Can fuzzy clustering avoid local minima and undesired partitions?

Abstract

Empirical evaluations and experience seem to provide evidence that fuzzy clustering is less sensitive w.r.t. to the initialisation than crisp clustering, i.e. fuzzy clustering often tends to converge to the same clustering result independent of the initialisation whereas the result for crisp clustering is highly dependent on the initialisation. This leads to the conjecture that the objective function used for fuzzy clustering has less undesired local minima than the one for hard clustering. In this paper, we demonstrate that fuzzy clustering does suffer from unwanted local minima based on concrete examples and show how these undesired local minima of the objective function in fuzzy clustering can vanish by using a suitable value for the fuzzifier. © Springer-Verlag Berlin Heidelberg 2013.