Spatio-Temporal Nearest Neighbor Index for Measuring Space-Time Clustering among Geographic Events

Abstract Extended from the spatially defined nearest neighbor index, the nearest neighbor index measures the levels of spatiotemporal clustering of a set of points, using only their spatial locations and the time associated with each point. The extended index is particularly suitable to use when there is no attribute information associated with geographic events except for locations and times when events occurred. In addition, it allows users to assess and visualize spatiotemporally distributed geographic events and to test if the events are more (or less) spatiotemporally clustered than would be expected by random chances. As a demonstration, this index was applied to crime and health data sets to demonstrate its usefulness. This article details the mathematical steps that formulate the extension. The calculation of the index values is fast and efficient with mathematical equations presented in the article.