Generalized kernel fuzzy clustering model

Abstract

This paper proposes a generalized kernel fuzzy clustering model and investigates the features of the proposed model. An additive clustering model has been proposed that considers the overlapping of clusters whose target data is similarity data. In addition, by introducing the concept of a fuzzy cluster to the additive clustering model, an additive fuzzy clustering model has been proposed. In these models, sharing common properties of clusters combine ”additively” and the given similarity between a pair of objects is estimated as the sum of the shared common properties. Therefore, in these models, the effects of the interaction of different clusters can not be considered. In order to solve this problem, we propose a generalized kernel fuzzy clustering model which is an extension of the additive fuzzy clustering model to a nonlinear fuzzy clustering model through the use of kernel functions. In this new model, the degree of objects to clusters is estimated in a mapped higher dimensional space using kernel functions. We show a better performance of the proposed model through several numerical examples.