Cluster tests for geographical areas with binary data
Consider an area subdivided into non-overlapping districts, e.g. a state divided into counties, and assume that some districts are marked for having some distinguishing property. Then the question arises whether the marked districts are distributed randomly or exhibit some spatial clustering. This question is pursued here to some extent theoretically, in particular using regular tesselations of the plane (hexagons in a honeycomb), and to some extent by simulations using these regular constellations as well as real situations, in particular 171 counties in six Bundeslnder of Germany. Connectivity regions (maximal regions of marked districts) turn out to be a bad choice in general. Instead, clusters are formed from triplets of marked districts. Approximate statistical tests are developed. They are simple enough to be used for data mining where potentially a large number of tests has to be performed.
spatial clusters data mining tests on clustering binary area data