Abstract
This paper addresses the clustering problem of hidden dynamical systems behind observed multivariate sequences by assuming an interval-based temporal structure in the sequences. Hybrid dynamical systems that have transition mechanisms between multiple linear dynamical systems have become common models to generate and analyze complex time-varying event. Although the system is a flexible model for human motion and behaviors, the parameter estimation problem of the system has a paradoxical nature: temporal segmentation and system identification should be solved simultaneously. The EM algorithm is a well-known method that solves this kind of paradoxical problem; however the method strongly depends on initial values and often converges to a local optimum. To overcome the problem, we propose a hierarchical clustering method of linear dynamical systems by constraining eigenvalues of the systems. Due to the constraints, the method enables parameter estimation of dynamical systems from a small amount of training data, and provides well-behaved initial parameters for the EM algorithm. Experimental results on simulated and real data show the method can organize hidden dynamical systems successfully.
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Kawashima, H., Matsuyama, T. (2005). Hierarchical Clustering of Dynamical Systems Based on Eigenvalue Constraints. In: Singh, S., Singh, M., Apte, C., Perner, P. (eds) Pattern Recognition and Data Mining. ICAPR 2005. Lecture Notes in Computer Science, vol 3686. Springer, Berlin, Heidelberg. https://doi.org/10.1007/11551188_25
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DOI: https://doi.org/10.1007/11551188_25
Publisher Name: Springer, Berlin, Heidelberg
Print ISBN: 978-3-540-28757-5
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