Potential-based fuzzy clustering and cluster validity for categorical data and its application in modeling cultural data

This paper introduces a novel hierarchical fuzzy algorithm for clustering categorical attributes, which consists of three basic design steps. It incorporates a potential-based clustering scheme with a cluster validity index into a framework that is based on the use of the weighted fuzzy c-modes. The novelty of the contribution lies in the following properties: (a) the potential-based clustering scheme reduces the dependence of the algorithm on initialization, (b) the weighted fuzzy c-modes provides flexibility in detecting the real data structure, and (c) the cluster validity index determines the appropriate number of clusters. The algorithm is applied to model (classify) cultural data related to a number of painters of the seventeenth century, where its performance is compared to the respective performance of an agglomerative hierarchical clustering algorithm.