Clustering using a genetic fuzzy least median of squares algorithm

Reliable clustering of a severely contaminated data must depend on robust estimation methods to determine the cluster prototypes. The Least Median of Squares (LMedS) can estimate the parameters of a single prototype with a 50% breakdown point. However this breakdown point cannot be achieved when a data set consists of multiple clusters. In addition to this limitation, the objective function of the LMedS is neither amenable to analytical optimization nor to numerical optimization because of its nondifferentiability. Therefore, a tedious and time-consuming random sampling process is usually performed to search the solution space. In this paper, we first generalize the LMedS to allow the simultaneous estimation of multiple prototypes. Then we propose the use of fuzzy memberships to make this method suitable for more complex data sets. Finally, we use a genetic algorithm to provide a fast and reliable optimization of the proposed objective functions.