analiza aiqbench
This paper provides a rigorous analytical framework that unifies pair-counting and information-theoretic clustering similarity measures by framing them as weighted expansions of co-occurrences. It demonstrates that pair-counting acts as a low-order quadratic approximation while information-theoretic metrics capture higher-order frequency structures, offering a principled basis for selecting appropriate evaluation metrics. For practitioners evaluating unsupervised models, this work clarifies the theoretical conditions under which different similarity regimes diverge, enabling more consistent and interpretable benchmarking.
Unifying Information-Theoretic and Pair-Counting Clustering Similarity
arXiv:2511.03000v2 Announce Type: replace-cross Abstract: Comparing clusterings is central to evaluating unsupervised models, yet the many existing similarity measures can produce widely divergent, sometimes contradictory, evaluations. Clustering similarity measures are typically organized into two principal families, pair-counting and information-theoretic, reflecting whether they quantify agreement through element pairs or aggregate information across full cluster contingency tables. Prior work has uncovered parallels between these families and applied empirical normalization or chance-correction schemes, but their deeper analytical connection remains only partially understood. Here, we develop an analytical framework that unifies these families through two complementary perspectives. First, both families are expressed as weighted expansions of observed versus expected co-occurrences, with pair-counting arising as a quadratic, low-order approximation and information-theoretic measures as higher-order, frequency-weighted extensions. Second, we generalize pair-counting to k-tuple agreement and show that information-theoretic measures can be viewed as systematically accumulating higher-order co-assignment structure beyond the pairwise level. We illustrate the approaches analytically for the Rand index and Mutual Information, and show how other indices in each family emerge as natural extensions. Together, these views clarify when and why the two regimes diverge, relating their sensitivities directly to weighting and approximation order, and provide a principled basis for selecting, interpreting, and extending clustering similarity measures across applications.
Abstract:Comparing clusterings is central to evaluating unsupervised models, yet the many existing similarity measures can produce widely divergent, sometimes contradictory, evaluations. Clustering similarity measures are typically organized into two principal families, pair-counting and information-theoretic, reflecting whether they quantify agreement through element pairs or aggregate information across full cluster contingency tables. Prior work has uncovered parallels between these families and applied empirical normalization or chance-correction schemes, but their deeper analytical connection remains only partially understood. Here, we develop an analytical framework that unifies these families through two complementary perspectives. First, both families are expressed as weighted expansions of observed versus expected co-occurrences, with pair-counting arising as a quadratic, low-order approximation and information-theoretic measures as higher-order, frequency-weighted extensions. Second, we generalize pair-counting to k-tuple agreement and show that information-theoretic measures can be viewed as systematically accumulating higher-order co-assignment structure beyond the pairwise level. We illustrate the approaches analytically for the Rand index and Mutual Information, and show how other indices in each family emerge as natural extensions. Together, these views clarify when and why the two regimes diverge, relating their sensitivities directly to weighting and approximation order, and provide a principled basis for selecting, interpreting, and extending clustering similarity measures across applications.
Machine Learning (stat.ML); Information Theory (cs.IT); Machine Learning (cs.LG)
arXiv:2511.03000 [stat.ML]
(or arXiv:2511.03000v2 [stat.ML] for this version)
https://doi.org/10.48550/arXiv.2511.03000 Focus to learn more arXiv-issued DOI via DataCite
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