The Dirichiet Tessellation as an Aid in Data Analysis

The Dirichlet tessellation is a subdivision of the plane generated by a finite set of distinct points; each point acquires a tile comprising that part of the plane nearer to it than to any of the other points. The definition extends to any number of dimensions, but the planar case is the first nontrivial one; a very efficient algorithm for computing the tessellation in this case has recently been developed by Green & Sibson (1978), and is outlined here. The tessellation construction has many applications in statistics and data analysis. Statistical applications range from its use as a computational technique in distance-based methods of point pattern analysis, through the use of tessellation statistics such as tile areas or contiguity lengths, to the investigation of tessellation-based models for, among other things, spread of infection on an irregular lattice and planar immigration/death processes. Data-analytic appli- cations include interpolation over the plane, contiguity-based scaling methods, and planar cluster analysis.