Optimization inspired by water waves applied to non-hierarchical grouping of objects

Abstract

Characterized as one of the strategies related to exploratory data analysis, a non-hierarchical grouping method consists of a procedure able to classify a collection of objects into a finite subset of groups or classes, such that objects belonging to a group are more similar to each other than objects comprised by a distinct group. In this circumstance, this study proposes the application of a meta-heuristic inspired by the behavior of water waves, to the determination of the non-hierarchical grouping of objects, and compares the results obtained by this method with the responses achieved by six other grouping strategies. Specifically, the squared errors obtained by the suggested algorithm, when classifying 29 benchmark collections were, through the Wilcoxon signed-rank test, compared with the results obtained by the meta-heuristics particle swarm, genetic algorithm, artificial bee colony and simulated annealing, and with the responses determined by the \textit{K-means} algorithm and by a variation of the meta-heuristic inspired by the water waves that included a decay operator, indicating that, in some circumstances, the proposed algorithm was able to obtain more congruent classifications than those established by other partitioning methods.