Fuzzy c-Means Revisited: Towards a Cluster-Center-Free Reformulation

Fuzzy c-means (FCM) as a method of clustering has been steadily grown since its inception. This method as well as its derivatives is all to find an optimal assignment of c centers (also called means, prototypes or centroids) to c clusters by minimizing an intra-cluster variance criterion. Commonly, one has to select c data points as initial centers for the expected c clusters in advance. However, there may be no "true" cluster centers in many complex situations. For example, evidence shows that it is very hard to "pick" the good initial centers for the manifold-structured non-convex clusters. Perhaps this is why FCM does often not work well for those manifold clusters. Moreover, as is known, FCM is significantly sensitive to the initial choice of c cluster centers even if for the sphere-shaped clusters. A question naturally arises: is there a possible way that can make FCM free of cluster centers? To this end, we revisit FCM here and aim to give a cluster-center-free reformulation of FCM that minimizes the intra-cluster variance as well. Experimental results on both synthetic and real-world datasets indicate the enhanced effectiveness of our newly reformulated FCM in finding many challenging clusters.