  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.
