Metric on Nonlinear Dynamical Systems with Perron-Frobenius Operators
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.
Cite
Text
Ishikawa et al. "Metric on Nonlinear Dynamical Systems with Perron-Frobenius Operators." Neural Information Processing Systems, 2018.Markdown
[Ishikawa et al. "Metric on Nonlinear Dynamical Systems with Perron-Frobenius Operators." Neural Information Processing Systems, 2018.](https://mlanthology.org/neurips/2018/ishikawa2018neurips-metric/)BibTeX
@inproceedings{ishikawa2018neurips-metric,
title = {{Metric on Nonlinear Dynamical Systems with Perron-Frobenius Operators}},
author = {Ishikawa, Isao and Fujii, Keisuke and Ikeda, Masahiro and Hashimoto, Yuka and Kawahara, Yoshinobu},
booktitle = {Neural Information Processing Systems},
year = {2018},
pages = {2856-2866},
url = {https://mlanthology.org/neurips/2018/ishikawa2018neurips-metric/}
}