A Kernel Subspace Method by Stochastic Realization for Learning Nonlinear Dynamical Systems
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.
Cite
Text
Kawahara et al. "A Kernel Subspace Method by Stochastic Realization for Learning Nonlinear Dynamical Systems." Neural Information Processing Systems, 2006.Markdown
[Kawahara et al. "A Kernel Subspace Method by Stochastic Realization for Learning Nonlinear Dynamical Systems." Neural Information Processing Systems, 2006.](https://mlanthology.org/neurips/2006/kawahara2006neurips-kernel/)BibTeX
@inproceedings{kawahara2006neurips-kernel,
title = {{A Kernel Subspace Method by Stochastic Realization for Learning Nonlinear Dynamical Systems}},
author = {Kawahara, Yoshinobu and Yairi, Takehisa and Machida, Kazuo},
booktitle = {Neural Information Processing Systems},
year = {2006},
pages = {665-672},
url = {https://mlanthology.org/neurips/2006/kawahara2006neurips-kernel/}
}