Exploratory method for analyzing changes in polygon distributions

In this paper I develop an exploratory method for analyzing changes in polygon distributions. Changes are deduced from a set of polygon distributions of different times, and represented by a directed graph. Three viewpoints for representing individual changes are proposed: topology, size, and direction. They are described qualitatively, and used for exploratory analysis of spatiotemporal distribution of changes. In addition to individual changes, their sequences are analyzed through classification, visualization, and calculation of summary statistics. The method proposed is applied to the analysis of changes in market areas of a convenience-store chain in Tokyo, Japan. The empirical study reveals the spatial structure of changes in a global scale.