Prototype-less Fuzzy Clustering

In contrast to standard fuzzy clustering, which optimizes a set of prototypes, one for each cluster, this paper studies fuzzy clustering without prototypes. Starting from an objective function that only involves the distances between data points and the membership degrees of the data points to the different clusters, an iterative update rule is derived. The properties of the resulting algorithm are then examined, especially w.r.t. to schemes that focus on a constrained neighborhood for each data point. Corresponding experimental results are reported that demonstrate the merits of this approach.