Multi-Objective Differential Evolution for Automatic Clustering with Application to Micro-Array Data Analysis

Abstract

This paper applies the Differential Evolution (DE) algorithm to the task of automatic fuzzy clustering in a Multi-objective Optimization (MO) framework. It compares the performances of two multi-objective variants of DE over the fuzzy clustering problem, where two conflicting fuzzy validity indices are simultaneously optimized. The resultant Pareto optimal set of solutions from each algorithm consists of a number of non-dominated solutions, from which the user can choose the most promising ones according to the problem specifications. A real-coded representation of the search variables, accommodating variable number of cluster centers, is used for DE. The performances of the multi-objective DE-variants have also been contrasted to that of two most well-known schemes of MO clustering, namely the Non Dominated Sorting Genetic Algorithm (NSGA II) and Multi-Objective Clustering with an unknown number of Clusters K (MOCK). Experimental results using six artificial and four real life datasets of varying range of complexities indicate that DE holds immense promise as a candidate algorithm for devising MO clustering schemes.

Keywords

• differential evolution
• multi-objective optimization
• fuzzy clustering
• micro-array data clustering