Metric on Nonlinear Dynamical Systems with Perron-Frobenius Operators
Isao Ishikawa, Keisuke Fujii, Masahiro Ikeda, Yuka Hashimoto, Yoshinobu Kawahara
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.
BibTeX
@inproceedings{NEURIPS2018_fa1e9c96,
author = {Ishikawa, Isao and Fujii, Keisuke and Ikeda, Masahiro and Hashimoto, Yuka and Kawahara, Yoshinobu},
booktitle = {Advances in Neural Information Processing Systems},
editor = {S. Bengio and H. Wallach and H. Larochelle and K. Grauman and N. Cesa-Bianchi and R. Garnett},
pages = {},
publisher = {Curran Associates, Inc.},
title = {Metric on Nonlinear Dynamical Systems with Perron-Frobenius Operators},
url = {https://proceedings.neurips.cc/paper_files/paper/2018/file/fa1e9c965314ccd7810fb5ea838303e5-Paper.pdf},
volume = {31},
year = {2018}
}