TY - JOUR

T1 - Dynamic mode decomposition with reproducing kernels for koopman spectral analysis

AU - Kawahara, Yoshinobu

N1 - Publisher Copyright:
© 2016 NIPS Foundation - All Rights Reserved.
Copyright:
Copyright 2017 Elsevier B.V., All rights reserved.

PY - 2016

Y1 - 2016

N2 - A spectral analysis of the Koopman operator, which is an infinite dimensional linear operator on an observable, gives a (modal) description of the global behavior of a nonlinear dynamical system without any explicit prior knowledge of its governing equations. In this paper, we consider a spectral analysis of the Koopman operator in a reproducing kernel Hilbert space (RKHS). We propose a modal decomposition algorithm to perform the analysis using finite-length data sequences generated from a nonlinear system. The algorithm is in essence reduced to the calculation of a set of orthogonal bases for the Krylov matrix in RKHS and the eigendecomposition of the projection of the Koopman operator onto the subspace spanned by the bases. The algorithm returns a decomposition of the dynamics into a finite number of modes, and thus it can be thought of as a feature extraction procedure for a nonlinear dynamical system. Therefore, we further consider applications in machine learning using extracted features with the presented analysis. We illustrate the method on the applications using synthetic and real-world data.

AB - A spectral analysis of the Koopman operator, which is an infinite dimensional linear operator on an observable, gives a (modal) description of the global behavior of a nonlinear dynamical system without any explicit prior knowledge of its governing equations. In this paper, we consider a spectral analysis of the Koopman operator in a reproducing kernel Hilbert space (RKHS). We propose a modal decomposition algorithm to perform the analysis using finite-length data sequences generated from a nonlinear system. The algorithm is in essence reduced to the calculation of a set of orthogonal bases for the Krylov matrix in RKHS and the eigendecomposition of the projection of the Koopman operator onto the subspace spanned by the bases. The algorithm returns a decomposition of the dynamics into a finite number of modes, and thus it can be thought of as a feature extraction procedure for a nonlinear dynamical system. Therefore, we further consider applications in machine learning using extracted features with the presented analysis. We illustrate the method on the applications using synthetic and real-world data.

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M3 - Conference article

AN - SCOPUS:85019213482

SP - 919

EP - 927

JO - Advances in Neural Information Processing Systems

JF - Advances in Neural Information Processing Systems

SN - 1049-5258

T2 - 30th Annual Conference on Neural Information Processing Systems, NIPS 2016

Y2 - 5 December 2016 through 10 December 2016

ER -