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.matrix.algorithm.whitening;
031
032import org.openimaj.citation.annotation.Reference;
033import org.openimaj.citation.annotation.ReferenceType;
034import org.openimaj.math.matrix.algorithm.pca.SvdPrincipalComponentAnalysis;
035import org.openimaj.math.statistics.normalisation.Normaliser;
036
037import Jama.Matrix;
038
039/**
040 * The ZCA Whitening transform. Works like PCA whitening, but after variance
041 * normalisation, rotates the data back to the original orientation. The benefit
042 * is that the data will still "look-like" the original input to some extent.
043 *
044 * @author Jonathon Hare (jsh2@ecs.soton.ac.uk)
045 */
046@Reference(
047                type = ReferenceType.Article,
048                author = { "Anthony J. Bell", "Terrence J. Sejnowski" },
049                title = "The `Independent Components' of Natural Scenes are Edge Filters.",
050                year = "1997",
051                journal = "VISION RESEARCH",
052                pages = { "3327", "", "3338" },
053                volume = "37")
054public class ZCAWhitening extends PCAWhitening {
055        /**
056         * Construct with the given variance regularization parameter and data
057         * normalisation strategy.
058         *
059         * @param eps
060         *            the variance normalisation regularizer (each principle
061         *            dimension is divided by sqrt(lamba + eps), where lamba is the
062         *            corresponding eigenvalue).
063         * @param ns
064         *            the normalisation to apply to each input data vector prior to
065         *            training the transform or applying the actual whitening.
066         */
067        public ZCAWhitening(double eps, Normaliser ns) {
068                super(eps, ns);
069        }
070
071        @Override
072        public void train(double[][] data) {
073                ns.normalise(data);
074                final double[][] normData = ns.normalise(data);
075
076                final SvdPrincipalComponentAnalysis pca = new SvdPrincipalComponentAnalysis();
077                pca.learnBasisNorm(new Matrix(normData));
078                transform = pca.getBasis().copy();
079                final double[] weight = pca.getEigenValues();
080                final double[][] td = transform.getArray();
081
082                for (int c = 0; c < weight.length; c++)
083                        weight[c] = 1 / Math.sqrt(weight[c] + eps);
084
085                for (int r = 0; r < td.length; r++)
086                        for (int c = 0; c < td[0].length; c++)
087                                td[r][c] = td[r][c] * weight[c];
088
089                transform = transform.times(pca.getBasis().transpose());
090        }
091}