Journal of Classification

, Volume 2, Issue 1, pp 193–218

Comparing partitions

Authors

  • Lawrence Hubert
    • Graduate School of EducationThe University of California
  • Phipps Arabie
    • Department of PsychologyUniversity of Illinois
Authors Of Articles

DOI: 10.1007/BF01908075

Cite this article as:
Hubert, L. & Arabie, P. Journal of Classification (1985) 2: 193. doi:10.1007/BF01908075

Abstract

The problem of comparing two different partitions of a finite set of objects reappears continually in the clustering literature. We begin by reviewing a well-known measure of partition correspondence often attributed to Rand (1971), discuss the issue of correcting this index for chance, and note that a recent normalization strategy developed by Morey and Agresti (1984) and adopted by others (e.g., Miligan and Cooper 1985) is based on an incorrect assumption. Then, the general problem of comparing partitions is approached indirectly by assessing the congruence of two proximity matrices using a simple cross-product measure. They are generated from corresponding partitions using various scoring rules. Special cases derivable include traditionally familiar statistics and/or ones tailored to weight certain object pairs differentially. Finally, we propose a measure based on the comparison of object triples having the advantage of a probabilistic interpretation in addition to being corrected for chance (i.e., assuming a constant value under a reasonable null hypothesis) and bounded between ±1.

Keywords

Measures of agreementMeasures of associationConsensus indices

Copyright information

© Springer-Verlag New York Inc 1985