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On Assessments of Agreement Between Fuzzy Partitions

Author

Listed:
  • Jeffrey L. Andrews

    (University of British Columbia – Okanagan Campus)

  • Ryan Browne

    (University of Waterloo)

  • Chelsey D. Hvingelby

    (University of British Columbia – Okanagan Campus)

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.

Suggested Citation

  • Jeffrey L. Andrews & Ryan Browne & Chelsey D. Hvingelby, 2022. "On Assessments of Agreement Between Fuzzy Partitions," Journal of Classification, Springer;The Classification Society, vol. 39(2), pages 326-342, July.
    • Handle: RePEc:spr:jclass:v:39:y:2022:i:2:d:10.1007_s00357-021-09407-3
    DOI: 10.1007/s00357-021-09407-3
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    References listed on IDEAS

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    1. Abby Flynt & Nema Dean & Rebecca Nugent, 2019. "sARI: a soft agreement measure for class partitions incorporating assignment probabilities," Advances in Data Analysis and Classification, Springer;German Classification Society - Gesellschaft für Klassifikation (GfKl);Japanese Classification Society (JCS);Classification and Data Analysis Group of the Italian Statistical Society (CLADAG);International Federation of Classification Societies (IFCS), vol. 13(1), pages 303-323, March.
    2. Lawrence Hubert & Phipps Arabie, 1985. "Comparing partitions," Journal of Classification, Springer;The Classification Society, vol. 2(1), pages 193-218, December.
    3. Stephen Johnson, 1967. "Hierarchical clustering schemes," Psychometrika, Springer;The Psychometric Society, vol. 32(3), pages 241-254, September.
    4. Ahmed N. Albatineh & Magdalena Niewiadomska-Bugaj & Daniel Mihalko, 2006. "On Similarity Indices and Correction for Chance Agreement," Journal of Classification, Springer;The Classification Society, vol. 23(2), pages 301-313, September.
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