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package de.lmu.ifi.dbs.elki.math.statistics.dependence;
/*
This file is part of ELKI:
Environment for Developing KDD-Applications Supported by Index-Structures
Copyright (C) 2014
Ludwig-Maximilians-Universität München
Lehr- und Forschungseinheit für Datenbanksysteme
ELKI Development Team
This program is free software: you can redistribute it and/or modify
it under the terms of the GNU Affero General Public License as published by
the Free Software Foundation, either version 3 of the License, or
(at your option) any later version.
This program is distributed in the hope that it will be useful,
but WITHOUT ANY WARRANTY; without even the implied warranty of
MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the
GNU Affero General Public License for more details.
You should have received a copy of the GNU Affero General Public License
along with this program. If not, see <http://www.gnu.org/licenses/>.
*/
import de.lmu.ifi.dbs.elki.math.MathUtil;
import de.lmu.ifi.dbs.elki.utilities.datastructures.arraylike.NumberArrayAdapter;
import de.lmu.ifi.dbs.elki.utilities.optionhandling.AbstractParameterizer;
/**
* Jensen-Shannon Divergence is closely related to mutual information.
*
* The output value is normalized, such that an evenly distributed and identical
* distribution will yield a value of 1. Independent distributions may still
* yield values close to .25, though.
*
* TODO: Offer normalized and non-normalized variants?
*
* @author Erich Schubert
*/
public class JensenShannonEquiwidthDependenceMeasure extends AbstractDependenceMeasure {
/**
* Static instance.
*/
public static final JensenShannonEquiwidthDependenceMeasure STATIC = new JensenShannonEquiwidthDependenceMeasure();
/**
* Constructor - use {@link #STATIC} instance.
*/
protected JensenShannonEquiwidthDependenceMeasure() {
super();
}
@Override
public <A, B> double dependence(NumberArrayAdapter<?, A> adapter1, A data1, NumberArrayAdapter<?, B> adapter2, B data2) {
final int len = size(adapter1, data1, adapter2, data2);
final int bins = (int) Math.round(Math.sqrt(len));
final int maxbin = bins - 1;
double min1 = adapter1.getDouble(data1, 0), max1 = min1;
double min2 = adapter2.getDouble(data2, 0), max2 = min2;
for(int i = 1; i < len; i++) {
final double vx = adapter1.getDouble(data1, i);
final double vy = adapter2.getDouble(data2, i);
if(vx < min1) {
min1 = vx;
}
else if(vx > max1) {
max1 = vx;
}
if(vy < min2) {
min2 = vy;
}
else if(vy > max2) {
max2 = vy;
}
}
final double scale1 = (max1 > min1) ? bins / (max1 - min1) : 1;
final double scale2 = (max2 > min2) ? bins / (max2 - min2) : 1;
int[] margin1 = new int[bins], margin2 = new int[bins];
int[][] counts = new int[bins][bins];
for(int i = 0; i < len; i++) {
int bin1 = (int) Math.floor((adapter1.getDouble(data1, i) - min1) * scale1);
int bin2 = (int) Math.floor((adapter2.getDouble(data2, i) - min2) * scale2);
bin1 = bin1 < bins ? bin1 : maxbin;
bin2 = bin2 < bins ? bin2 : maxbin;
margin1[bin1]++;
margin2[bin2]++;
counts[bin1][bin2]++;
}
// calculating relative frequencies
double e = 0;
for(int bin1 = 0; bin1 < counts.length; bin1++) {
// Margin value for row i.
final int sum1 = margin1[bin1];
// Skip empty rows early.
if(sum1 == 0) {
continue;
}
// Inverse pX
final double pX = sum1 / (double) len;
final int[] row = counts[bin1];
for(int bin2 = 0; bin2 < row.length; bin2++) {
final int sum2 = margin2[bin2];
if(sum2 > 0) {
final int cell = row[bin2];
// JS divergence of pXY and (pX * pY)
double pXY = cell / (double) len;
final double pXpY = pX * sum2 / len;
final double iavg = 2. / (pXY + pXpY);
e += pXY > 0. ? pXY * Math.log(pXY * iavg) : 0.;
e += pXpY * Math.log(pXpY * iavg);
}
}
}
// Expected value for evenly distributed and identical:
// pX = pY = 1/b and thus pXpY = 1/b^2.
// for i==j, pXY=1/b and thus iavg = 2*b*b/(b+1)
// otherwise, pXY=0 and thus iavg = 2*b*b
// pXY: e += log(b*2/(b+1)) = log(b) + log(2/(b+1))
// pXpY1: e += 1/b*log(2/(b+1)) = 1/b*log(2/(b+1))
// pXpY2: e += (b-1)/b*log(2) = (b-1)/b*log(2)
final double exp = Math.log(bins) + (1. + 1. / bins) * Math.log(2. / (bins + 1)) + (bins - 1.) / bins * MathUtil.LOG2;
// e *= .5; // Average, but we need to adjust exp then, too!
return e / exp;
}
/**
* Parameterization class.
*
* @author Erich Schubert
*
* @apiviz.exclude
*/
public static class Parameterizer extends AbstractParameterizer {
@Override
protected JensenShannonEquiwidthDependenceMeasure makeInstance() {
return STATIC;
}
}
}
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