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 {\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.