Dynamic mode decomposition with reproducing kernels for koopman spectral analysis

研究成果: ジャーナルへの寄稿Conference article

19 引用 (Scopus)

抜粋

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.

元の言語英語
ページ(範囲)919-927
ページ数9
ジャーナルAdvances in Neural Information Processing Systems
出版物ステータス出版済み - 1 1 2016
外部発表Yes
イベント30th Annual Conference on Neural Information Processing Systems, NIPS 2016 - Barcelona, スペイン
継続期間: 12 5 201612 10 2016

All Science Journal Classification (ASJC) codes

  • Computer Networks and Communications
  • Information Systems
  • Signal Processing

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