Minimization subproblems and heuristics for an applied clustering problem

A practical problem that requires the classification of a set of points of ℝⁿ using a criterion not sensitive to bounded outliers is studied in this paper. A fixed-point (k-means) algorithm is defined that uses an arbitrary distance function. Finite convergence is proved. A robust distance defined by Boente et al. is selected for applications. Smooth approximations of this distance are defined and suitable heuristics are introduced to enhance the probability of finding global optimizers. A real-life example is presented and commented.