVectors[T <: Vector] = {
    +    new PredictOperation[KMeans, Seq[LabeledVector], T, Double](){
    +
    +      override def getModel(
    +          self: KMeans,
    +          predictParameters: ParameterMap)
    +        : DataSet[Seq[LabeledVector]] = {
    +
    +        self.centroids match {
    +          case Some(model) => model
    +          case None => {
    +            throw new RuntimeException("The KMeans model has not been trained. Call first
fit" +
    +              "before calling the predict operation.")
    +          }
    +        }
    +      }
    +
    +      override def predict(value: T, model: Seq[LabeledVector]): Double = {
    +        findNearestCentroid(value, model)._1
    +      }
    +    }
    +  }
    +
    +  /**
    +   * [[FitOperation]] which iteratively computes centroids that match the given input
DataSet by
    +   * adjusting the given initial centroids.
    +   *
    +   * @return A new  [[FitOperation]] to train the model using the training data set.
    +   */
    +  implicit def fitKMeans = {
    +    new FitOperation[KMeans, Vector] {
    +      override def fit(instance: KMeans, fitParameters: ParameterMap, trainingDS: DataSet[Vector])
    +      : Unit = {
    +        val resultingParameters = instance.parameters ++ fitParameters
    +
    +        // =================  INITIALIZATION OF KMEANS ==========================
    +        val centroids: DataSet[Seq[LabeledVector]] = init(trainingDS, resultingParameters)
    +
    +        val numIterations: Int = resultingParameters.get(NumIterations).get
    +
    +        val finalCentroids = centroids.iterate(numIterations) { currentCentroids =>
    +          val newCentroids: DataSet[LabeledVector] = trainingDS
    +            .mapWithBcVariable(currentCentroids)
    +              { (dataPoint, centroids) => selectNearestCentroid(dataPoint, centroids)
}
    +            .map(x => (x.label, x.vector, 1.0)).withForwardedFields("label->_1;
vector->_2")
    +            .groupBy(x => x._1)
    +            .reduce((p1, p2) =>
    +              (p1._1, (p1._2.asBreeze + p2._2.asBreeze).fromBreeze, p1._3 + p2._3))
    +            // TODO replace addition of Breeze vectors by future build in flink function
    +            .withForwardedFields("_1")
    +            .map(x => {
    +              BLAS.scal(1.0 / x._3, x._2)
    +              LabeledVector(x._1, x._2)
    +            })
    +            .withForwardedFields("_1->label")
    +
    +          // currentCentroids contains only one element. So, this is output only once
    +          currentCentroids.mapWithBcSet(newCentroids){
    +            (_,newCenters) => newCenters
    +          }
    +        }
    +        instance.centroids = Some(finalCentroids)
    +      }
    +    }
    +  }
    +
    +  /**
    +   * Converts a given vector into a labeled vector where the label denotes the label
of the closest
    +   * centroid.
    +   *
    +   * @param dataPoint The vector to determine the nearest centroid.
    +   * @param centroids A collection of the centroids.
    +   * @return A [[LabeledVector]] consisting of the input vector and the label of the
closest
    +   *         centroid.
    +   */
    +  @ForwardedFields(Array("*->vector"))
    +  private def selectNearestCentroid(dataPoint: Vector, centroids: Seq[LabeledVector])
= {
    +    val nearest = findNearestCentroid(dataPoint, centroids)
    +    LabeledVector(nearest._1, dataPoint)
    +  }
    +
    +  /**
    +   * Finds the nearest centroid to a point and returns the distance to this centroid
and label of it
    +   *
    +   * @param dataPoint The vector to determine the nearest centroid.
    +   * @param centroids A collection of the centroids.
    +   * @return A tuple of distance to the nearest centroid and label of this centroid
    +   */
    +  private def findNearestCentroid(dataPoint: Vector, centroids: Seq[LabeledVector]) =
{
    +    var minDistance: Double = Double.MaxValue
    +    var closestCentroidLabel: Double = -1
    +    centroids.foreach(centroid => {
    +      val distance = euclidean.distance(dataPoint, centroid.vector)
    +      if (distance < minDistance) {
    +        minDistance = distance
    +        closestCentroidLabel = centroid.label
    +      }
    +    })
    +    (closestCentroidLabel, minDistance)
    +  }
    +
    +  /**
    +   * Returns the initial centroids for the KMeans algorithm based upon the information
in
    +   * parameter
    +   *
    +   * @param data The training data set
    +   * @param parameter Parameter Map containing user parameters
    +   * @return Initial centroids for KMeans clustering
    +   */
    +  private def init(data: DataSet[Vector], parameter: ParameterMap): DataSet[Seq[LabeledVector]]
= {
    +    parameter.get(InitialCentroids) match {
    +      case Some(value) => data.getExecutionEnvironment.fromElements(value)
    +      case None => {
    +
    +        val k = parameter.get(NumClusters) match{
    +          case Some(value) => value
    +          case None => throw new RuntimeException("Specify the number of clusters.")
    +        }
    +        val l = parameter.get(OversamplingFactor) match{
    +          case Some(value) => value
    +          case None => 2 * k  // default value
    +        }
    +        val r = parameter.get(KMeansParRounds).get
    +
    +        val blocks = data.getParallelism
    +
    +        parameter.get(InitialStrategy) match {
    +          case Some("random") => {
    +            random(data.map(x => (x,1)), k)
    +          }
    +          case Some("kmeans++") => {
    +            kmeans(data.map(x => (x,1)), k, blocks)
    +          }
    +          case Some("kmeans||") => {
    +            parInit(data, k, blocks, l ,r)
    +          }
    +          case default => {
    +            throw new RuntimeException("Specify a valid initialization strategy.")
    +          }
    +        }
    +      }
    +    }
    +  }
    +
    +  /**
    +   * Pick k centers from data one by one using kmeans|| initialization scheme
    +   *
    +   * The k-means|| algorithm works as described by the original authors
    +   * (http://theory.stanford.edu/~sergei/papers/vldb12-kmpar.pdf):
    +   *
    +   * Given a data set X with |X| points, the k-means|| algorithm proceeds as follows:
    +   *
    +   * 1. Initialize C \leftarrow \{\}
    +   * 2. Let p be a point sampled uniformly at random from X. C \leftarrow C \cup \{p\}
    +   * 3. for i \leftarrow 1 to r
    +   * Let C' be the set of formed by independently sampling every point x in X with probability
    +   * \ell\cdot\frac{d(x,C)}{sigma_nolimits{p \in X }d(p,C)}
    +   * C \leftarrow C \cup C'
    +   * 4. Assign weights to all point c in C as the number of points from X which are closest
to c
    +   * 5. Run kmeans++ initialization on the weighted set C and return k centers
    +   *
    +   * @param data Training data set
    +   * @param k Number of clusters
    +   * @param blocks Blocks in the data
    +   * @param oversampling Oversampling rate (\ell)
    +   * @param rounds Number of rounds (r)
    +   * @return Initial centroids
    +   */
    +  private def parInit(
    +      data: DataSet[Vector],
    +      k: Int,
    +      blocks: Int,
    +      oversampling: Double,
    +      rounds: Int)
    +    : DataSet[Seq[LabeledVector]] = {
    +    // first pick one center randomly
    +    val oversamplingFactor = data.getExecutionEnvironment.fromElements(oversampling)
    +
    +    val initialCentroids = random(data.map(x => (x,1)), 1).map(x => x.head)
    +    val unionOfSamples = initialCentroids.iterate(rounds){
    +      currentSet => {
    +        // current cost
    +        val currentCost = data.mapWithBcSet(currentSet){
    +          (vector, pointSet) => Math.pow(findNearestCentroid(vector, pointSet)._2,
2)
    +        }
    +        val sampledSet = data.filter(new RichFilterFunction[Vector] {
    +          var currentSet: Seq[LabeledVector] = _
    +          var cost: Double = _
    +          var rng: Random = _
    +          var oversamplingFactor: Double = _
    +          override def open(parameter: Configuration): Unit ={
    +            currentSet = getRuntimeContext.getBroadcastVariable(PARINIT_SET).asScala
    +            cost = getRuntimeContext.getBroadcastVariable(PARINIT_COST).get(0)
    +            oversamplingFactor = getRuntimeContext.getBroadcastVariable(PARINIT_SAMPLE).get(0)
    +            rng = new Random()
    +          }
    +          override def filter(value: Vector): Boolean = {
    +            rng.nextDouble() <
    +              oversamplingFactor * Math.pow(findNearestCentroid(value, currentSet)._2,
2) / cost
    +          }
    +        }).withBroadcastSet(currentCost, PARINIT_COST)
    +          .withBroadcastSet(currentSet, PARINIT_SET)
    +          .withBroadcastSet(oversamplingFactor, PARINIT_SAMPLE)
    +
    +        // keep taking unions of independent samples at each step
    +        currentSet.union(sampledSet.map(x => LabeledVector(0, x)))
    +      }
    +    }
    +
    +    // now assign weights to points in the set
    +    val weightedSample = data.mapWithBcSet(unionOfSamples){
    +      (vector, sampledSet) => {
    +        val samples = sampledSet.toList
    +        var minDistance: Double = Double.MaxValue
    +        var closestCentroidIndex: Int = -1
    +        for (i <- 0 to samples.size - 1) {
    +          val distance = EuclideanDistanceMetric().distance(vector, samples(i).vector)
    +          if (distance < minDistance) {
    +            minDistance = distance
    +            closestCentroidIndex = i
    +          }
    +        }
    +        // just assign a label of 1. We'll figure this out later.
    +        (closestCentroidIndex, samples(closestCentroidIndex).vector, 1)
    +      }
    +    }.groupBy(0)
    +      .reduce((a, b) => (a._1, a._2, a._3 + b._3))
    +      .map(x => (x._2,x._3))
    +
    +    // finally, do a kmeans++ on this weighted set
    +    kmeans(weightedSample, k, blocks)
    +  }
    +
    +  /**
    +   * Randomly initializes centroids from the data.
    +   * Data is considered to be weighted.
    +   *
    +   * @param data Training data set
    +   * @param k Number of centroids to be picked
    +   * @return Initial random centroids
    +   */
    +  private def random(
    +      data: DataSet[(Vector, Int)],
    +      k: Int)
    +    : DataSet[Seq[LabeledVector]] = {
    +    // we'll sample 10 times as many points as we actually need
    +    // TODO Modify to use the Random Sample Operator as and when added.
    +
    +    val fraction = data.map(x => 1).reduce(_ + _).map(x => 10 * (k + 0.0) / x)
    --- End diff --
    
    How about k.toDouble or 10.0*k?


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