Extending the Bicriterion Approach for Anticlustering: Exact and Hybrid Approaches
Martin Papenberg, Martin Breuer, Max Diekhoff, Nguyen K Tran, Gunnar W Klau
TL;DR
This paper improves anticlustering methods by combining exact algorithms with heuristics to achieve better data partitioning in psychology research.
Contribution
The paper introduces a hybrid anticlustering approach combining exact dispersion optimization with diversity heuristics.
Findings
A new exact algorithm for maximum dispersion scales well with large datasets.
BILS-Hybrid-All outperformed other methods in simulation and application tests.
Hybrid approaches maintain optimal dispersion while improving diversity.
Abstract
Numerous applications in psychological research require that a data set is partitioned via the inverse of a clustering criterion. This anticlustering seeks for high similarity between groups (maximum diversity) or high pairwise dissimilarity within groups (maximum dispersion). Brusco et al. (2020) proposed a bicriterion heuristic (BILS) that simultaneously seeks for maximum diversity and dispersion, introducing the bicriterion approach for anticlustering. We investigate if the bicriterion approach can be improved using exact algorithms that guarantee globally optimal criterion values. Despite the theoretical computational intractability of anticlustering, we present a new exact algorithm for maximum dispersion that scales to quite large data sets ( ). However, a fully exact bicriterion approach was only feasible for small data sets (about ). We therefore developed hybrid approaches…
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Taxonomy
TopicsChemistry and Chemical Engineering