Persistence of Weighted Ordinal Partition Networks for Dynamic State Detection

One of the most important problems arising in time series analysis is that bifurcation, or change point detection. That is, given a collection over varying parameter, when has structure underlying dynamical system changed? For this task, we turn to field topological data (TDA), which encodes information about shape and data. The idea utilizing tools from TDA for signal processing tasks, known as (TSP), gained much attention recent years, largely through standard pipeline computes persistent homology cloud generated by Takens' embedding. However, procedure limited computation since simplicial complex case large, but also great deal redundant reason, more method encoding attractor, constructs an ordinal partition network (OPN) representing passed between certain regions state space. result weighted graph whose attractor. Our previous work began find ways package OPN manner amenable TDA; however, only used did nothing encode additional weighting information. In paper, take next step: building analyze with showing framework provides resilience noise perturbations improves accuracy dynamic