Metric on nonlinear dynamical systems with Perron-Frobenius operators

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

研究成果: Contribution to journalConference article査読

8 被引用数 (Scopus)

抄録

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.

本文言語英語
ページ(範囲)2856-2866
ページ数11
ジャーナルAdvances in Neural Information Processing Systems
2018-December
出版ステータス出版済み - 2018
外部発表はい
イベント32nd Conference on Neural Information Processing Systems, NeurIPS 2018 - Montreal, カナダ
継続期間: 12 2 201812 8 2018

All Science Journal Classification (ASJC) codes

  • コンピュータ ネットワークおよび通信
  • 情報システム
  • 信号処理

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