/*
* 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.math.stat.clustering;
import java.util.ArrayList;
import java.util.Collection;
import java.util.List;
import java.util.Random;
import org.apache.commons.math.exception.ConvergenceException;
import org.apache.commons.math.exception.MathIllegalArgumentException;
import org.apache.commons.math.exception.NumberIsTooSmallException;
import org.apache.commons.math.exception.util.LocalizedFormats;
import org.apache.commons.math.stat.descriptive.moment.Variance;
import org.apache.commons.math.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>
* @version $Id: KMeansPlusPlusClusterer.java 1131229 2011-06-03 20:49:25Z luc $
* @since 2.0
*/
public class KMeansPlusPlusClusterer<T extends Clusterable<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
}
/** Random generator for choosing initial centers. */
private final Random 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>
* @param random random generator to use for choosing initial centers
*/
public KMeansPlusPlusClusterer(final Random random) {
this(random, EmptyClusterStrategy.LARGEST_VARIANCE);
}
/** Build a clusterer.
* @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
* @since 2.2
*/
public KMeansPlusPlusClusterer(final Random random, final EmptyClusterStrategy emptyStrategy) {
this.random = random;
this.emptyStrategy = emptyStrategy;
}
/**
* Runs the K-means++ clustering algorithm.
*
* @param points the points to cluster
* @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
* @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
*/
public List<Cluster<T>> cluster(final Collection<T> points, final int k,
final int maxIterations)
throws MathIllegalArgumentException {
// 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<Cluster<T>> clusters = chooseInitialCenters(points, k, random);
// 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<Cluster<T>> newClusters = new ArrayList<Cluster<T>>();
for (final Cluster<T> cluster : clusters) {
final T 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 = cluster.getCenter().centroidOf(cluster.getPoints());
}
newClusters.add(new Cluster<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 <T> type of the points to 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 static <T extends Clusterable<T>> int
assignPointsToClusters(final List<Cluster<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++;
}
Cluster<T> cluster = clusters.get(clusterIndex);
cluster.addPoint(p);
assignments[pointIndex++] = clusterIndex;
}
return assignedDifferently;
}
/**
* Use K-means++ to choose the initial centers.
*
* @param <T> type of the points to cluster
* @param points the points to choose the initial centers from
* @param k the number of centers to choose
* @param random random generator to use
* @return the initial centers
*/
private static <T extends Clusterable<T>> List<Cluster<T>>
chooseInitialCenters(final Collection<T> points, final int k, final Random random) {
final List<T> pointSet = new ArrayList<T>(points);
final List<Cluster<T>> resultSet = new ArrayList<Cluster<T>>();
// Choose one center uniformly at random from among the data points.
final T firstPoint = pointSet.remove(random.nextInt(pointSet.size()));
resultSet.add(new Cluster<T>(firstPoint));
final double[] dx2 = new double[pointSet.size()];
while (resultSet.size() < k) {
// For each data point x, compute D(x), the distance between x and
// the nearest center that has already been chosen.
double sum = 0;
for (int i = 0; i < pointSet.size(); i++) {
final T p = pointSet.get(i);
int nearestClusterIndex = getNearestCluster(resultSet, p);
final Cluster<T> nearest = resultSet.get(nearestClusterIndex);
final double d = p.distanceFrom(nearest.getCenter());
sum += d * d;
dx2[i] = sum;
}
// 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() * sum;
for (int i = 0 ; i < dx2.length; i++) {
if (dx2[i] >= r) {
final T p = pointSet.remove(i);
resultSet.add(new Cluster<T>(p));
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
*/
private T getPointFromLargestVarianceCluster(final Collection<Cluster<T>> clusters) {
double maxVariance = Double.NEGATIVE_INFINITY;
Cluster<T> selected = null;
for (final Cluster<T> cluster : clusters) {
if (!cluster.getPoints().isEmpty()) {
// compute the distance variance of the current cluster
final T center = cluster.getCenter();
final Variance stat = new Variance();
for (final T point : cluster.getPoints()) {
stat.increment(point.distanceFrom(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
*/
private T getPointFromLargestNumberCluster(final Collection<Cluster<T>> clusters) {
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
*/
private T getFarthestPoint(final Collection<Cluster<T>> clusters) {
double maxDistance = Double.NEGATIVE_INFINITY;
Cluster<T> selectedCluster = null;
int selectedPoint = -1;
for (final Cluster<T> cluster : clusters) {
// get the farthest point
final T center = cluster.getCenter();
final List<T> points = cluster.getPoints();
for (int i = 0; i < points.size(); ++i) {
final double distance = points.get(i).distanceFrom(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 <T> type of the points to cluster
* @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 static <T extends Clusterable<T>> int
getNearestCluster(final Collection<Cluster<T>> clusters, final T point) {
double minDistance = Double.MAX_VALUE;
int clusterIndex = 0;
int minCluster = 0;
for (final Cluster<T> c : clusters) {
final double distance = point.distanceFrom(c.getCenter());
if (distance < minDistance) {
minDistance = distance;
minCluster = clusterIndex;
}
clusterIndex++;
}
return minCluster;
}
}