Descriptive Measures of Point Distributions Summarized with Respect to Spatial Scale in Visualization

Abstract

Visual exploration plays a critical role in point pattern analysis. It permits analysts to grasp a wide variety of spatial patterns in point distributions that are not necessarily detectable by mathematical and statistical methods. Since spatial patterns are scale-dependent, grid and kernel density maps are effective in analysis that can visualize point distributions at various scales from small to large. Visual exploration of these maps, however, takes a considerable amount of time even if the maps are generated automatically in GIS software. In addition, visual exploration inevitably becomes subjective and unstable when treating numerous maps simultaneously. It is not easy to evaluate and memorize spatial patterns in maps in a consistent and objective way. To resolve the problem, this article proposes new quantitative measures summarizing the characteristics of point distributions. The measures can be visualized as maps that help analysts to capture the overall spatial pattern of point distributions efficiently. Numerical experiments and applications to real data analysis are performed to test the validity of the proposed measures. The results reveal the effectiveness of the measures, as well as their shortcomings, to be resolved in future research.