A collaborative multi-objective approach for clustering task based on distance measures and clustering validity indices

Abstract

Clustering algorithm has the task of classifying a set of elements so that the elements within the same group are as similar as possible and, in the same way, that the elements of different groups (clusters) are as different as possible. This paper presents the Multi-objective Clustering Algorithm (MCA) combined with the NSGA-II, based on two intra- and three inter-clustering measures, combined 2-to-2, to define the optimal number of clusters and classify the elements among these clusters. As the NSGA-II is a multi-objective algorithm, the results are presented as a Pareto front in terms of the two measures considered in the objective functions. Moreover, a procedure named Cluster Collaborative Indices Procedure (CCIP) is proposed, which aims to analyze and compare the Pareto front solutions generated by different criteria (Elbow, Davies-Bouldin, Calinski-Harabasz, CS, and Dumn indices) in a collaborative way. The most appropriate solution is suggested for the decision-maker to support their final choice, considering all solutions provided by the measured combination. The methodology was tested in a benchmark dataset and also in a real dataset, and in both cases, the results were satisfactory to define the optimal number of clusters and to classify the elements of the dataset.