Multiphase Learning for an Interval-Based Hybrid Dynamical System

This paper addresses the parameter estimation problem of an interval-based hybrid dynamical system (interval system). The interval system has a two-layer architecture that comprises a finite state automaton and multiple linear dynamical systems. The automaton controls the activation timing of the dynamical systems based on a stochastic transition model between intervals. Thus, the interval system can generate and analyze complex multivariate sequences that consist of temporal regimes of dynamic primitives. Although the interval system is a powerful model to represent human behaviors such as gestures and facial expressions, the learning process has a paradoxical nature: temporal segmentation of primitives and identification of constituent dynamical systems need to be solved simultaneously. To overcome this problem, we propose a multiphase parameter estimation method that consists of a bottom-up clustering phase of linear dynamical systems and a refinement phase of all the system parameters. Experimental results show the method can organize hidden dynamical systems behind the training data and refine the system parameters successfully. key words: hybrid dynamical system, interval transition, system identification, clustering of dynamical systems, expectationmaximization algorithm