Metric on Nonlinear Dynamical Systems with Perron-Frobenius Operators
Machine Learning
2018-11-01 v2 Machine Learning
Dynamical Systems
Functional Analysis
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
@article{arxiv.1805.12324,
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},
journal= {arXiv preprint arXiv:1805.12324},
year = {2018}
}
Comments
accepted to NIPS2018