Class DiscreteDistribution

java.lang.Object
edu.uci.ics.jung.algorithms.util.DiscreteDistribution

public class DiscreteDistribution extends Object
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.
  • Constructor Summary

    Constructors
    Constructor
    Description
     
  • Method Summary

    Modifier and Type
    Method
    Description
    static double
    cosine(double[] dist, double[] reference)
    Returns the cosine distance between the two specified distributions, which must have the same number of elements.
    static double
    entropy(double[] dist)
    Returns the entropy of this distribution.
    static double
    KullbackLeibler(double[] dist, double[] reference)
    Returns the Kullback-Leibler divergence between the two specified distributions, which must have the same number of elements.
    static double[]
    mean(double[][] distributions)
    Returns the mean of the specified array of distributions, represented as normalized arrays of double values.
    static double[]
    mean(Collection<double[]> distributions)
    Returns the mean of the specified Collection of distributions, which are assumed to be normalized arrays of double values.
    static void
    normalize(double[] counts, double alpha)
    Normalizes, with Lagrangian smoothing, the specified double array, so that the values sum to 1 (i.e., can be treated as probabilities).
    static double
    squaredError(double[] dist, double[] reference)
    Returns the squared difference between the two specified distributions, which must have the same number of elements.
    static double
    symmetricKL(double[] dist, double[] reference)
     

    Methods inherited from class java.lang.Object

    clone, equals, finalize, getClass, hashCode, notify, notifyAll, toString, wait, wait, wait
  • Constructor Details

    • DiscreteDistribution

      public DiscreteDistribution()
  • Method Details

    • KullbackLeibler

      public static double KullbackLeibler(double[] dist, double[] reference)
      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.
      Parameters:
      dist - the distribution whose divergence from reference is being measured
      reference - the reference distribution
      Returns:
      sum_i of dist[i] * Math.log(dist[i] / reference[i])
      See Also:
    • symmetricKL

      public static double symmetricKL(double[] dist, double[] reference)
      Parameters:
      dist - the distribution whose divergence from reference is being measured
      reference - the reference distribution
      Returns:
      KullbackLeibler(dist, reference) + KullbackLeibler(reference, dist)
      See Also:
    • squaredError

      public static double squaredError(double[] dist, double[] reference)
      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]).
      Parameters:
      dist - the distribution whose distance from reference is being measured
      reference - the reference distribution
      Returns:
      sum_i (dist[i] - reference[i])^2
    • cosine

      public static double cosine(double[] dist, double[] reference)
      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)).
      Parameters:
      dist - the distribution whose distance from reference is being measured
      reference - the reference distribution
      Returns:
      the cosine distance between dist and reference, considered as vectors
    • entropy

      public static double entropy(double[] dist)
      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]))
      Parameters:
      dist - the distribution whose entropy is being measured
      Returns:
      sum_i -(dist[i] * Math.log(dist[i]))
    • normalize

      public static void normalize(double[] counts, double alpha)
      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.
      Parameters:
      counts - the array to be converted into a probability distribution
      alpha - the value to add to each entry prior to normalization
    • mean

      public static double[] mean(Collection<double[]> distributions)
      Returns the mean of the specified Collection of distributions, which are assumed to be normalized arrays of double values.
      Parameters:
      distributions - the distributions whose mean is to be calculated
      Returns:
      the mean of the distributions
      See Also:
    • mean

      public static double[] mean(double[][] distributions)
      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.
      Parameters:
      distributions - the distributions whose mean is to be calculated
      Returns:
      the mean of the distributions