Java tutorial
/* * 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.commons.math3.ml.clustering; import java.util.ArrayList; import java.util.Collection; import java.util.Collections; import java.util.List; import org.apache.commons.math3.exception.ConvergenceException; import org.apache.commons.math3.exception.MathIllegalArgumentException; import org.apache.commons.math3.exception.NumberIsTooSmallException; import org.apache.commons.math3.exception.util.LocalizedFormats; import org.apache.commons.math3.ml.distance.DistanceMeasure; import org.apache.commons.math3.ml.distance.EuclideanDistance; import org.apache.commons.math3.random.JDKRandomGenerator; import org.apache.commons.math3.random.RandomGenerator; import org.apache.commons.math3.stat.descriptive.moment.Variance; import org.apache.commons.math3.util.MathUtils; /** * Clustering algorithm based on David Arthur and Sergei Vassilvitski k-means++ algorithm. * @param <T> type of the points to cluster * @see <a href="http://en.wikipedia.org/wiki/K-means%2B%2B">K-means++ (wikipedia)</a> * @since 3.2 */ public class KMeansPlusPlusClusterer<T extends Clusterable> extends Clusterer<T> { /** Strategies to use for replacing an empty cluster. */ public static enum EmptyClusterStrategy { /** Split the cluster with largest distance variance. */ LARGEST_VARIANCE, /** Split the cluster with largest number of points. */ LARGEST_POINTS_NUMBER, /** Create a cluster around the point farthest from its centroid. */ FARTHEST_POINT, /** Generate an error. */ ERROR } /** The number of clusters. */ private final int k; /** The maximum number of iterations. */ private final int maxIterations; /** Random generator for choosing initial centers. */ private final RandomGenerator random; /** Selected strategy for empty clusters. */ private final EmptyClusterStrategy emptyStrategy; /** Build a clusterer. * <p> * The default strategy for handling empty clusters that may appear during * algorithm iterations is to split the cluster with largest distance variance. * <p> * The euclidean distance will be used as default distance measure. * * @param k the number of clusters to split the data into */ public KMeansPlusPlusClusterer(final int k) { this(k, -1); } /** Build a clusterer. * <p> * The default strategy for handling empty clusters that may appear during * algorithm iterations is to split the cluster with largest distance variance. * <p> * The euclidean distance will be used as default distance measure. * * @param k the number of clusters to split the data into * @param maxIterations the maximum number of iterations to run the algorithm for. * If negative, no maximum will be used. */ public KMeansPlusPlusClusterer(final int k, final int maxIterations) { this(k, maxIterations, new EuclideanDistance()); } /** Build a clusterer. * <p> * The default strategy for handling empty clusters that may appear during * algorithm iterations is to split the cluster with largest distance variance. * * @param k the number of clusters to split the data into * @param maxIterations the maximum number of iterations to run the algorithm for. * If negative, no maximum will be used. * @param measure the distance measure to use */ public KMeansPlusPlusClusterer(final int k, final int maxIterations, final DistanceMeasure measure) { this(k, maxIterations, measure, new JDKRandomGenerator()); } /** Build a clusterer. * <p> * The default strategy for handling empty clusters that may appear during * algorithm iterations is to split the cluster with largest distance variance. * * @param k the number of clusters to split the data into * @param maxIterations the maximum number of iterations to run the algorithm for. * If negative, no maximum will be used. * @param measure the distance measure to use * @param random random generator to use for choosing initial centers */ public KMeansPlusPlusClusterer(final int k, final int maxIterations, final DistanceMeasure measure, final RandomGenerator random) { this(k, maxIterations, measure, random, EmptyClusterStrategy.LARGEST_VARIANCE); } /** Build a clusterer. * * @param k the number of clusters to split the data into * @param maxIterations the maximum number of iterations to run the algorithm for. * If negative, no maximum will be used. * @param measure the distance measure to use * @param random random generator to use for choosing initial centers * @param emptyStrategy strategy to use for handling empty clusters that * may appear during algorithm iterations */ public KMeansPlusPlusClusterer(final int k, final int maxIterations, final DistanceMeasure measure, final RandomGenerator random, final EmptyClusterStrategy emptyStrategy) { super(measure); this.k = k; this.maxIterations = maxIterations; this.random = random; this.emptyStrategy = emptyStrategy; } /** * Return the number of clusters this instance will use. * @return the number of clusters */ public int getK() { return k; } /** * Returns the maximum number of iterations this instance will use. * @return the maximum number of iterations, or -1 if no maximum is set */ public int getMaxIterations() { return maxIterations; } /** * Returns the random generator this instance will use. * @return the random generator */ public RandomGenerator getRandomGenerator() { return random; } /** * Returns the {@link EmptyClusterStrategy} used by this instance. * @return the {@link EmptyClusterStrategy} */ public EmptyClusterStrategy getEmptyClusterStrategy() { return emptyStrategy; } /** * Runs the K-means++ clustering algorithm. * * @param points the points to cluster * @return a list of clusters containing the points * @throws MathIllegalArgumentException if the data points are null or the number * of clusters is larger than the number of data points * @throws ConvergenceException if an empty cluster is encountered and the * {@link #emptyStrategy} is set to {@code ERROR} */ @Override public List<CentroidCluster<T>> cluster(final Collection<T> points) throws MathIllegalArgumentException, ConvergenceException { // sanity checks MathUtils.checkNotNull(points); // number of clusters has to be smaller or equal the number of data points if (points.size() < k) { throw new NumberIsTooSmallException(points.size(), k, false); } // create the initial clusters List<CentroidCluster<T>> clusters = chooseInitialCenters(points); // create an array containing the latest assignment of a point to a cluster // no need to initialize the array, as it will be filled with the first assignment int[] assignments = new int[points.size()]; assignPointsToClusters(clusters, points, assignments); // iterate through updating the centers until we're done final int max = (maxIterations < 0) ? Integer.MAX_VALUE : maxIterations; for (int count = 0; count < max; count++) { boolean emptyCluster = false; List<CentroidCluster<T>> newClusters = new ArrayList<CentroidCluster<T>>(); for (final CentroidCluster<T> cluster : clusters) { final Clusterable newCenter; if (cluster.getPoints().isEmpty()) { switch (emptyStrategy) { case LARGEST_VARIANCE: newCenter = getPointFromLargestVarianceCluster(clusters); break; case LARGEST_POINTS_NUMBER: newCenter = getPointFromLargestNumberCluster(clusters); break; case FARTHEST_POINT: newCenter = getFarthestPoint(clusters); break; default: throw new ConvergenceException(LocalizedFormats.EMPTY_CLUSTER_IN_K_MEANS); } emptyCluster = true; } else { newCenter = centroidOf(cluster.getPoints(), cluster.getCenter().getPoint().length); } newClusters.add(new CentroidCluster<T>(newCenter)); } int changes = assignPointsToClusters(newClusters, points, assignments); clusters = newClusters; // if there were no more changes in the point-to-cluster assignment // and there are no empty clusters left, return the current clusters if (changes == 0 && !emptyCluster) { return clusters; } } return clusters; } /** * Adds the given points to the closest {@link Cluster}. * * @param clusters the {@link Cluster}s to add the points to * @param points the points to add to the given {@link Cluster}s * @param assignments points assignments to clusters * @return the number of points assigned to different clusters as the iteration before */ private int assignPointsToClusters(final List<CentroidCluster<T>> clusters, final Collection<T> points, final int[] assignments) { int assignedDifferently = 0; int pointIndex = 0; for (final T p : points) { int clusterIndex = getNearestCluster(clusters, p); if (clusterIndex != assignments[pointIndex]) { assignedDifferently++; } CentroidCluster<T> cluster = clusters.get(clusterIndex); cluster.addPoint(p); assignments[pointIndex++] = clusterIndex; } return assignedDifferently; } /** * Use K-means++ to choose the initial centers. * * @param points the points to choose the initial centers from * @return the initial centers */ private List<CentroidCluster<T>> chooseInitialCenters(final Collection<T> points) { // Convert to list for indexed access. Make it unmodifiable, since removal of items // would screw up the logic of this method. final List<T> pointList = Collections.unmodifiableList(new ArrayList<T>(points)); // The number of points in the list. final int numPoints = pointList.size(); // Set the corresponding element in this array to indicate when // elements of pointList are no longer available. final boolean[] taken = new boolean[numPoints]; // The resulting list of initial centers. final List<CentroidCluster<T>> resultSet = new ArrayList<CentroidCluster<T>>(); // Choose one center uniformly at random from among the data points. final int firstPointIndex = random.nextInt(numPoints); final T firstPoint = pointList.get(firstPointIndex); resultSet.add(new CentroidCluster<T>(firstPoint)); // Must mark it as taken taken[firstPointIndex] = true; // To keep track of the minimum distance squared of elements of // pointList to elements of resultSet. final double[] minDistSquared = new double[numPoints]; // Initialize the elements. Since the only point in resultSet is firstPoint, // this is very easy. for (int i = 0; i < numPoints; i++) { if (i != firstPointIndex) { // That point isn't considered double d = distance(firstPoint, pointList.get(i)); minDistSquared[i] = d * d; } } while (resultSet.size() < k) { // Sum up the squared distances for the points in pointList not // already taken. double distSqSum = 0.0; for (int i = 0; i < numPoints; i++) { if (!taken[i]) { distSqSum += minDistSquared[i]; } } // Add one new data point as a center. Each point x is chosen with // probability proportional to D(x)2 final double r = random.nextDouble() * distSqSum; // The index of the next point to be added to the resultSet. int nextPointIndex = -1; // Sum through the squared min distances again, stopping when // sum >= r. double sum = 0.0; for (int i = 0; i < numPoints; i++) { if (!taken[i]) { sum += minDistSquared[i]; if (sum >= r) { nextPointIndex = i; break; } } } // If it's not set to >= 0, the point wasn't found in the previous // for loop, probably because distances are extremely small. Just pick // the last available point. if (nextPointIndex == -1) { for (int i = numPoints - 1; i >= 0; i--) { if (!taken[i]) { nextPointIndex = i; break; } } } // We found one. if (nextPointIndex >= 0) { final T p = pointList.get(nextPointIndex); resultSet.add(new CentroidCluster<T>(p)); // Mark it as taken. taken[nextPointIndex] = true; if (resultSet.size() < k) { // Now update elements of minDistSquared. We only have to compute // the distance to the new center to do this. for (int j = 0; j < numPoints; j++) { // Only have to worry about the points still not taken. if (!taken[j]) { double d = distance(p, pointList.get(j)); double d2 = d * d; if (d2 < minDistSquared[j]) { minDistSquared[j] = d2; } } } } } else { // None found -- // Break from the while loop to prevent // an infinite loop. break; } } return resultSet; } /** * Get a random point from the {@link Cluster} with the largest distance variance. * * @param clusters the {@link Cluster}s to search * @return a random point from the selected cluster * @throws ConvergenceException if clusters are all empty */ private T getPointFromLargestVarianceCluster(final Collection<CentroidCluster<T>> clusters) throws ConvergenceException { double maxVariance = Double.NEGATIVE_INFINITY; Cluster<T> selected = null; for (final CentroidCluster<T> cluster : clusters) { if (!cluster.getPoints().isEmpty()) { // compute the distance variance of the current cluster final Clusterable center = cluster.getCenter(); final Variance stat = new Variance(); for (final T point : cluster.getPoints()) { stat.increment(distance(point, center)); } final double variance = stat.getResult(); // select the cluster with the largest variance if (variance > maxVariance) { maxVariance = variance; selected = cluster; } } } // did we find at least one non-empty cluster ? if (selected == null) { throw new ConvergenceException(LocalizedFormats.EMPTY_CLUSTER_IN_K_MEANS); } // extract a random point from the cluster final List<T> selectedPoints = selected.getPoints(); return selectedPoints.remove(random.nextInt(selectedPoints.size())); } /** * Get a random point from the {@link Cluster} with the largest number of points * * @param clusters the {@link Cluster}s to search * @return a random point from the selected cluster * @throws ConvergenceException if clusters are all empty */ private T getPointFromLargestNumberCluster(final Collection<? extends Cluster<T>> clusters) throws ConvergenceException { int maxNumber = 0; Cluster<T> selected = null; for (final Cluster<T> cluster : clusters) { // get the number of points of the current cluster final int number = cluster.getPoints().size(); // select the cluster with the largest number of points if (number > maxNumber) { maxNumber = number; selected = cluster; } } // did we find at least one non-empty cluster ? if (selected == null) { throw new ConvergenceException(LocalizedFormats.EMPTY_CLUSTER_IN_K_MEANS); } // extract a random point from the cluster final List<T> selectedPoints = selected.getPoints(); return selectedPoints.remove(random.nextInt(selectedPoints.size())); } /** * Get the point farthest to its cluster center * * @param clusters the {@link Cluster}s to search * @return point farthest to its cluster center * @throws ConvergenceException if clusters are all empty */ private T getFarthestPoint(final Collection<CentroidCluster<T>> clusters) throws ConvergenceException { double maxDistance = Double.NEGATIVE_INFINITY; Cluster<T> selectedCluster = null; int selectedPoint = -1; for (final CentroidCluster<T> cluster : clusters) { // get the farthest point final Clusterable center = cluster.getCenter(); final List<T> points = cluster.getPoints(); for (int i = 0; i < points.size(); ++i) { final double distance = distance(points.get(i), center); if (distance > maxDistance) { maxDistance = distance; selectedCluster = cluster; selectedPoint = i; } } } // did we find at least one non-empty cluster ? if (selectedCluster == null) { throw new ConvergenceException(LocalizedFormats.EMPTY_CLUSTER_IN_K_MEANS); } return selectedCluster.getPoints().remove(selectedPoint); } /** * Returns the nearest {@link Cluster} to the given point * * @param clusters the {@link Cluster}s to search * @param point the point to find the nearest {@link Cluster} for * @return the index of the nearest {@link Cluster} to the given point */ private int getNearestCluster(final Collection<CentroidCluster<T>> clusters, final T point) { double minDistance = Double.MAX_VALUE; int clusterIndex = 0; int minCluster = 0; for (final CentroidCluster<T> c : clusters) { final double distance = distance(point, c.getCenter()); if (distance < minDistance) { minDistance = distance; minCluster = clusterIndex; } clusterIndex++; } return minCluster; } /** * Computes the centroid for a set of points. * * @param points the set of points * @param dimension the point dimension * @return the computed centroid for the set of points */ private Clusterable centroidOf(final Collection<T> points, final int dimension) { final double[] centroid = new double[dimension]; for (final T p : points) { final double[] point = p.getPoint(); for (int i = 0; i < centroid.length; i++) { centroid[i] += point[i]; } } for (int i = 0; i < centroid.length; i++) { centroid[i] /= points.size(); } return new DoublePoint(centroid); } }