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

Multivariate Behavioral Research
L M Collins, C W Dent

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.

References

Jan 1, 1983·IEEE Transactions on Pattern Analysis and Machine Intelligence·G W MilliganL M Sokol
Jan 1, 1985·Multivariate Behavioral Research·G W Milligan, D A Schilling
Oct 1, 1986·Multivariate Behavioral Research·G W Milligan, M C Cooper

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Citations

Oct 10, 2001·Behavior Research Methods, Instruments, & Computers : a Journal of the Psychonomic Society, Inc·B Thomann
Dec 21, 2007·International Journal of Aging & Human Development·Ruby R Brougham, David A Walsh
Sep 16, 2005·International Journal of Aging & Human Development·Ruby R Brougham, David A Walsh
Jun 28, 2017·Journal of Medical Imaging·Malay SinghHwee Kuan Lee
Jan 1, 2012·ISRN Bioinformatics·Lingling An, R W Doerge
Jun 14, 2019·Scientific Reports·Alexander J GatesYong-Yeol Ahn
Aug 11, 2018·Scientific Reports·Ayan SinhaKarthik Ramani
Dec 25, 2019·Physical Review. E·Joaquín CalatayudMartin Rosvall
Jan 15, 2020··Luca RossiObaida Hanteer

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