Consider the problem of classifying motions, encoded as dynamical models of a certain class. Standard nearest neighbor classification then reduces to find a suitable distance function in the space of the models. In this paper we present a supervised differential-geometric method to learn a Riemannian metric for a given class of dynamical models in order to improve classification performances. Given a training set of models the optimal metric is selected among a family of pullback metrics induced by the Fisher information tensor through a parameterized diffeomorphism. Experimental results concerning action and identity recognition based on simple scalar features are shown, proving how learning a metric actually improves classification rates when compared with Fisher geodesic distance and other classical distance functions.