Abstract
Recurrence analysis has proven to be a robust methodology for characterizing complex behaviors, with numerous successful applications in multiple domains. However, most of the prior works addressed chaotic behaviors evolving over time. Very little has been done in investigating complex recurrences over space (geometry). This paper presents a precise Recurrence Quantification Analysis (RQA) framework to characterize and quantify the sophisticated recurrence characteristics of spatial data. We first extend the concepts of the traditional recurrence plot for time series to complex spatial dynamics in order to construct a generalized recurrence hypercube for image data. Then, we develop a set of novel quantifiers to characterize two primary recurrence characteristics, trapping and shifting, in the recurrence hypercube to delineate subtle spatial recurrences. Notably, trapping indicates the occurrences of a continuous range of similar system statuses; and shifting represents the reoccurrences of a system's evolving patterns. A real-world case study in colon cancer detection illustrates that the proposed RQAs successfully characterize subtle spatial dynamics in histopathological images and can be used to accurately identify tumor tissues with AUC>0.98, suggesting many possible real-world applications for this methodology.