Initial-state invariant Binet-Cauchy kernels for the comparison of Linear Dynamical Systems

Abstract

Linear Dynamical Systems (LDSs) have been extensively used for modeling and recognition of dynamic visual phenomena such as human activities, dynamic textures, facial deformations and lip articulations. In these applications, a huge number of LDSs identified from high-dimensional time-series need to be compared. Over the past decade, three computationally efficient distances have emerged: the Martin distance [1], distances obtained from the subspace angles between observability subspaces [2], and distances obtained from the family of Binet-Cauchy kernels [3]. The main contribution of this work is to show that the first two distances are particular cases of the latter family obtained by making the Binet-Cauchy kernels invariant to the initial states of the LDSs. We also extend Binet-Cauchy kernels to take into account the mean of the dynamical process. We evaluate the performance of our metrics on several datasets and show similar or better human activity recognition results.