Metric on Nonlinear Dynamical Systems with Perron-Frobenius Operators

Isao Ishikawa, Keisuke Fujii, Masahiro Ikeda, Yuka Hashimoto, Yoshinobu Kawahara
5/31/2018
stat.MLcs.LGmath.DS

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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.

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Cite this paper

@article{ishikawa2018metric,
  title  = {Metric on Nonlinear Dynamical Systems with Perron-Frobenius Operators},
  author = {Isao Ishikawa and Keisuke Fujii and Masahiro Ikeda and Yuka Hashimoto and Yoshinobu Kawahara},
  year   = {2018},
  eprint = {1805.12324},
  archivePrefix = {arXiv},
  url    = {https://arxiv.org/abs/1805.12324}
}

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