A multi-objective clustering approach based on different clustering measures combinations

Abstract

Clustering methods aim to categorize the elements of a dataset into groups according to the similarities and dissimilarities of the elements. This paper proposes the Multi-objective Clustering Algorithm (MCA), which combines clustering methods with the Nondominated Sorting Genetic Algorithm II. In this way, the proposed algorithm can automatically define the optimal number of clusters and partition the elements based on clustering measures. For this, 6 intra-clustering and 7 inter-clustering measures are explored, combining them 2-to-2, to define the most appropriate pair of measures to be used in a bi-objective approach. Out of the 42 possible combinations, 6 of them were considered the most appropriate, since they showed an explicitly conflicting behavior among the measures. The results of these 6 Pareto fronts were combined into two Pareto fronts, according to the measure of intra-clustering that the combination has in common. The elements of these Pareto fronts were analyzed in terms of dominance, so the nondominanted ones were kept, generating a hybrid Pareto front composed of solutions provided by different combinations of measures. The presented approach was validated on three benchmark datasets and also on a real dataset. The results were satisfactory since the proposed algorithm could estimate the optimal number of clusters and suitable dataset partitions. The obtained results were compared with the classical k-means and DBSCAN algorithms, and also two hybrid approaches, the Clustering Differential Evolution, and the Game-Based k-means algorithms. The MCA results demonstrated that they are competitive, mainly for the advancement of providing a set of optimum solutions for the decision-maker.