--- /dev/null
+/*
+ * Copyright (c) 2003, the JUNG Project and the Regents of the University
+ * of California
+ * All rights reserved.
+ *
+ * This software is open-source under the BSD license; see either
+ * "license.txt" or
+ * http://jung.sourceforge.net/license.txt for a description.
+ *
+ * Created on Feb 18, 2004
+ */
+package edu.uci.ics.jung.algorithms.util;
+
+import java.util.Collection;
+import java.util.Iterator;
+
+/**
+ * A utility class for calculating properties of discrete distributions.
+ * Generally, these distributions are represented as arrays of
+ * <code>double</code> values, which are assumed to be normalized
+ * such that the entries in a single array sum to 1.
+ *
+ * @author Joshua O'Madadhain
+ */
+public class DiscreteDistribution
+{
+
+ /**
+ * Returns the Kullback-Leibler divergence between the
+ * two specified distributions, which must have the same
+ * number of elements. This is defined as
+ * the sum over all <code>i</code> of
+ * <code>dist[i] * Math.log(dist[i] / reference[i])</code>.
+ * Note that this value is not symmetric; see
+ * <code>symmetricKL</code> for a symmetric variant.
+ * @see #symmetricKL(double[], double[])
+ */
+ public static double KullbackLeibler(double[] dist, double[] reference)
+ {
+ double distance = 0;
+
+ checkLengths(dist, reference);
+
+ for (int i = 0; i < dist.length; i++)
+ {
+ if (dist[i] > 0 && reference[i] > 0)
+ distance += dist[i] * Math.log(dist[i] / reference[i]);
+ }
+ return distance;
+ }
+
+ /**
+ * Returns <code>KullbackLeibler(dist, reference) + KullbackLeibler(reference, dist)</code>.
+ * @see #KullbackLeibler(double[], double[])
+ */
+ public static double symmetricKL(double[] dist, double[] reference)
+ {
+ return KullbackLeibler(dist, reference)
+ + KullbackLeibler(reference, dist);
+ }
+
+ /**
+ * Returns the squared difference between the
+ * two specified distributions, which must have the same
+ * number of elements. This is defined as
+ * the sum over all <code>i</code> of the square of
+ * <code>(dist[i] - reference[i])</code>.
+ */
+ public static double squaredError(double[] dist, double[] reference)
+ {
+ double error = 0;
+
+ checkLengths(dist, reference);
+
+ for (int i = 0; i < dist.length; i++)
+ {
+ double difference = dist[i] - reference[i];
+ error += difference * difference;
+ }
+ return error;
+ }
+
+ /**
+ * Returns the cosine distance between the two
+ * specified distributions, which must have the same number
+ * of elements. The distributions are treated as vectors
+ * in <code>dist.length</code>-dimensional space.
+ * Given the following definitions
+ * <ul>
+ * <li/><code>v</code> = the sum over all <code>i</code> of <code>dist[i] * dist[i]</code>
+ * <li/><code>w</code> = the sum over all <code>i</code> of <code>reference[i] * reference[i]</code>
+ * <li/><code>vw</code> = the sum over all <code>i</code> of <code>dist[i] * reference[i]</code>
+ * </ul>
+ * the value returned is defined as <code>vw / (Math.sqrt(v) * Math.sqrt(w))</code>.
+ */
+ public static double cosine(double[] dist, double[] reference)
+ {
+ double v_prod = 0; // dot product x*x
+ double w_prod = 0; // dot product y*y
+ double vw_prod = 0; // dot product x*y
+
+ checkLengths(dist, reference);
+
+ for (int i = 0; i < dist.length; i++)
+ {
+ vw_prod += dist[i] * reference[i];
+ v_prod += dist[i] * dist[i];
+ w_prod += reference[i] * reference[i];
+ }
+ // cosine distance between v and w
+ return vw_prod / (Math.sqrt(v_prod) * Math.sqrt(w_prod));
+ }
+
+ /**
+ * Returns the entropy of this distribution.
+ * High entropy indicates that the distribution is
+ * close to uniform; low entropy indicates that the
+ * distribution is close to a Dirac delta (i.e., if
+ * the probability mass is concentrated at a single
+ * point, this method returns 0). Entropy is defined as
+ * the sum over all <code>i</code> of
+ * <code>-(dist[i] * Math.log(dist[i]))</code>
+ */
+ public static double entropy(double[] dist)
+ {
+ double total = 0;
+
+ for (int i = 0; i < dist.length; i++)
+ {
+ if (dist[i] > 0)
+ total += dist[i] * Math.log(dist[i]);
+ }
+ return -total;
+ }
+
+ /**
+ * Throws an <code>IllegalArgumentException</code> if the two arrays are not of the same length.
+ */
+ protected static void checkLengths(double[] dist, double[] reference)
+ {
+ if (dist.length != reference.length)
+ throw new IllegalArgumentException("Arrays must be of the same length");
+ }
+
+ /**
+ * Normalizes, with Lagrangian smoothing, the specified <code>double</code>
+ * array, so that the values sum to 1 (i.e., can be treated as probabilities).
+ * The effect of the Lagrangian smoothing is to ensure that all entries
+ * are nonzero; effectively, a value of <code>alpha</code> is added to each
+ * entry in the original array prior to normalization.
+ * @param counts
+ * @param alpha
+ */
+ public static void normalize(double[] counts, double alpha)
+ {
+ double total_count = 0;
+
+ for (int i = 0; i < counts.length; i++)
+ total_count += counts[i];
+
+ for (int i = 0; i < counts.length; i++)
+ counts[i] = (counts[i] + alpha)
+ / (total_count + counts.length * alpha);
+ }
+
+ /**
+ * Returns the mean of the specified <code>Collection</code> of
+ * distributions, which are assumed to be normalized arrays of
+ * <code>double</code> values.
+ * @see #mean(double[][])
+ */
+ public static double[] mean(Collection<double[]> distributions)
+ {
+ if (distributions.isEmpty())
+ throw new IllegalArgumentException("Distribution collection must be non-empty");
+ Iterator<double[]> iter = distributions.iterator();
+ double[] first = iter.next();
+ double[][] d_array = new double[distributions.size()][first.length];
+ d_array[0] = first;
+ for (int i = 1; i < d_array.length; i++)
+ d_array[i] = iter.next();
+
+ return mean(d_array);
+ }
+
+ /**
+ * Returns the mean of the specified array of distributions,
+ * represented as normalized arrays of <code>double</code> values.
+ * Will throw an "index out of bounds" exception if the
+ * distribution arrays are not all of the same length.
+ */
+ public static double[] mean(double[][] distributions)
+ {
+ double[] d_mean = new double[distributions[0].length];
+ for (int j = 0; j < d_mean.length; j++)
+ d_mean[j] = 0;
+
+ for (int i = 0; i < distributions.length; i++)
+ for (int j = 0; j < d_mean.length; j++)
+ d_mean[j] += distributions[i][j] / distributions.length;
+
+ return d_mean;
+ }
+
+}
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Code Review / controller.git / blobdiff