Generalized Adjusted Rand Indices for cluster ensembles

Authors:
Shaohong Zhang;Hau-San Wong;Ying Shen
Affiliations:
Department of Computer Science, City University of Hong Kong, Tat Chee Avenue, Hong Kong, PR China;Department of Computer Science, City University of Hong Kong, Tat Chee Avenue, Hong Kong, PR China;Department of Computer Science, City University of Hong Kong, Tat Chee Avenue, Hong Kong, PR China
Venue:
Pattern Recognition
Year:
2012

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Abstract

In this paper, Adjusted Rand Index (ARI) is generalized to two new measures based on matrix comparison: (i) Adjusted Rand Index between a similarity matrix and a cluster partition (ARImp), to evaluate the consistency of a set of clustering solutions with their corresponding consensus matrix in a cluster ensemble, and (ii) Adjusted Rand Index between similarity matrices (ARImm), to evaluate the consistency between two similarity matrices. Desirable properties of ARI are preserved in the two new measures, and new properties are discussed. These properties include: (i) detection of uncorrelatedness; (ii) computation of ARImp/ARImm in a distributed environment; and (iii) characterization of the degree of uncertainty of a consensus matrix. All of these properties are investigated from both the perspectives of theoretical analysis and experimental validation. We have also performed a number of experiments to show the usefulness and effectiveness of the two proposed measures in practical applications.