001/**
002 * Copyright (c) 2011, The University of Southampton and the individual contributors.
003 * All rights reserved.
004 *
005 * Redistribution and use in source and binary forms, with or without modification,
006 * are permitted provided that the following conditions are met:
007 *
008 *   *  Redistributions of source code must retain the above copyright notice,
009 *      this list of conditions and the following disclaimer.
010 *
011 *   *  Redistributions in binary form must reproduce the above copyright notice,
012 *      this list of conditions and the following disclaimer in the documentation
013 *      and/or other materials provided with the distribution.
014 *
015 *   *  Neither the name of the University of Southampton nor the names of its
016 *      contributors may be used to endorse or promote products derived from this
017 *      software without specific prior written permission.
018 *
019 * THIS SOFTWARE IS PROVIDED BY THE COPYRIGHT HOLDERS AND CONTRIBUTORS "AS IS" AND
020 * ANY EXPRESS OR IMPLIED WARRANTIES, INCLUDING, BUT NOT LIMITED TO, THE IMPLIED
021 * WARRANTIES OF MERCHANTABILITY AND FITNESS FOR A PARTICULAR PURPOSE ARE
022 * DISCLAIMED. IN NO EVENT SHALL THE COPYRIGHT OWNER OR CONTRIBUTORS BE LIABLE FOR
023 * ANY DIRECT, INDIRECT, INCIDENTAL, SPECIAL, EXEMPLARY, OR CONSEQUENTIAL DAMAGES
024 * (INCLUDING, BUT NOT LIMITED TO, PROCUREMENT OF SUBSTITUTE GOODS OR SERVICES;
025 * LOSS OF USE, DATA, OR PROFITS; OR BUSINESS INTERRUPTION) HOWEVER CAUSED AND ON
026 * ANY THEORY OF LIABILITY, WHETHER IN CONTRACT, STRICT LIABILITY, OR TORT
027 * (INCLUDING NEGLIGENCE OR OTHERWISE) ARISING IN ANY WAY OUT OF THE USE OF THIS
028 * SOFTWARE, EVEN IF ADVISED OF THE POSSIBILITY OF SUCH DAMAGE.
029 */
030package org.openimaj.math.statistics.distribution.metrics;
031
032import org.openimaj.math.matrix.MatrixUtils;
033import org.openimaj.math.statistics.distribution.MultivariateGaussian;
034import org.openimaj.util.comparator.DistanceComparator;
035
036import Jama.Matrix;
037
038/**
039 * Calculate the KL divergence of two multivariate gaussians. Equation taken
040 * from:
041 * http://en.wikipedia.org/wiki/Multivariate_normal_distribution#Kullback.E2
042 * .80.93Leibler_divergence
043 * 
044 * @author Sina Samangooei (ss@ecs.soton.ac.uk)
045 */
046public class GaussianKLDivergence implements DistanceComparator<MultivariateGaussian> {
047
048        @Override
049        public boolean isDistance() {
050                return true;
051        }
052
053        @Override
054        public double compare(MultivariateGaussian o1, MultivariateGaussian o2) {
055                final Matrix sig0 = o1.getCovariance();
056                final Matrix sig1 = o2.getCovariance();
057                final Matrix mu0 = o1.getMean();
058                final Matrix mu1 = o2.getMean();
059                final int K = o1.numDims();
060
061                final Matrix sig1inv = sig1.inverse();
062                final double sigtrace = MatrixUtils.trace(sig1inv.times(sig0));
063
064                final Matrix mudiff = mu1.minus(mu0);
065                final double xt_s_x = mudiff.transpose().times(sig1inv).times(mudiff).get(0, 0);
066                final double ln_norm_sig = Math.log(sig0.norm1() / sig1.norm1());
067
068                return 0.5 * (sigtrace + xt_s_x - K - ln_norm_sig);
069        }
070
071}