Identifying clusters in spatial area data

Abstract

A task peculiar to spatial data is to find spatial clusters. Three alternative tests will be given here for the case that a region is divided into a number of districts and each district is assigned a numerical value, i. e. the value for a variable of interest. A cluster of districts with high (or low) values cannot just be based on the adjacency of districts since then a random assignment would already produce too many and too large clusters. Thus the cluster definition is based on district triplets, essentially three districts meeting at a common corner. Two tests are designed for a division of the area into marked and unmarked districts. The third, more elaborate test uses the given values directly.