Hilbert space embeddings in dynamical systems

This paper recovers the diffusion kernels of Kondor and Lafferty, generalised versions of directed graph kernels of Gatner, novel kernels on matrices and new similarity measures on Markov Models.

Abstract

In this paper we study Hilbert space embeddings of dynamical systems and embeddings generated via dynamical systems. This is achieved by following the behavioural framework invented by Willems, namely by comparing trajectories of states. As important special cases we recover the diffusion kernels of Kondor and Lafferty, generalised versions of directed graph kernels of Gätner, novel kernels on matrices and new similarity measures on Markov Models.