Abstract:
Switching Linear Dynamic System (SLDS) models are a popular technique for modeling complex nonlinear dynamic systems. An SLDS has significantly more descriptive power than an HMM by using continuous hidden states. However, the use of SLDS models in practical applications is challenging for several 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 systematic way to robustly interpret systematic variations governed by higher order parameters.

The contributions in this paper address all three challenges above. First, we present a data-driven MCMC sampling method for SLDSs as a robust and efficient approximate inference method. Second, we present segmental switching linear dynamic systems (S-SLDS), where the geometric distributions are replaced with arbitrary duration models. Third, we extend the standard model with a parametric model 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 proposed inference methods and extensions for SLDSs provide a robust framework to interpret complex motions. The framework is applied to the honey bee dance interpretation task in the context of the ongoing BioTracking project at Georgia Institute of Technology. The experimental results suggest that the enhanced models provide an effective framework for a wide range of motion analysis applications.

Keywords: probabilistic inference, time-series modeling, switching linear dynamic systems, honeybee dance

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