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On Assessments of Agreement Between Fuzzy Partitions

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Abstract

We extend the literature regarding assessments of agreement between soft/fuzzy/probabilistic cluster allocations by providing closed-form approaches for two measures which behave as fuzzy generalizations of the popular adjusted Rand index (ARI): one novel and one previously requiring a Monte Carlo estimation process. Both of these measures retain the reflexive property of the ARI—an arguably essential property for the interpretability of a cluster agreement measure—and both are feasible in their closed-form for sample sizes ranging into five digits or more using standard consumer computers. We describe the approximate computational complexity in each case, and apply both measures in simulated and real data contexts.

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Acknowledgements

This research was supported by the Natural Sciences and Engineering Research Council of Canada through their Discovery Grants program (RGPIN-2018-04444 for Browne and RGPIN-2020-04646 for Andrews). Infrastructure support was provided by the Canada Foundation for Innovation through the John Evans Leaders Fund (Andrews, #35578).

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Authors and Affiliations

  1. Department of Statistics, University of British Columbia – Okanagan Campus, Kelowna, BC, Canada

    Jeffrey L. Andrews & Chelsey D. Hvingelby

  2. Department of Statistics and Actuarial Science, University of Waterloo, Waterloo, ON, Canada

    Ryan Browne

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  1. Jeffrey L. Andrews
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  3. Chelsey D. Hvingelby
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Correspondence to Jeffrey L. Andrews.

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Andrews, J.L., Browne, R. & Hvingelby, C.D. On Assessments of Agreement Between Fuzzy Partitions. J Classif 39, 326–342 (2022). https://doi.org/10.1007/s00357-021-09407-3

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