Paper Info
Title
Dynamic Mode Decomposition with Reproducing Kernels for Koopman Spectral Analysis.
Abstract
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.
Year
Venue
Field
2016
ADVANCES IN NEURAL INFORMATION PROCESSING SYSTEMS 29 (NIPS 2016)
Dynamic mode decomposition,Mathematical optimization,Nonlinear system,Observable,Matrix (mathematics),Computer science,Artificial intelligence,Eigendecomposition of a matrix,Linear map,Operator (computer programming),Machine learning,Reproducing kernel Hilbert space
DocType
Volume
ISSN
Conference
29
1049-5258
Citations 
PageRank 
References 
0
0.34
0
Authors
1
Name
Order
Citations
PageRank
Kawahara, Yoshinobu131731.30