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Random models for adjusting fuzzy rand index extensions

Author

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  • Ryan DeWolfe

    (University of British Columbia—Okanagan Campus)

  • Jeffrey L. Andrews

    (University of British Columbia—Okanagan Campus)

Abstract

The adjusted Rand index (ARI) is a widely used method for comparing hard clusterings, but requires a choice of random model that is often left implicit. Several recent works have extended the Rand index to fuzzy clusterings and adjusted for chance agreement with the permutation model, but the assumptions of this random model are difficult to justify for fuzzy clusterings. Previous work on random models for hard clusterings has shown that different random models can impact similarity rankings, so matching the assumptions of the random model to the algorithm is essential. We propose a single framework computing the ARI with three new random models that are intuitive and explainable for both hard and fuzzy clusterings. The theory and assumptions of the proposed models are contrasted with the existing permutation model, and computations on synthetic and benchmark data show that each model has distinct behaviour, meaning accurate model selection is important for the reliability of results.

Suggested Citation

  • Ryan DeWolfe & Jeffrey L. Andrews, 2025. "Random models for adjusting fuzzy rand index extensions," 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. 19(2), pages 361-385, June.
    • Handle: RePEc:spr:advdac:v:19:y:2025:i:2:d:10.1007_s11634-025-00625-w
    DOI: 10.1007/s11634-025-00625-w
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