Heterogeneous recurrence analysis of spatial data

Nonlinear dynamical systems often generate significant amounts of observational data such as time series, as well as high-dimensional spatial data. To delineate recurrence dynamics in the spatial data, prior efforts either extended the recurrence plot, which is a widely used tool for time series, to a four-dimensional hyperspace or utilized the network approach for recurrence analysis. However, very little has been done to differentiate heterogeneous types of recurrences in the spatial data (e.g., recurrence variations of state transitions in the spatial domain). Therefore, we propose a novel heterogeneous recurrence approach for spatial data analysis. First, spatial data are traversed with the Hilbert Space-Filling Curve to transform the variations of recurrence patterns from the spatial domain to the state-space domain. Second, we design an Iterated Function System to derive the fractal representation for the state-space trajectory of spatial data. Such a fractal representation effectively captures self-similar behaviors of recurrence variations and multi-state transitions in the spatial data. Third, we develop the Heterogeneous Recurrence Quantification Analysis of spatial data. Experimental results in both simulation and real-world case studies show that the proposed approach yields superior performance in the extraction of salient features to characterize and quantify heterogeneous recurrence dynamics in spatial data.

This article may be downloaded for personal use only. Any other use requires prior permission of the author and AIP Publishing. This article appeared in [Heterogeneous recurrence analysis of spatial data. Chaos: An Interdisciplinary Journal of Nonlinear Science 30, 1 p013119 (2020)] and may be found at https://doi.org/10.1063/1.5129959.

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Work Title Heterogeneous recurrence analysis of spatial data
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Open Access
Creators
  1. Hui Yang
  2. Cheng Bang Chen
  3. Soundar Kumara
License In Copyright (Rights Reserved)
Work Type Article
Publisher
  1. Chaos
Publication Date January 16, 2020
Publisher Identifier (DOI)
  1. https://doi.org/10.1063/1.5129959
Deposited April 27, 2022

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