Metric on nonlinear dynamical systems with Perron-Frobenius operators

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

Research output: Contribution to journalConference article

2 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 - Jan 1 2018
Externally publishedYes
Event32nd Conference on Neural Information Processing Systems, NeurIPS 2018 - Montreal, Canada
Duration: Dec 2 2018Dec 8 2018

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Nonlinear dynamical systems
Hilbert spaces
Pattern recognition
Learning systems
Mathematical operators
Time series
Dynamical systems

All Science Journal Classification (ASJC) codes

  • Computer Networks and Communications
  • Information Systems
  • Signal Processing

Cite this

Metric on nonlinear dynamical systems with Perron-Frobenius operators. / Ishikawa, Isao; Fujii, Keisuke; Ikeda, Masahiro; Hashimoto, Yuka; Kawahara, Yoshinobu.

In: Advances in Neural Information Processing Systems, Vol. 2018-December, 01.01.2018, p. 2856-2866.

Research output: Contribution to journalConference article

Ishikawa, I, Fujii, K, Ikeda, M, Hashimoto, Y & Kawahara, Y 2018, 'Metric on nonlinear dynamical systems with Perron-Frobenius operators', Advances in Neural Information Processing Systems, vol. 2018-December, pp. 2856-2866.
Ishikawa, Isao ; Fujii, Keisuke ; Ikeda, Masahiro ; Hashimoto, Yuka ; Kawahara, Yoshinobu. / Metric on nonlinear dynamical systems with Perron-Frobenius operators. In: Advances in Neural Information Processing Systems. 2018 ; Vol. 2018-December. pp. 2856-2866.
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