An Additive Fuzzy Clustering Model

Abstract

The purpose of this paper is to propose an additive fuzzy clustering model for similarity data and investigate its characteristic features. This method is regarded as a structural analysis of the similarity between the pair of objects. The cluster is defined, in this method, as the subset in which the objects share a common property. Then the similarity represents the degree of shared properties. Although, in a hard clustering method, the additive clustering models have been discussed, the number of clusters tend to increase describing the structure of observed similarities, because the models are discussed based on whether an object belongs to one cluster or not, namely, whether each object has the common property or not. Then we will show that it is rather natural to describe the model based on the fuzzy clusters because such a model will be able to explain the similarity by using fewer substantial clusters.