## 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.

Original language | English |
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Pages (from-to) | 919-927 |

Number of pages | 9 |

Journal | Advances in Neural Information Processing Systems |

Publication status | Published - 2016 |

Externally published | Yes |

Event | 30th Annual Conference on Neural Information Processing Systems, NIPS 2016 - Barcelona, Spain Duration: Dec 5 2016 → Dec 10 2016 |

## All Science Journal Classification (ASJC) codes

- Computer Networks and Communications
- Information Systems
- Signal Processing