An analysis of the admissibility of the objective functions applied in evolutionary multi-objective clustering

Abstract

A variety of clustering criteria have been applied as an objective function in Evolutionary Multi-Objective Clustering approaches (EMOCs). However, most EMOCs do not provide detailed analysis regarding the choice and usage of the objective functions. In general, the choice of the objective functions only considers the desired clustering properties, and most EMOCs present in the literature do not consider aspects of multi-objective optimization, such as the search direction, in their design. Aiming to support a better choice and definition of the objectives in the EMOCs, this paper proposes an analysis of the clustering criteria admissibility to examine the search direction and evaluate their potential in finding optimal results. We consider the fundamentals of the evaluation of a heuristic function to analyze the clustering criteria and demonstrate how they can influence the optimization. As a result, this study provides a detailed analysis of the main objective functions found in the literature and evaluates how the initialization interferes with their admissibility. Also, we highlight some common practices and issues found in some established EMOCs. Furthermore, we provide insights regarding how to combine and use the clustering criteria in the EMOCs.