Learning and Inferring Motion Patterns using Parametric Segmental Switching Linear Dynamic Systems

Abstract Switching Linear Dynamic System (SLDS) models are a popular technique for modeling complex nonlinear dynamic systems. An SLDS can describe complex temporal patterns more concisely and accurately than an HMM by using continuous hidden states. However, the use of SLDS models in practical applications is challenging for three reasons. First, exact inference in SLDS models is computationally intractable. Second, the geometric duration model induced in standard SLDSs limits their representational power. Third, standard SLDSs do not provide a principled way to interpret systematic variations governed by higher order parameters. The contributions in this paper address all of these three challenges. First, we present a data-driven MCMC (DD-MCMC) sampling method for approximate inference in SLDSs. We show DD-MCMC provides an efficient method for estimation and learning in SLDS models. Second, we present segmental SLDSs (S-SLDS), where the geometric distributions of the switching state durations are replaced with arbitrary duration models. Third, we extend the standard SLDS model with additional global parameters that can capture systematic temporal and spatial variations. The resulting parametric SLDS model (P-SLDS) uses EM to robustly interpret parametrized motions by incorporating additional global parameters that underly systematic variations of the overall motion. The overall development of the extensions for SLDSs provide a principled framework to interpret complex motions. The framework is applied to the honey bee dance interpretation task in the context of the on-going BioTracking project at the Georgia Institute of Technology. The experimental results suggest that the enhanced models provide an effective framework for a wide range of motion analysis applications.