/**
* 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.mahout.clustering.cdbw;
import org.apache.hadoop.conf.Configuration;
import org.apache.hadoop.fs.Path;
import org.apache.mahout.clustering.Cluster;
import org.apache.mahout.clustering.GaussianAccumulator;
import org.apache.mahout.clustering.OnlineGaussianAccumulator;
import org.apache.mahout.clustering.evaluation.RepresentativePointsDriver;
import org.apache.mahout.clustering.evaluation.RepresentativePointsMapper;
import org.apache.mahout.clustering.iterator.ClusterWritable;
import org.apache.mahout.common.ClassUtils;
import org.apache.mahout.common.distance.DistanceMeasure;
import org.apache.mahout.common.iterator.sequencefile.PathFilters;
import org.apache.mahout.common.iterator.sequencefile.PathType;
import org.apache.mahout.common.iterator.sequencefile.SequenceFileDirValueIterable;
import org.apache.mahout.math.RandomAccessSparseVector;
import org.apache.mahout.math.Vector;
import org.apache.mahout.math.Vector.Element;
import org.apache.mahout.math.VectorWritable;
import org.slf4j.Logger;
import org.slf4j.LoggerFactory;
import java.util.ArrayList;
import java.util.HashMap;
import java.util.List;
import java.util.Map;
import java.util.TreeMap;
/**
* This class calculates the CDbw metric as defined in
* http://www.db-net.aueb.gr/index.php/corporate/content/download/227/833/file/HV_poster2002.pdf
*/
public final class CDbwEvaluator {
private static final Logger log = LoggerFactory.getLogger(CDbwEvaluator.class);
private final Map<Integer,List<VectorWritable>> representativePoints;
private final Map<Integer,Double> stDevs = new HashMap<>();
private final List<Cluster> clusters;
private final DistanceMeasure measure;
private Double interClusterDensity = null;
// these are symmetric so we only compute half of them
private Map<Integer,Map<Integer,Double>> minimumDistances = null;
// these are symmetric too
private Map<Integer,Map<Integer,Double>> interClusterDensities = null;
// these are symmetric too
private Map<Integer,Map<Integer,int[]>> closestRepPointIndices = null;
/**
* For testing only
*
* @param representativePoints
* a Map<Integer,List<VectorWritable>> of representative points keyed by clusterId
* @param clusters
* a Map<Integer,Cluster> of the clusters keyed by clusterId
* @param measure
* an appropriate DistanceMeasure
*/
public CDbwEvaluator(Map<Integer,List<VectorWritable>> representativePoints, List<Cluster> clusters,
DistanceMeasure measure) {
this.representativePoints = representativePoints;
this.clusters = clusters;
this.measure = measure;
for (Integer cId : representativePoints.keySet()) {
computeStd(cId);
}
}
/**
* Initialize a new instance from job information
*
* @param conf
* a Configuration with appropriate parameters
* @param clustersIn
* a String path to the input clusters directory
*/
public CDbwEvaluator(Configuration conf, Path clustersIn) {
measure = ClassUtils
.instantiateAs(conf.get(RepresentativePointsDriver.DISTANCE_MEASURE_KEY), DistanceMeasure.class);
representativePoints = RepresentativePointsMapper.getRepresentativePoints(conf);
clusters = loadClusters(conf, clustersIn);
for (Integer cId : representativePoints.keySet()) {
computeStd(cId);
}
}
/**
* Load the clusters from their sequence files
*
* @param clustersIn
* a String pathname to the directory containing input cluster files
* @return a List<Cluster> of the clusters
*/
private static List<Cluster> loadClusters(Configuration conf, Path clustersIn) {
List<Cluster> clusters = new ArrayList<>();
for (ClusterWritable clusterWritable : new SequenceFileDirValueIterable<ClusterWritable>(clustersIn, PathType.LIST,
PathFilters.logsCRCFilter(), conf)) {
Cluster cluster = clusterWritable.getValue();
clusters.add(cluster);
}
return clusters;
}
/**
* Compute the standard deviation of the representative points for the given cluster. Store these in stDevs, indexed
* by cI
*
* @param cI
* a int clusterId.
*/
private void computeStd(int cI) {
List<VectorWritable> repPts = representativePoints.get(cI);
GaussianAccumulator accumulator = new OnlineGaussianAccumulator();
for (VectorWritable vw : repPts) {
accumulator.observe(vw.get(), 1.0);
}
accumulator.compute();
double d = accumulator.getAverageStd();
stDevs.put(cI, d);
}
/**
* Compute the density of points near the midpoint between the two closest points of the clusters (eqn 2) used for
* inter-cluster density calculation
*
* @param uIJ
* the Vector midpoint between the closest representative points of the clusters
* @param cI
* the int clusterId of the i-th cluster
* @param cJ
* the int clusterId of the j-th cluster
* @param avgStd
* the double average standard deviation of the two clusters
* @return a double
*/
private double density(Vector uIJ, int cI, int cJ, double avgStd) {
List<VectorWritable> repI = representativePoints.get(cI);
List<VectorWritable> repJ = representativePoints.get(cJ);
double sum = 0.0;
// count the number of representative points of the clusters which are within the
// average std of the two clusters from the midpoint uIJ (eqn 3)
for (VectorWritable vwI : repI) {
if (uIJ != null && measure.distance(uIJ, vwI.get()) <= avgStd) {
sum++;
}
}
for (VectorWritable vwJ : repJ) {
if (uIJ != null && measure.distance(uIJ, vwJ.get()) <= avgStd) {
sum++;
}
}
int nI = repI.size();
int nJ = repJ.size();
return sum / (nI + nJ);
}
/**
* Compute the CDbw validity metric (eqn 8). The goal of this metric is to reward clusterings which have a high
* intraClusterDensity and also a high cluster separation.
*
* @return a double
*/
public double getCDbw() {
return intraClusterDensity() * separation();
}
/**
* The average density within clusters is defined as the percentage of representative points that reside in the
* neighborhood of the clusters' centers. The goal is the density within clusters to be significantly high. (eqn 5)
*
* @return a double
*/
public double intraClusterDensity() {
double avgDensity = 0;
int count = 0;
for (Element elem : intraClusterDensities().nonZeroes()) {
double value = elem.get();
if (!Double.isNaN(value)) {
avgDensity += value;
count++;
}
}
return avgDensity / count;
}
/**
* This function evaluates the density of points in the regions between each clusters (eqn 1). The goal is the density
* in the area between clusters to be significant low.
*
* @return a Map<Integer,Map<Integer,Double>> of the inter-cluster densities
*/
public Map<Integer,Map<Integer,Double>> interClusterDensities() {
if (interClusterDensities != null) {
return interClusterDensities;
}
interClusterDensities = new TreeMap<>();
// find the closest representative points between the clusters
for (int i = 0; i < clusters.size(); i++) {
int cI = clusters.get(i).getId();
Map<Integer,Double> map = new TreeMap<>();
interClusterDensities.put(cI, map);
for (int j = i + 1; j < clusters.size(); j++) {
int cJ = clusters.get(j).getId();
double minDistance = minimumDistance(cI, cJ); // the distance between the closest representative points
Vector uIJ = midpointVector(cI, cJ); // the midpoint between the closest representative points
double stdSum = stDevs.get(cI) + stDevs.get(cJ);
double density = density(uIJ, cI, cJ, stdSum / 2);
double interDensity = minDistance * density / stdSum;
map.put(cJ, interDensity);
if (log.isDebugEnabled()) {
log.debug("minDistance[{},{}]={}", cI, cJ, minDistance);
log.debug("interDensity[{},{}]={}", cI, cJ, density);
log.debug("density[{},{}]={}", cI, cJ, interDensity);
}
}
}
return interClusterDensities;
}
/**
* Calculate the separation of clusters (eqn 4) taking into account both the distances between the clusters' closest
* points and the Inter-cluster density. The goal is the distances between clusters to be high while the
* representative point density in the areas between them are low.
*
* @return a double
*/
public double separation() {
double minDistanceSum = 0;
Map<Integer,Map<Integer,Double>> distances = minimumDistances();
for (Map<Integer,Double> map : distances.values()) {
for (Double dist : map.values()) {
if (!Double.isInfinite(dist)) {
minDistanceSum += dist * 2; // account for other half of calculated triangular minimumDistances matrix
}
}
}
return minDistanceSum / (1.0 + interClusterDensity());
}
/**
* This function evaluates the average density of points in the regions between clusters (eqn 1). The goal is the
* density in the area between clusters to be significant low.
*
* @return a double
*/
public double interClusterDensity() {
if (interClusterDensity != null) {
return interClusterDensity;
}
double sum = 0.0;
int count = 0;
Map<Integer,Map<Integer,Double>> distances = interClusterDensities();
for (Map<Integer,Double> row : distances.values()) {
for (Double density : row.values()) {
if (!Double.isNaN(density)) {
sum += density;
count++;
}
}
}
log.debug("interClusterDensity={}", sum);
interClusterDensity = sum / count;
return interClusterDensity;
}
/**
* The average density within clusters is defined as the percentage of representative points that reside in the
* neighborhood of the clusters' centers. The goal is the density within clusters to be significantly high. (eqn 5)
*
* @return a Vector of the intra-densities of each clusterId
*/
public Vector intraClusterDensities() {
Vector densities = new RandomAccessSparseVector(Integer.MAX_VALUE);
// compute the average standard deviation of the clusters
double stdev = 0.0;
for (Integer cI : representativePoints.keySet()) {
stdev += stDevs.get(cI);
}
int c = representativePoints.size();
stdev /= c;
for (Cluster cluster : clusters) {
Integer cI = cluster.getId();
List<VectorWritable> repPtsI = representativePoints.get(cI);
int r = repPtsI.size();
double sumJ = 0.0;
// compute the term density (eqn 6)
for (VectorWritable pt : repPtsI) {
// compute f(x, vIJ) (eqn 7)
Vector repJ = pt.get();
double densityIJ = measure.distance(cluster.getCenter(), repJ) <= stdev ? 1.0 : 0.0;
// accumulate sumJ
sumJ += densityIJ / stdev;
}
densities.set(cI, sumJ / r);
}
return densities;
}
/**
* Calculate and cache the distances between the clusters' closest representative points. Also cache the indices of
* the closest representative points used for later use
*
* @return a Map<Integer,Vector> of the closest distances, keyed by clusterId
*/
private Map<Integer,Map<Integer,Double>> minimumDistances() {
if (minimumDistances != null) {
return minimumDistances;
}
minimumDistances = new TreeMap<>();
closestRepPointIndices = new TreeMap<>();
for (int i = 0; i < clusters.size(); i++) {
Integer cI = clusters.get(i).getId();
Map<Integer,Double> map = new TreeMap<>();
Map<Integer,int[]> treeMap = new TreeMap<>();
closestRepPointIndices.put(cI, treeMap);
minimumDistances.put(cI, map);
List<VectorWritable> closRepI = representativePoints.get(cI);
for (int j = i + 1; j < clusters.size(); j++) {
// find min{d(closRepI, closRepJ)}
Integer cJ = clusters.get(j).getId();
List<VectorWritable> closRepJ = representativePoints.get(cJ);
double minDistance = Double.MAX_VALUE;
int[] midPointIndices = null;
for (int xI = 0; xI < closRepI.size(); xI++) {
VectorWritable aRepI = closRepI.get(xI);
for (int xJ = 0; xJ < closRepJ.size(); xJ++) {
VectorWritable aRepJ = closRepJ.get(xJ);
double distance = measure.distance(aRepI.get(), aRepJ.get());
if (distance < minDistance) {
minDistance = distance;
midPointIndices = new int[] {xI, xJ};
}
}
}
map.put(cJ, minDistance);
treeMap.put(cJ, midPointIndices);
}
}
return minimumDistances;
}
private double minimumDistance(int cI, int cJ) {
Map<Integer,Double> distances = minimumDistances().get(cI);
if (distances != null) {
return distances.get(cJ);
} else {
return minimumDistances().get(cJ).get(cI);
}
}
private Vector midpointVector(int cI, int cJ) {
Map<Integer,Double> distances = minimumDistances().get(cI);
if (distances != null) {
int[] ks = closestRepPointIndices.get(cI).get(cJ);
if (ks == null) {
return null;
}
return representativePoints.get(cI).get(ks[0]).get().plus(representativePoints.get(cJ).get(ks[1]).get())
.divide(2);
} else {
int[] ks = closestRepPointIndices.get(cJ).get(cI);
if (ks == null) {
return null;
}
return representativePoints.get(cJ).get(ks[1]).get().plus(representativePoints.get(cI).get(ks[0]).get())
.divide(2);
}
}
}