Metric on nonlinear dynamical systems with Perron-Frobenius operators

Isao Ishikawa, Keisuke Fujii, Masahiro Ikeda, Yuka Hashimoto, Yoshinobu Kawahara

Research output: Contribution to journalConference articlepeer-review

7 Citations (Scopus)

Abstract

The development of a metric for structural data is a long-term problem in pattern recognition and machine learning. In this paper, we develop a general metric for comparing nonlinear dynamical systems that is defined with Perron-Frobenius operators in reproducing kernel Hilbert spaces. Our metric includes the existing fundamental metrics for dynamical systems, which are basically defined with principal angles between some appropriately-chosen subspaces, as its special cases. We also describe the estimation of our metric from finite data. We empirically illustrate our metric with an example of rotation dynamics in a unit disk in a complex plane, and evaluate the performance with real-world time-series data.

Original languageEnglish
Pages (from-to)2856-2866
Number of pages11
JournalAdvances in Neural Information Processing Systems
Volume2018-December
Publication statusPublished - 2018
Externally publishedYes
Event32nd Conference on Neural Information Processing Systems, NeurIPS 2018 - Montreal, Canada
Duration: Dec 2 2018Dec 8 2018

All Science Journal Classification (ASJC) codes

  • Computer Networks and Communications
  • Information Systems
  • Signal Processing

Fingerprint

Dive into the research topics of 'Metric on nonlinear dynamical systems with Perron-Frobenius operators'. Together they form a unique fingerprint.

Cite this