2018/05/31 by Isao Ishikawa, Ishikawa, Isao, Keisuke Fujii +7 · 1 citation
Mathematics · Agricultural and Biological Sciences · #Morphological variations and asymmetry #Advanced Scientific Research Methods
paper · pdf · doi:10.48550/arxiv.1805.12324
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.