Soft clustering: Fuzzy and rough approaches and their extensions and derivatives

Clustering is one of the most widely used approaches in data mining with real life applications in virtually any domain. The huge interest in clustering has led to a possibly three-digit number of algorithms with the k-means family probably the most widely used group of methods. Besides classic bivalent approaches, clustering algorithms belonging to the domain of soft computing have been proposed and successfully applied in the past four decades. Bezdek’s fuzzy c-means is a prominent example for such soft computing cluster algorithms with many effective real life applications. More recently, Lingras and West enriched this area by introducing rough k-means. In this article we compare k-means to fuzzy c-means and rough k-means as important representatives of soft clustering. On the basis of this comparison, we then survey important extensions and derivatives of these algorithms; our particular interest here is on hybrid clustering, merging fuzzy and rough concepts. We also give some examples where k-means, rough k-means, and fuzzy c-means have been used in studies.