Fuzzy clustering with weighted medoids for relational data

The well known k-medoids clustering approach groups objects through finding k representative objects based on the pairwise (dis)similarities of objects in the data set. In real applications, using only one object to capture or interpret each cluster may not be sufficient enough which in turn could affect the accuracy of the data analysis. In this paper, we propose a new fuzzy clustering approach called PFC for (dis)similarity-based data or relational data analysis. In PFC, objects in each fuzzy cluster carry various weights called prototype weights to represent their degrees of representativeness in that cluster. This mechanism enables each cluster to be represented by more than one objects. Compared with existing clustering approaches for relational data, PFC is able to capture the underlying structures of the data more accurately and provide richer information for the description of the resulting clusters. We introduce the detailed formulation of PFC and provide the analytical as well as experimental studies to demonstrate the merits of the proposed approach.