Subset Partitioning via Anticlustering

The method of anticlustering partitions a pool of elements into groups (i.e., anticlusters) with the goal of maximizing between-group similarity or within-group heterogeneity. The anticlustering approach thereby reverses the logic of cluster analysis that strives for high within-group homogeneity and low similarity of the different groups. Computationally, anticlustering is accomplished by maximizing instead of minimizing a clustering objective function, such as the intra-cluster variance (used in k-means clustering) or the sum of pairwise distances within clusters. The function anticlustering() implements exact and heuristic anticlustering algorithms as described in Papenberg and Klau (2021; ). The exact algorithms require that the GNU linear programming kit (< https://www.gnu.org/software/glpk/glpk.html>) is available and the R package 'Rglpk' (< https://cran.R-project.org/package=Rglpk>) is installed. A bicriterion anticlustering method proposed by Brusco et al. (2020; ) is available through the function bicriterion_anticlustering(). Some other functions are available to solve classical clustering problems. The function balanced_clustering() applies a cluster analysis under size constraints, i.e., creates equal-sized clusters. The function matching() can be used for (unrestricted, bipartite, or K-partite) matching. The function wce() can be used optimally solve the (weighted) cluster editing problem, also known as correlation clustering, clique partitioning problem or transitivity clustering.