Comparing partitions View Full Text


Ontology type: schema:ScholarlyArticle     


Article Info

DATE

1985-12

AUTHORS

Lawrence Hubert, Phipps Arabie

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. More... »

PAGES

193-218

Journal

TITLE

Journal of Classification

ISSUE

1

VOLUME

2

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    DOI

    http://dx.doi.org/10.1007/bf01908075

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