Multiphase Learning for an Interval-Based Hybrid Dynamical System

  • Authors:
  • Hiroaki Kawashima;Takashi Matsuyama

  • Affiliations:
  • The authors are with the Graduate School of Informatics, Kyoto University, Kyoto-shi, 606-8501 Japan. E-mail: hiroaki@vision.kuee.kyoto-u.ac.jp;The authors are with the Graduate School of Informatics, Kyoto University, Kyoto-shi, 606-8501 Japan. E-mail: hiroaki@vision.kuee.kyoto-u.ac.jp

  • Venue:
  • IEICE Transactions on Fundamentals of Electronics, Communications and Computer Sciences
  • Year:
  • 2005

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Abstract

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.