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On the Equivalence of Cohen’s Kappa and the Hubert-Arabie Adjusted Rand Index

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Abstract

It is shown that one can calculate the Hubert-Arabie adjusted Rand index by first forming the fourfold contingency table counting the number of pairs of objects that were placed in the same cluster in both partitions, in the same cluster in one partition but in different clusters in the other partition, and in different clusters in both, and then computing Cohen’s κ on this fourfold table.

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References

  • ALBATINEH, A.N., NIEWIADOMSKA-BUGAJ, M., and MIHALKO, D. (2006), “On Similarity Indices and Correction for Chance Agreement,” Journal of Classification, 23, 301–313.

    Article  MathSciNet  Google Scholar 

  • BATAGELJ, V., and BREN, M. (1995), “Comparing Resemblance Measures,” Journal of Classification, 12, 73–90.

    Article  MATH  MathSciNet  Google Scholar 

  • BAULIEU, F.B. (1989), “A Classification of Presence/Absence Based Dissimilarity Coefficients,” Journal of Classification, 6, 233–246.

    Article  MATH  MathSciNet  Google Scholar 

  • COHEN, J. (1960), “A Coefficient of Agreement for Nominal Scales,” Educational and Psychological Measurement, 20, 37–46.

    Article  Google Scholar 

  • FOWLKES, E.B., and MALLOWS, C. L. (1983), “A Method for Comparing Two Hierarchical Clusterings,” Journal of the American Statistical Association, 78, 553–569.

    Article  MATH  Google Scholar 

  • GOWER, J.C., and LEGENDRE, P. (1986), “Metric and Euclidean Properties of Dissimilarity Coefficients,” Journal of Classification, 3, 5–48.

    Article  MATH  MathSciNet  Google Scholar 

  • HUBERT, L.J., and ARABIE, P. (1985), “Comparing Partitions,” Journal of Classification, 2, 193–218.

    Article  Google Scholar 

  • RAND, W.M. (1971), “Objective Criteria for the Evaluation of Clustering Methods,” Journal of the American Statistical Association, 66, 846–850.

    Article  Google Scholar 

  • SALTSTONE, R., and STANGE, K. (1996), “A Computer Program to Calculate Hubert and Arabie’s Adjusted Rand Index,” Journal of Classification, 13, 169–172.

    Article  Google Scholar 

  • SOKAL, R.R., and MICHENER, C.D. (1958), “A Statistical Method for Evaluating Systematic Relationships,” University of Kansas Science Bulletin, 38, 1409–1438.

    Google Scholar 

  • STEINLEY, D. (2004), “Properties of the Hubert-Arabie Adjusted Rand Index,” Psychological Methods, 9, 386–396.

    Article  Google Scholar 

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Authors and Affiliations

  1. Psychometrics and Research Methodology Group, Leiden University, Institute for Psychological Research, Leiden University, Wassenaarseweg 52, P.O. Box 9555, 2300 RB, Leiden, The Netherlands

    Matthijs J. Warrens

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  1. Matthijs J. Warrens
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Correspondence to Matthijs J. Warrens.

Additional information

The author thanks Willem Heiser, Mark de Rooij, Marian Hickendorff and three anonymous reviewers for their helpful comments and valuable suggestions on earlier versions of this article.

Published online xx, xx, xxxx.

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Warrens, M.J. On the Equivalence of Cohen’s Kappa and the Hubert-Arabie Adjusted Rand Index. J Classif 25, 177–183 (2008). https://doi.org/10.1007/s00357-008-9023-7

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