Robust Fuzzy Clustering as a Multi-Objective Optimization Procedure

In this paper, a multi-objective genetic algorithm for data clustering based on the robust fuzzy least trimmed squares estimator is proposed. The clustering methodology addresses two critical issues in unsupervised data clustering - the ability to produce meaningful classification in noisy data, and the requirement that the number of clusters be known a priori. The GA-driven clustering routine optimizes number of clusters as well as cluster assignment, and cluster prototypes. A two-parameter, mapped, fixed point coding scheme is used to represent assignment of data into either the true retained set and the noisy trimmed set, and the optimal number of clusters in the retained set A three-objective criterion is used as the minimization functional for the GA. Results on well-known data sets from literature suggest that the proposed methodology is comparable (in many cases superior) to conventional robust fuzzy clustering algorithms that assume a known value for optimal number of clusters.