Recurrence network modeling and analysis of spatial data.

Nonlinear dynamical systems exhibit complex recurrence behaviors. Recurrence plot is widely used to graphically represent the patterns of recurrence dynamics and further facilitates the quantification of recurrence patterns, namely, recurrence quantification analysis. However, traditional recurrence methods tend to be limited in their ability to handle spatial data due to high dimensionality and geometric characteristics. Prior efforts have been made to generalize the recurrence plot to a four-dimensional space for spatial data analysis, but this framework can only provide graphical visualization of recurrence patterns in the projected reduced-dimension space (i.e., two- or three- dimensions). In this paper, we propose a new weighted recurrence network approach for spatial data analysis. A weighted network model is introduced to represent the recurrence patterns in spatial data, which account for both pixel intensities and spatial distance simultaneously. Note that each network node represents a location in the high-dimensional spatial data. Network edges and weights preserve complex spatial structures and recurrence patterns. Network representation is shown to be an effective means to provide a complete picture of recurrence patterns in the spatial data. Furthermore, we leverage network statistics to characterize and quantify recurrence properties and features in the spatial data. Experimental results in both simulation and real-world case studies show that the generalized recurrence network approach yields superior performance in the visualization of recurrence patterns in spatial data and in the extraction of salient features to characterize recurrence dynamics in spatial systems.