Package elki.distance.probabilistic

Class ChiDistance

  • All Implemented Interfaces:
    Distance<NumberVector>, NumberVectorDistance<NumberVector>, PrimitiveDistance<NumberVector>, SpatialPrimitiveDistance<NumberVector>
    @Alias("chi")
@Priority(100)
@Reference(authors="J. Puzicha, J. M. Buhmann, Y. Rubner, C. Tomasi",title="Empirical evaluation of dissimilarity measures for color and texture",booktitle="Proc. 7th IEEE International Conference on Computer Vision",url="https://doi.org/10.1109/ICCV.1999.790412",bibkey="DBLP:conf/iccv/PuzichaRTB99") @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 ChiDistance
extends ChiSquaredDistance
    χ distance function, symmetric version. This is the square root of the ChiSquaredDistance, and can serve as a fast approximation to SqrtJensenShannonDivergenceDistance.

    This implementation assumes \(\sum_i x_i=\sum_i y_i\), and is defined as: \[ \chi(\vec{x},\vec{y}):= \sqrt{2 \sum\nolimits_i \tfrac{(x_i-x_i)^2}{x_i+y_i}} \]

    Reference:

    J. Puzicha, J. M. Buhmann, Y. Rubner, C. Tomasi
    Empirical evaluation of dissimilarity measures for color and texture
    Proc. 7th IEEE International Conference on Computer Vision

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

    Since:
    0.7.5
    Author:
    Erich Schubert