Manifold Learning for Multi-dimensional Auto-regressive Dynamical Models

Abstract

We present a general differential-geometric framework for learning dis- tance functions for dynamical models. Given a training set of models, the optimal metric is selected among a family of pullback metrics induced by the Fisher infor- mation tensor through a parameterized automorphism. The problem of classifying motions, encoded as dynamical models of a certain class, can then be posed on the learnt manifold. In particular, we consider the class of multidimensional autoregres- sive models of order 2. Experimental results concerning identity recognition are shown that prove how such optimal pullback Fisher metrics greatly improve classi- fication performances.