A kernel subspace method by stochastic realization for learning nonlinear dynamical systems

Yoshinobu Kawahara; Takehisa Yairi; Kazuo MacHida

A kernel subspace method by stochastic realization for learning nonlinear dynamical systems

Yoshinobu Kawahara, Takehisa Yairi, Kazuo MacHida

Research output: Chapter in Book/Report/Conference proceeding › Conference contribution

Abstract

In this paper, we present a subspace method for learning nonlinear dynamical systems based on stochastic realization, in which state vectors are chosen using kernel canonical correlation analysis, and then state-space systems are identified through regression with the state vectors. We construct the theoretical underpinning and derive a concrete algorithm for nonlinear identification. The obtained algorithm needs no iterative optimization procedure and can be implemented on the basis of fast and reliable numerical schemes. The simulation result shows that our algorithm can express dynamics with a high degree of accuracy.

Original language	English
Title of host publication	Advances in Neural Information Processing Systems 19 - Proceedings of the 2006 Conference
Pages	665-672
Number of pages	8
Publication status	Published - Dec 1 2007
Externally published	Yes
Event	20th Annual Conference on Neural Information Processing Systems, NIPS 2006 - Vancouver, BC, Canada Duration: Dec 4 2006 → Dec 7 2006

Publication series

Name	Advances in Neural Information Processing Systems
ISSN (Print)	1049-5258

Conference

Conference	20th Annual Conference on Neural Information Processing Systems, NIPS 2006
Country/Territory	Canada
City	Vancouver, BC
Period	12/4/06 → 12/7/06

All Science Journal Classification (ASJC) codes

Computer Networks and Communications
Information Systems
Signal Processing

Cite this

A kernel subspace method by stochastic realization for learning nonlinear dynamical systems. / Kawahara, Yoshinobu; Yairi, Takehisa; MacHida, Kazuo.

Advances in Neural Information Processing Systems 19 - Proceedings of the 2006 Conference. 2007. p. 665-672 (Advances in Neural Information Processing Systems).

Research output: Chapter in Book/Report/Conference proceeding › Conference contribution

Kawahara, Y, Yairi, T & MacHida, K 2007, A kernel subspace method by stochastic realization for learning nonlinear dynamical systems. in Advances in Neural Information Processing Systems 19 - Proceedings of the 2006 Conference. Advances in Neural Information Processing Systems, pp. 665-672, 20th Annual Conference on Neural Information Processing Systems, NIPS 2006, Vancouver, BC, Canada, 12/4/06.

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A kernel subspace method by stochastic realization for learning nonlinear dynamical systems

Abstract

Publication series

Conference

All Science Journal Classification (ASJC) codes

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