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HIERARCHICAL CLUSTERING AND THE CONCEPT OF SPACE DISTORTION
Author(s) -
Hubert Lawrence,
Schultz James
Publication year - 1975
Publication title -
british journal of mathematical and statistical psychology
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 3.157
H-Index - 51
eISSN - 2044-8317
pISSN - 0007-1102
DOI - 10.1111/j.2044-8317.1975.tb00556.x
Subject(s) - cluster analysis , distortion (music) , link (geometry) , mathematics , preprocessor , algorithm , hierarchical clustering , space (punctuation) , set (abstract data type) , metric (unit) , metric space , monte carlo method , computer science , discrete mathematics , combinatorics , artificial intelligence , statistics , amplifier , computer network , operations management , bandwidth (computing) , economics , programming language , operating system
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.