  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.
