A method for analyzing the expansion and shrinkage of point pattern

Abstract

AbstractThis article proposes a new method for analyzing the spatial expansion and shrinkage of point patterns. Spatial expansions of epidemic diseases and market areas are represented as the expansions of point patterns when disease cases and store customers are represented as points. The spatial expansion and shrinkage have been studied in many scientific fields. Existing analytical methods, however, are not sufficient for treating complicated spatiotemporal patterns. To answer this demand, this article develops a new method for analyzing the expansion and shrinkage of points. Three vector measures evaluate the degree and direction of expansion and shrinkage as functions of location and time. They are visualized as vector maps, which are valid for capturing the global spatiotemporal pattern as well as for discussing the local variation. Summary measures of these vectors allow us to grasp the overall spatiotemporal pattern efficiently. To test the validity of the proposed method, this article applies it to the analysis of visitors to Shinjuku and Ginza in Tokyo. The proposed measures permitted us to evaluate the spatiotemporal pattern of the visitors in detail and to consider its underlying structure from various perspectives, which indicated the soundness of the technique.