A Multivariate Fuzzy Kohonen Clustering Network

Usually, in a fuzzy clustering, the memberships are the same for all the variables (features), i.e., the variables are considered equally important for the definition of the memberships. Fuzzy Kohonen Clustering network (FKCN) is a self-organizing fuzzy neural network that uses fuzzy membership values from the popular Fuzzy c-Means as learning rates. The replacement of the arbitrary learning rate by a fuzzy membership function can produce better clustering results. This paper introduces a new variant of the FKCN algorithm that finds a set of weights and a multivariate fuzzy partition minimizing an objective function. Here, the multivariate memberships allow to take account the intra-class and inter-class dispersion structures of the input data. Experiments with different configurations of synthetic data sets and applications with real data sets demonstrate the usefulness of this fuzzy clustering network model.