A Distributional Approach for Soft Clustering Comparison and Evaluation

The development of external evaluation criteria for soft clustering (SC) has received limited attention: existing methods do not provide a general approach to extend comparison measures to SC, and are unable to account for the uncertainty represented in the results of SC algorithms. In this article, we propose a general method to address these limitations, grounding on a novel interpretation of SC as distributions over hard clusterings, which we call \emph{distributional measures}. We provide an in-depth study of complexity- and metric-theoretic properties of the proposed approach, and we describe approximation techniques that can make the calculations tractable. Finally, we illustrate our approach through a simple but illustrative experiment.
Comment: This is the extended version of article "A Distributional Approach for Soft Clustering Comparison and Evaluation", accepted at BELIEF 2022 (http://hebergement.universite-paris-saclay.fr/belief2022/). Please cite the proceedings version of the article