Random models for adjusting fuzzy rand index extensions

Ryan DeWolfe () and Jeffrey L. Andrews
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Ryan DeWolfe: University of British Columbia—Okanagan Campus
Jeffrey L. Andrews: University of British Columbia—Okanagan Campus

Advances in Data Analysis and Classification, 2025, vol. 19, issue 2, No 4, 385 pages

Abstract: 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.

Keywords: Clustering comparison; Adjustment for chance; Fuzzy clustering; Adjusted Rand index; Dirichlet distribution; 62H30; 62H86 (search for similar items in EconPapers)
Date: 2025
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DOI: 10.1007/s11634-025-00625-w

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