A Genetic Algorithm Implementation of the Fuzzy Least Trimmed Squares Clustering

Abstract

This paper describes a new approach to finding a global solution for the fuzzy least trimmed squares clustering. The least trimmed squares (LTS) estimator is known to be a high breakdown estimator, in both regression and clustering. From the point of view of implementation, the feasible solution algorithm is one of the few known techniques that guarantees a global solution for the LTS estimator. The feasible solution algorithm divides a noisy data set into two parts -the non-noisy retained set and the noisy trimmed set, by implementing a pairwise swap of datum between the two sets until a least squares estimator provides the best fit on the retained set. We present a novel genetic algorithm-based implementation of the feasible solution algorithm for fuzzy least trimmed squares clustering, and also substantiate the efficacy of our method by three examples.