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Algorithms for the JUNG project
/*
* Copyright (c) 2003, The JUNG Authors
*
* All rights reserved.
*
* This software is open-source under the BSD license; see either
* "license.txt" or
* https://github.com/jrtom/jung/blob/master/LICENSE for a description.
*
* Created on Feb 18, 2004
*/
package edu.uci.ics.jung.algorithms.util;
import java.util.Collection;
import java.util.Iterator;
import com.google.common.base.Preconditions;
/**
* A utility class for calculating properties of discrete distributions.
* Generally, these distributions are represented as arrays of
* double 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 i of
* dist[i] * Math.log(dist[i] / reference[i]).
* Note that this value is not symmetric; see
* symmetricKL for a symmetric variant.
* @see #symmetricKL(double[], double[])
* @param dist the distribution whose divergence from {@code reference} is being measured
* @param reference the reference distribution
* @return sum_i of {@code dist[i] * Math.log(dist[i] / reference[i])}
*/
public static double KullbackLeibler(double[] dist, double[] reference)
{
double distance = 0;
Preconditions.checkArgument(dist.length == reference.length,
"input arrays must be of the same length");
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;
}
/**
* @param dist the distribution whose divergence from {@code reference} is being measured
* @param reference the reference distribution
* @return KullbackLeibler(dist, reference) + KullbackLeibler(reference, dist)
* @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 i of the square of
* (dist[i] - reference[i]).
* @param dist the distribution whose distance from {@code reference} is being measured
* @param reference the reference distribution
* @return sum_i {@code (dist[i] - reference[i])^2}
*/
public static double squaredError(double[] dist, double[] reference)
{
double error = 0;
Preconditions.checkArgument(dist.length == reference.length,
"input arrays must be of the same length");
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 dist.length-dimensional space.
* Given the following definitions
*
* v = the sum over all i of dist[i] * dist[i]
* w = the sum over all i of reference[i] * reference[i]
* vw = the sum over all i of dist[i] * reference[i]
*
* the value returned is defined as vw / (Math.sqrt(v) * Math.sqrt(w)).
* @param dist the distribution whose distance from {@code reference} is being measured
* @param reference the reference distribution
* @return the cosine distance between {@code dist} and {@code reference}, considered as vectors
*/
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
Preconditions.checkArgument(dist.length == reference.length,
"input arrays must be of the same length");
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 i of
* -(dist[i] * Math.log(dist[i]))
*
* @param dist the distribution whose entropy is being measured
* @return sum_i {@code -(dist[i] * Math.log(dist[i]))}
*/
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;
}
/**
* Normalizes, with Lagrangian smoothing, the specified double
* 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 alpha is added to each
* entry in the original array prior to normalization.
* @param counts the array to be converted into a probability distribution
* @param alpha the value to add to each entry prior to normalization
*/
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 Collection of
* distributions, which are assumed to be normalized arrays of
* double values.
* @see #mean(double[][])
* @param distributions the distributions whose mean is to be calculated
* @return the mean of the distributions
*/
public static double[] mean(Collection distributions)
{
if (distributions.isEmpty())
throw new IllegalArgumentException("Distribution collection must be non-empty");
Iterator 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 double values.
* Will throw an "index out of bounds" exception if the
* distribution arrays are not all of the same length.
* @param distributions the distributions whose mean is to be calculated
* @return the mean of the distributions
*/
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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