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|---|---|---|
| 1 | /* | |
| 2 | * Copyright (c) 2003, the JUNG Project and the Regents of the University | |
| 3 | * of California | |
| 4 | * All rights reserved. | |
| 5 | * | |
| 6 | * This software is open-source under the BSD license; see either | |
| 7 | * "license.txt" or | |
| 8 | * http://jung.sourceforge.net/license.txt for a description. | |
| 9 | * | |
| 10 | * Created on Feb 18, 2004 | |
| 11 | */ | |
| 12 | package edu.uci.ics.jung.statistics; | |
| 13 | ||
| 14 | import java.util.Collection; | |
| 15 | import java.util.Iterator; | |
| 16 | ||
| 17 | /** | |
| 18 | * A utility class for calculating properties of discrete distributions. | |
| 19 | * Generally, these distributions are represented as arrays of | |
| 20 | * <code>double</code> values, which are assumed to be normalized | |
| 21 | * such that the entries in a single array sum to 1. | |
| 22 | * | |
| 23 | * @author Joshua O'Madadhain | |
| 24 | */ | |
| 25 | 0 | public class DiscreteDistribution |
| 26 | { | |
| 27 | ||
| 28 | /** | |
| 29 | * Returns the Kullback-Leibler divergence between the | |
| 30 | * two specified distributions, which must have the same | |
| 31 | * number of elements. This is defined as | |
| 32 | * the sum over all <code>i</code> of | |
| 33 | * <code>dist[i] * Math.log(dist[i] / reference[i])</code>. | |
| 34 | * Note that this value is not symmetric; see | |
| 35 | * <code>symmetricKL</code> for a symmetric variant. | |
| 36 | * @see #symmetricKL(double[], double[]) | |
| 37 | */ | |
| 38 | public static double KullbackLeibler(double[] dist, double[] reference) | |
| 39 | { | |
| 40 | 0 | double distance = 0; |
| 41 | ||
| 42 | 0 | checkLengths(dist, reference); |
| 43 | ||
| 44 | 0 | for (int i = 0; i < dist.length; i++) |
| 45 | { | |
| 46 | 0 | if (dist[i] > 0 && reference[i] > 0) |
| 47 | 0 | distance += dist[i] * Math.log(dist[i] / reference[i]); |
| 48 | } | |
| 49 | 0 | return distance; |
| 50 | } | |
| 51 | ||
| 52 | /** | |
| 53 | * Returns <code>KullbackLeibler(dist, reference) + KullbackLeibler(reference, dist)</code>. | |
| 54 | * @see #KullbackLeibler(double[], double[]) | |
| 55 | */ | |
| 56 | public static double symmetricKL(double[] dist, double[] reference) | |
| 57 | { | |
| 58 | 0 | return KullbackLeibler(dist, reference) |
| 59 | + KullbackLeibler(reference, dist); | |
| 60 | } | |
| 61 | ||
| 62 | /** | |
| 63 | * Returns the squared difference between the | |
| 64 | * two specified distributions, which must have the same | |
| 65 | * number of elements. This is defined as | |
| 66 | * the sum over all <code>i</code> of the square of | |
| 67 | * <code>(dist[i] - reference[i])</code>. | |
| 68 | */ | |
| 69 | public static double squaredError(double[] dist, double[] reference) | |
| 70 | { | |
| 71 | 34 | double error = 0; |
| 72 | ||
| 73 | 34 | checkLengths(dist, reference); |
| 74 | ||
| 75 | 68 | for (int i = 0; i < dist.length; i++) |
| 76 | { | |
| 77 | 34 | double difference = dist[i] - reference[i]; |
| 78 | 34 | error += difference * difference; |
| 79 | } | |
| 80 | 34 | return error; |
| 81 | } | |
| 82 | ||
| 83 | /** | |
| 84 | * Returns the cosine distance between the two | |
| 85 | * specified distributions, which must have the same number | |
| 86 | * of elements. The distributions are treated as vectors | |
| 87 | * in <code>dist.length</code>-dimensional space. | |
| 88 | * Given the following definitions | |
| 89 | * <ul> | |
| 90 | * <li/><code>v</code> = the sum over all <code>i</code> of <code>dist[i] * dist[i]</code> | |
| 91 | * <li/><code>w</code> = the sum over all <code>i</code> of <code>reference[i] * reference[i]</code> | |
| 92 | * <li/><code>vw</code> = the sum over all <code>i</code> of <code>dist[i] * reference[i]</code> | |
| 93 | * </ul> | |
| 94 | * the value returned is defined as <code>vw / (Math.sqrt(v) * Math.sqrt(w))</code>. | |
| 95 | */ | |
| 96 | public static double cosine(double[] dist, double[] reference) | |
| 97 | { | |
| 98 | 0 | double v_prod = 0; // dot product x*x |
| 99 | 0 | double w_prod = 0; // dot product y*y |
| 100 | 0 | double vw_prod = 0; // dot product x*y |
| 101 | ||
| 102 | 0 | checkLengths(dist, reference); |
| 103 | ||
| 104 | 0 | for (int i = 0; i < dist.length; i++) |
| 105 | { | |
| 106 | 0 | vw_prod += dist[i] * reference[i]; |
| 107 | 0 | v_prod += dist[i] * dist[i]; |
| 108 | 0 | w_prod += reference[i] * reference[i]; |
| 109 | } | |
| 110 | // cosine distance between v and w | |
| 111 | 0 | return vw_prod / (Math.sqrt(v_prod) * Math.sqrt(w_prod)); |
| 112 | } | |
| 113 | ||
| 114 | /** | |
| 115 | * Returns the entropy of this distribution. | |
| 116 | * High entropy indicates that the distribution is | |
| 117 | * close to uniform; low entropy indicates that the | |
| 118 | * distribution is close to a Dirac delta (i.e., if | |
| 119 | * the probability mass is concentrated at a single | |
| 120 | * point, this method returns 0). Entropy is defined as | |
| 121 | * the sum over all <code>i</code> of | |
| 122 | * <code>-(dist[i] * Math.log(dist[i]))</code> | |
| 123 | */ | |
| 124 | public static double entropy(double[] dist) | |
| 125 | { | |
| 126 | 0 | double total = 0; |
| 127 | ||
| 128 | 0 | for (int i = 0; i < dist.length; i++) |
| 129 | { | |
| 130 | 0 | if (dist[i] > 0) |
| 131 | 0 | total += dist[i] * Math.log(dist[i]); |
| 132 | } | |
| 133 | 0 | return -total; |
| 134 | } | |
| 135 | ||
| 136 | /** | |
| 137 | * Throws an <code>IllegalArgumentException</code> if the two arrays are not of the same length. | |
| 138 | */ | |
| 139 | protected static void checkLengths(double[] dist, double[] reference) | |
| 140 | { | |
| 141 | 34 | if (dist.length != reference.length) |
| 142 | 0 | throw new IllegalArgumentException("Arrays must be of the same length"); |
| 143 | 34 | } |
| 144 | ||
| 145 | /** | |
| 146 | * Normalizes, with Lagrangian smoothing, the specified <code>double</code> | |
| 147 | * array, so that the values sum to 1 (i.e., can be treated as probabilities). | |
| 148 | * The effect of the Lagrangian smoothing is to ensure that all entries | |
| 149 | * are nonzero; effectively, a value of <code>alpha</code> is added to each | |
| 150 | * entry in the original array prior to normalization. | |
| 151 | * @param counts | |
| 152 | * @param alpha | |
| 153 | */ | |
| 154 | public static void normalize(double[] counts, double alpha) | |
| 155 | { | |
| 156 | 0 | double total_count = 0; |
| 157 | ||
| 158 | 0 | for (int i = 0; i < counts.length; i++) |
| 159 | 0 | total_count += counts[i]; |
| 160 | ||
| 161 | 0 | for (int i = 0; i < counts.length; i++) |
| 162 | 0 | counts[i] = (counts[i] + alpha) |
| 163 | / (total_count + counts.length * alpha); | |
| 164 | 0 | } |
| 165 | ||
| 166 | /** | |
| 167 | * Returns the mean of the specified <code>Collection</code> of | |
| 168 | * distributions, which are assumed to be normalized arrays of | |
| 169 | * <code>double</code> values. | |
| 170 | * @see #mean(double[][]) | |
| 171 | */ | |
| 172 | public static double[] mean(Collection distributions) | |
| 173 | { | |
| 174 | 2 | if (distributions.isEmpty()) |
| 175 | 0 | throw new IllegalArgumentException("Distribution collection must be non-empty"); |
| 176 | 2 | Iterator iter = distributions.iterator(); |
| 177 | 2 | double[] first = (double[])iter.next(); |
| 178 | 2 | double[][] d_array = new double[distributions.size()][first.length]; |
| 179 | 2 | d_array[0] = first; |
| 180 | 5 | for (int i = 1; i < d_array.length; i++) |
| 181 | 3 | d_array[i] = (double[])iter.next(); |
| 182 | ||
| 183 | 2 | return mean(d_array); |
| 184 | } | |
| 185 | ||
| 186 | /** | |
| 187 | * Returns the mean of the specified array of distributions, | |
| 188 | * represented as normalized arrays of <code>double</code> values. | |
| 189 | * Will throw an "index out of bounds" exception if the | |
| 190 | * distribution arrays are not all of the same length. | |
| 191 | */ | |
| 192 | public static double[] mean(double[][] distributions) | |
| 193 | { | |
| 194 | 6 | double[] d_mean = new double[distributions[0].length]; |
| 195 | 12 | for (int j = 0; j < d_mean.length; j++) |
| 196 | 6 | d_mean[j] = 0; |
| 197 | ||
| 198 | 21 | for (int i = 0; i < distributions.length; i++) |
| 199 | 30 | for (int j = 0; j < d_mean.length; j++) |
| 200 | 15 | d_mean[j] += distributions[i][j] / distributions.length; |
| 201 | ||
| 202 | 6 | return d_mean; |
| 203 | } | |
| 204 | ||
| 205 | } |
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this report was generated by version 1.0.5 of jcoverage. |
copyright © 2003, jcoverage ltd. all rights reserved. |