Clustering with qualitative information

Abstract

We consider the problem of clustering a collection of elements based on pairwise judgments of similarity and dissimilarity. Bansal et al. (in: Proceedings of 43rd FOCS, 2002, pp. 238-247) cast the problem thus: given a graph G whose edges are labeled "+" (similar) or "-" (dissimilar), partition the vertices into clusters so that the number of pairs correctly (resp., incorrectly) classified with respect to the input labeling is maximized (resp., minimized). It is worthwhile studying both complete graphs, in which every edge is labeled, and general graphs, in which some input edges might not have labels. We answer several questions left open by Bansal et al. (2002) and provide a sound overview..