Omega: A General Formulation of the Rand Index of Cluster Recovery Suitable for Non-disjoint Solutions

1988/04/01 by Linda M. Collins, Clyde W. Dent · 158 citations
Agricultural and Biological Sciences · Computer Science · Mathematics · Physics and Astronomy · #Advanced Clustering Algorithms Research #Artificial intelligence #Cluster (spacecraft) #Cluster analysis #Combinatorics #Complex Network Analysis Techniques #Computer science #Disjoint sets #Economics #Generalization #Index (typography) #Mathematics #Omega #Philosophy #Rand corporation #Rand index #Sensory Analysis and Statistical Methods #World Wide Web

paper · doi:10.1207/s15327906mbr2302_6

published in Multivariate Behavioral Research 23(2), 231-242 (Taylor & Francis)

openalex publication_date 1988/04/01 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/29

Abstract

Cluster recovery indices are more important than ever, because of the necessity for comparing the large number of clustering procedures available today. Of the cluster recovery indices prominent in contemporary literature, the Hubert and Arabie (1985) adjustment to the Rand index (1971) has been demonstrated to have the most desirable properties (Milligan & Cooper, 1986). However, use of the Hubert and Arabie adjustment to the Rand index is limited to cluster solutions involving non-overlapping, or disjoint, clusters. The present paper introduces a generalization of the Hubert and Arabie adjusted Rand index. This generalization, called the Omega index, can be applied to situations where both, one, or neither of the solutions being compared is non-disjoint. In the special case where both solutions are disjoint, the Omega index is equivalent to the Hubert and Arabie adjusted Rand index.

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