Information distance estimation between mixtures of multivariate Gaussians

There are efficient software programs for extracting from image sequences certain mixtures of distributions, such as multivariate Gaussians, to represent the important features needed for accurate document retrieval from databases. This note describes a method to use information geometric methods to measure distances between distributions in mixtures of 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 is not essential and comparative values suffice for proximity testing. For two mixtures of 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 compare several choices for the incorporation of weightings in distance estimation and provide illustrative results from simulations of differently weighted mixtures of multivariate Gaussians