TY - JOUR
T1 - Omega
T2 - A General Formulation of the Rand Index of Cluster Recovery Suitable for Non-disjoint Solutions
AU - Collins, Linda M.
AU - Dent, Clyde W.
N1 - Funding Information:
This research was supported by grant BNS8403126 from the National Science Foundation and by grant ROlDA3673 from the National Institute on Drug Abuse. Requests for reprints should be sent to Linda M.C ollins, Department of Psychology, University of Southern California, Los Angeles, CA 90089-1061.
PY - 1988/4
Y1 - 1988/4
N2 - 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.
AB - 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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U2 - 10.1207/s15327906mbr2302_6
DO - 10.1207/s15327906mbr2302_6
M3 - Article
AN - SCOPUS:84885969802
SN - 0027-3171
VL - 23
SP - 231
EP - 242
JO - Multivariate Behavioral Research
JF - Multivariate Behavioral Research
IS - 2
ER -