An Extended Objective Function for Prototype-less Fuzzy Clustering

While in standard fuzzy clustering one optimizes a set of prototypes, one for each cluster, we study fuzzy clustering without prototypes. We define an objective function, which only depends on the distances between data points and the membership degrees of the data points to the clusters, and derive an iterative membership update rule. The properties of the resulting algorithm are then examined, especially w.r.t. to an additional parameter of the objective function (compared to the one proposed in [7]) that can be seen as a more flexible alternative to the fuzzifier. Corresponding experimental results are reported that demonstrate the merits of our approach.