Bicriterion methods for partitioning dissimilarity matrices

Partitioning indices associated with the within‐cluster sums of pairwise dissimilarities often exhibit a systematic bias towards clusters of a particular size, whereas minimization of the partition diameter (i.e. the maximum dissimilarity element across all pairs of objects within the same cluster) does not typically have this problem. However, when the partition‐diameter criterion is used, there is often a myriad of alternative optimal solutions that can vary significantly with respect to their substantive interpretation. We propose a bicriterion partitioning approach that considers both diameter and within‐cluster sums in the optimization problem and facilitates selection from among the alternative optima. We developed several MATLAB‐based exchange algorithms that rapidly provide excellent solutions to bicriterion partitioning problems. These algorithms were evaluated using synthetic data sets, as well as an empirical dissimilarity matrix.