Information distance estimation between mixtures of multivariate Gaussians

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 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