Finding spatial clusters

Abstract

The special challenge in analysing geographical data comes from the spatial distribution of the objects. We are interested here in finding out whether a given property is randomly distributed or concentrated somewhere. More exactly: consider a two-dimensional region subdivided into non-overlapping fields, e.g. a state divided into counties, and assume that some fields are marked for having a distinguishing property. Do the marked fields exhibit some spatial clustering? Two tests feasible in data mining situations are proposed here, based on the number fields in clusters (defined by means of triplets, i. e. essentially three marked fields with a common boundary point) and on the number of edges of marked fields shared by another marked field. For regular settings such as honeycombs (sets of hexagons) some theoretical results are reported. In addition, simulations have been performed on honeycombs as well as on real subdivisions of a region and the tests have been applied to real data.