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.HashMap; import java.util.HashSet; import java.util.List; import java.util.Map; import java.util.Set; import org.apache.commons.math3.exception.NotPositiveException; import org.apache.commons.math3.exception.NullArgumentException; import org.apache.commons.math3.ml.distance.DistanceMeasure; import org.apache.commons.math3.ml.distance.EuclideanDistance; import org.apache.commons.math3.util.MathUtils; /** * DBSCAN (density-based spatial clustering of applications with noise) algorithm. * <p> * The DBSCAN algorithm forms clusters based on the idea of density connectivity, i.e. * a point p is density connected to another point q, if there exists a chain of * points p<sub>i</sub>, with i = 1 .. n and p<sub>1</sub> = p and p<sub>n</sub> = q, * such that each pair <p<sub>i</sub>, p<sub>i+1</sub>> is directly density-reachable. * A point q is directly density-reachable from point p if it is in the ε-neighborhood * of this point. * <p> * Any point that is not density-reachable from a formed cluster is treated as noise, and * will thus not be present in the result. * <p> * The algorithm requires two parameters: * <ul> * <li>eps: the distance that defines the ε-neighborhood of a point * <li>minPoints: the minimum number of density-connected points required to form a cluster * </ul> * * @param <T> type of the points to cluster * @see <a href="http://en.wikipedia.org/wiki/DBSCAN">DBSCAN (wikipedia)</a> * @see <a href="http://www.dbs.ifi.lmu.de/Publikationen/Papers/KDD-96.final.frame.pdf"> * A Density-Based Algorithm for Discovering Clusters in Large Spatial Databases with Noise</a> * @since 3.2 */ public class DBSCANClusterer<T extends Clusterable> extends Clusterer<T> { /** Maximum radius of the neighborhood to be considered. */ private final double eps; /** Minimum number of points needed for a cluster. */ private final int minPts; /** Status of a point during the clustering process. */ private enum PointStatus { /** The point has is considered to be noise. */ NOISE, /** The point is already part of a cluster. */ PART_OF_CLUSTER } /** * Creates a new instance of a DBSCANClusterer. * <p> * The euclidean distance will be used as default distance measure. * * @param eps maximum radius of the neighborhood to be considered * @param minPts minimum number of points needed for a cluster * @throws NotPositiveException if {@code eps < 0.0} or {@code minPts < 0} */ public DBSCANClusterer(final double eps, final int minPts) throws NotPositiveException { this(eps, minPts, new EuclideanDistance()); } /** * Creates a new instance of a DBSCANClusterer. * * @param eps maximum radius of the neighborhood to be considered * @param minPts minimum number of points needed for a cluster * @param measure the distance measure to use * @throws NotPositiveException if {@code eps < 0.0} or {@code minPts < 0} */ public DBSCANClusterer(final double eps, final int minPts, final DistanceMeasure measure) throws NotPositiveException { super(measure); if (eps < 0.0d) { throw new NotPositiveException(eps); } if (minPts < 0) { throw new NotPositiveException(minPts); } this.eps = eps; this.minPts = minPts; } /** * Returns the maximum radius of the neighborhood to be considered. * @return maximum radius of the neighborhood */ public double getEps() { return eps; } /** * Returns the minimum number of points needed for a cluster. * @return minimum number of points needed for a cluster */ public int getMinPts() { return minPts; } /** * Performs DBSCAN cluster analysis. * * @param points the points to cluster * @return the list of clusters * @throws NullArgumentException if the data points are null */ @Override public List<Cluster<T>> cluster(final Collection<T> points) throws NullArgumentException { // sanity checks MathUtils.checkNotNull(points); final List<Cluster<T>> clusters = new ArrayList<Cluster<T>>(); final Map<Clusterable, PointStatus> visited = new HashMap<Clusterable, PointStatus>(); for (final T point : points) { if (visited.get(point) != null) { continue; } final List<T> neighbors = getNeighbors(point, points); if (neighbors.size() >= minPts) { // DBSCAN does not care about center points final Cluster<T> cluster = new Cluster<T>(); clusters.add(expandCluster(cluster, point, neighbors, points, visited)); } else { visited.put(point, PointStatus.NOISE); } } return clusters; } /** * Expands the cluster to include density-reachable items. * * @param cluster Cluster to expand * @param point Point to add to cluster * @param neighbors List of neighbors * @param points the data set * @param visited the set of already visited points * @return the expanded cluster */ private Cluster<T> expandCluster(final Cluster<T> cluster, final T point, final List<T> neighbors, final Collection<T> points, final Map<Clusterable, PointStatus> visited) { cluster.addPoint(point); visited.put(point, PointStatus.PART_OF_CLUSTER); List<T> seeds = new ArrayList<T>(neighbors); int index = 0; while (index < seeds.size()) { final T current = seeds.get(index); PointStatus pStatus = visited.get(current); // only check non-visited points if (pStatus == null) { final List<T> currentNeighbors = getNeighbors(current, points); if (currentNeighbors.size() >= minPts) { seeds = merge(seeds, currentNeighbors); } } if (pStatus != PointStatus.PART_OF_CLUSTER) { visited.put(current, PointStatus.PART_OF_CLUSTER); cluster.addPoint(current); } index++; } return cluster; } /** * Returns a list of density-reachable neighbors of a {@code point}. * * @param point the point to look for * @param points possible neighbors * @return the List of neighbors */ private List<T> getNeighbors(final T point, final Collection<T> points) { final List<T> neighbors = new ArrayList<T>(); for (final T neighbor : points) { if (point != neighbor && distance(neighbor, point) <= eps) { neighbors.add(neighbor); } } return neighbors; } /** * Merges two lists together. * * @param one first list * @param two second list * @return merged lists */ private List<T> merge(final List<T> one, final List<T> two) { final Set<T> oneSet = new HashSet<T>(one); for (T item : two) { if (!oneSet.contains(item)) { one.add(item); } } return one; } }