Reduction of Search Space for the Mean Partition Problem

Abstract

The contributions of this paper are threefold. First, it conducts a formal comparison of the primary approaches to consensus clustering, using the concepts of agreement and consent. Secondly, it presents theoretical evidence justifying the preference for mean-based methods, which rely on consent, over other agreement-based procedural methods like the q-rule, which are now mostly used as quality evaluators in practice. Thirdly, the paper computes the exact reduction achieved by criteria available in existing literature to assess the quality of mean-based consensus solutions and reduce the search space’s size. Finally, it compiles the regions where consensus functions associated with well-known dissimilarity measures, such as the Mirkin metric and Variation of Information, accumulate their consensus solutions.