A Kernel Subspace Method by Stochastic Realization for Learning Nonlinear Dynamical Systems

Part of Advances in Neural Information Processing Systems 19 (NIPS 2006)

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Yoshinobu Kawahara, Takehisa Yairi, Kazuo Machida


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.