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.normalisation;
031
032/**
033 * z-score normalisation (standardisation). Upon training, the mean and variance
034 * of each dimension is computed; normalisation works by subtracting the mean
035 * and dividing by the standard deviation.
036 * <p>
037 * This implementation includes an optional regularisation parameter that is
038 * added to the variance before the division.
039 *
040 * @author Jonathon Hare (jsh2@ecs.soton.ac.uk)
041 *
042 */
043public class ZScore implements TrainableNormaliser, Denormaliser {
044        double[] mean;
045        double[] sigma;
046        double eps = 0;
047
048        /**
049         * Construct without regularisation.
050         */
051        public ZScore() {
052        }
053
054        /**
055         * Construct with regularisation.
056         *
057         * @param eps
058         *            the variance normalisation regulariser (each dimension is
059         *            divided by sqrt(var + eps).
060         */
061        public ZScore(double eps) {
062                this.eps = eps;
063        }
064
065        @Override
066        public void train(double[][] data) {
067                mean = new double[data[0].length];
068                sigma = new double[data[0].length];
069
070                for (int r = 0; r < data.length; r++)
071                        for (int c = 0; c < data[0].length; c++)
072                                mean[c] += data[r][c];
073
074                for (int c = 0; c < data[0].length; c++)
075                        mean[c] /= data.length;
076
077                for (int r = 0; r < data.length; r++) {
078                        for (int c = 0; c < data[0].length; c++) {
079                                final double delta = (data[r][c] - mean[c]);
080                                sigma[c] += delta * delta;
081                        }
082                }
083
084                for (int c = 0; c < data[0].length; c++)
085                        sigma[c] = Math.sqrt(eps + (sigma[c] / (data.length - 1)));
086        }
087
088        @Override
089        public double[] normalise(double[] vector) {
090                final double[] out = new double[vector.length];
091                for (int c = 0; c < out.length; c++)
092                        out[c] = (vector[c] - mean[c]) / sigma[c];
093                return out;
094        }
095
096        @Override
097        public double[][] normalise(double[][] data) {
098                final double[][] out = new double[data.length][];
099                for (int c = 0; c < out.length; c++)
100                        out[c] = normalise(data[c]);
101                return out;
102        }
103
104        @Override
105        public double[] denormalise(double[] vector) {
106                final double[] out = new double[vector.length];
107                for (int c = 0; c < out.length; c++)
108                        out[c] = sigma[c] * vector[c] + mean[c];
109                return out;
110        }
111
112        @Override
113        public double[][] denormalise(double[][] data) {
114                final double[][] out = new double[data.length][];
115                for (int c = 0; c < out.length; c++)
116                        out[c] = denormalise(data[c]);
117                return out;
118        }
119}