Analysis of spatial point patterns using bundles of product density LISA functions

The analysis of a spatial point pattern is often in volved with looking for spatial structure, such as clustering or regularity in the points (or events). For example, it is of biological interest to characterize the pattern of tree locations in a forest. This has traditionally been done using global summaries, such as the K-function or its differential, the product density function. In this article, we define a local version of the product density function for each event, derived under a definition of a local indicator of spatial association (LISA). These product density LISA functions can then be grouped into bundles of similar functions using multivariate hierarchical clustering techniques. The bundles can then be visualized by a replotting of the data, obtained via classical multidimensional scaling of the statistical distances between functions. Thus, we propose a different way of looking for structure based on how an event relates to nearby events. We apply this method to a point pattern of pine saplings in a Finnish forest and show remarkable, heretofore undiscovered, spatial structure in the data.