On the Interaction Between Distance Functions and Clustering Criteria in Multi-objective Clustering

Abstract

Multi-criterion algorithms for clustering have gained some traction due to their ability to cater to a diverse range of cluster properties. Here, we investigate the interaction between the clustering criteria employed in a multi-objective algorithm and the distance functions on which these criteria operate. We do so by contrasting the multi-criterion evolutionary algorithm Δ -MOCK with a bi-objective version of the evolutionary multi-view clustering approach MVMC, which uses a single clustering criterion but can incorporate multiple dissimilarity matrices. Using a benchmark suite representing a diverse range of cluster properties, we illustrate that comparable results to Δ -MOCK can be achieved using MVMC with two complementary distance functions. We then establish the mathematical equivalence of Δ -MOCK’s connectivity objective to a compactness criterion operating on a redefined distance function. We conclude by discussing the implications of our findings for future work on the representation of clusters in multi-objective evolutionary clustering.