Multiphase Learning for an Interval-Based Hybrid Dynamical System

Hiroaki KAWASHIMA  Takashi MATSUYAMA  

Publication
IEICE TRANSACTIONS on Fundamentals of Electronics, Communications and Computer Sciences   Vol.E88-A   No.11   pp.3022-3035
Publication Date: 2005/11/01
Online ISSN: 
Print ISSN: 0916-8508
Type of Manuscript: Special Section PAPER (Special Section on Concurrent/Hybrid Systems: Theory and Applications)
Category: 
Keyword: 
hybrid dynamical system,  interval transition,  system identification,  clustering of dynamical systems,  expectation-maximization algorithm,  

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Summary: 
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.