An Information geometric framework for the optimization on discrete probability spaces: Application to human trajectory classification

Abstract

This paper presents an iterative algorithm using a information geometric framework to perform the optimization on a discrete probability spaces. In the proposed methodology, the probabilities are considered as points in a statistical manifold. This differs greatly regarding the traditional approaches in which the probabilities lie on a simplex mesh constraint. We present an application for estimating the switching probabilities in a space-variant HMM to perform human activity recognition from trajectories; a core contribution in this paper. More specifically, the HMM is equipped with a space-variant vector fields that are not constant but depending on the objects's localization. To achieve this, we apply the iterative optimization of switching probabilities based on the natural gradient vector, with respect to the Fisher information metric. Experiments on synthetic and real world problems, focused on human activity recognition in long-range surveillance settings show that the proposed methodology compares favorably with the state-of-the-art.