HIERARCHICAL CLUSTERING AND THE CONCEPT OF SPACE DISTORTION

Abstract

Using an occupancy model developed from combinatorics, the prototypic single‐link and complete‐link hierarchical clustering methods are considered to be at the two extremes of a space distortion clustering continuum. Two approaches for attacking the space distortion problem are suggested: (i) using an intermediate r ‐diameter criterion that includes the single‐link and complete‐link methods as special cases, and (ii) preprocessing the original proximity measures to force a metric structure on the input data that will lead to a better correspondence between the results produced by the two extreme clustering strategies. In addition to several numerical examples that typify the effect of using an r ‐diameter criterion or, alternatively, an initial preprocessing of a given set of proximity measures, Monte Carlo results are presented illustrating empirically the space distortion properties of the single‐link and complete‐link methods.