A novel fuzzy clustering algorithm

In this paper we proposed a novel fuzzy clustering algorithm, called a fuzzy compactness and separation (FCS), based on a fuzzy scatter matrix. The compactness is measured by a fuzzy within variation and the separation is measured by a fuzzy between variation. The proposed FCS objective function is a modification of the FS validity index proposed by Fukuyama and Sugeno (1989) and also a generalization of the fuzzy c-means (FCM). The FCS algorithm assigns a hard kernel boundary for each cluster such that hard memberships and fuzzy memberships could be co-existed in the clustering results. Thus, FCS can be seen as a clustering algorithm with a novel sense between hard c-means and fuzzy c-means. Some numerical examples are demonstrated to show its properties and effectiveness.