Information distance estimation between mixtures of multivariate Gaussians.

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    There are efficient software programs for
    extracting from large data sets and image sequences certain mixtures of probability distributions, such as multivariate Gaussians, to represent the important features and
    their mutual correlations needed for accurate document retrieval from databases.
    This note describes a method to use information geometric methods for distance measures
    between distributions in mixtures of arbitrary multivariate Gaussians.
    There is no general analytic solution for the information
    geodesic distance between two $k$-variate Gaussians,
    but for many purposes the absolute information distance may not be essential and comparative
    values suffice for proximity testing and document retrieval.
    Also, for two {\em mixtures} of different multivariate Gaussians
    we must resort to approximations to incorporate the weightings.
    In practice, the relation between
    a reasonable approximation and a true geodesic distance is likely to be monotonic, which
    is adequate for many applications. Here we consider some choices for the incorporation of
    weightings in distance estimation and provide illustrative results from simulations of
    differently weighted mixtures of multivariate Gaussians.
    Original languageEnglish
    Pages (from-to)439-447
    Number of pages9
    JournalAIMS Mathematics
    Issue number4
    Publication statusPublished - 19 Oct 2018


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