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Metric on Nonlinear Dynamical Systems with Perron-Frobenius Operators

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

Room 210 #77

Keywords: [ Dynamical Systems ] [ Spaces of Functions and Kernels ]


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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