Fuzzy clustering as blurring

A family of fuzzy clustering algorithms that are Picard iterations based on alternate membership evaluations and cluster center shifts are compared with the blurring process, a deterministic dynamic system that moves data points to weighted means in their neighborhoods. It is shown in this paper that when the initial cluster centers are assigned as data points themselves, some fuzzy clustering algorithms, particularly the maximum-entropy clustering, become blurring processes. Some basic results obtained in the blurring process thus can be applied to these special runs of fuzzy clustering, and may serve as counterexamples for fuzzy clustering in general