Binet-Cauchy Kernels on Dynamical Systems and its Application to the Analysis of Dynamic Scenes

摘要

We propose a family of kernels based on the Binet-Cauchy theorem, and its extension to Fredholm operators. Our derivation provides a unifying framework for all kernels on dynamical systems currently used in machine learning, including kernels derived from the behavioral framework, diffusion processes, marginalized kernels, kernels on graphs, and the kernels on sets arising from the subspace angle approach. In the case of linear time-invariant systems, we derive explicit formulae for computing the proposed Binet-Cauchy kernels by solving Sylvester equations, and relate the proposed kernels to existing kernels based on cepstrum coefficients and subspace angles. We show efficient methods for computing our kernels which make them viable for the practitioner.