A test for spatial homogeneity in cluster analysis

This paper proposes a measure of spatial homogeneity for sets of d-dimensional points based on nearest neighbor distances. Tests for spatial uniformity are examined which assess the tendency of the entire data set to aggregate and evaluate the character of individual clusters. The sizes and powers of three statistical tests of uniformity against aggregation, regularity, and unimodality are studied to determine robustness. The paper also studies the effects of normalization and incorrect prior information. A percentile frame sampling procedure is proposed that does not require a sampling window but is superior to a toroidal frame and to buffer zone sampling in particular situations. Examples test two data sets for homogeneity and search the results of a hierarchical clustering for homogeneous clusters.This work was partially supported by NSF Grant ECS-8300204.