Package elki.distance.probabilistic

Class SqrtJensenShannonDivergenceDistance

  • All Implemented Interfaces:
    Distance<NumberVector>, NumberVectorDistance<NumberVector>, PrimitiveDistance<NumberVector>, SpatialPrimitiveDistance<NumberVector>
    @Reference(authors="D. M. Endres, J. E. Schindelin",
           title="A new metric for probability distributions",
           booktitle="IEEE Transactions on Information Theory 49(7)",
           url="https://doi.org/10.1109/TIT.2003.813506",
           bibkey="DBLP:journals/tit/EndresS03")
public class SqrtJensenShannonDivergenceDistance
extends JensenShannonDivergenceDistance
    The square root of Jensen-Shannon divergence is a metric.

    \[\sqrt{JS}(\vec{x},\vec{y}):=\sqrt{\tfrac12\sum\nolimits_i x_i\log\tfrac{2x_i}{x_i+y_i}+y_i\log\tfrac{2y_i}{x_i+y_i}} = \sqrt{JS(\vec{x},\vec{y})}\]

    A proof of triangle inequality (for "\(D_{PQ}\)") can be found in Endres and Schindelin.

    References:

    D. M. Endres, J. E. Schindelin
    A new metric for probability distributions
    IEEE Transactions on Information Theory 49(7)

    Since:
    0.6.0
    Author:
    Erich Schubert