Persistence of Weighted Ordinal Partition Networks for Dynamic State Detection.

One of the most important problems arising in time series analysis is that of classifying the states of a dynamical system. That is, given a collection of time series, is it possible to perform two -state classification (chaotic versus periodic) of the underlying system? For this task, we turn to the field of topological data analysis, which encodes information about the shape and structure of data. In this paper, we investigate a more recent method for encoding the structure of the attractor as a weighted graph, known as the ordinal partition network, representing information about when the dynamical system has passed between certain regions of state space. We provide methods to incorporate the weighting information and show that this framework provides more resilience to noise or perturbations in the system as well as improving the accuracy of dynamic state identification.