Some Variants of Fuzzy c-Directions Clustering Algorithms for Spherical Data

Abstract

Fuzzy c-means (FCM) is the most fundamental fuzzy clustering algorithm for vectorial data, and several variants of this algorithm have been proposed, such as q-divergence based FCM, Yang-type FCM, and extended q-divergence-based FCM. However, only Yang-type fuzzification technique has been applied to fuzzy c-directions (FCD) clustering for spherical data. In this regard, this study presents two fuzzy clustering algorithms for fuzzy c-directions. The first algorithm is referred to as the q-divergence based FCD, which is constructed by replacing the object-cluster dissimilarity used in q-divergence-based FCM with that in FCD for spherical data. The second algorithm is referred to as the extended q-divergence-(breakpoint)based FCD, which is also constructed by replacing the object-cluster dissimilarity used in extended q-(breakpoint)divergence-based FCM with that in FCD for spherical data. Based on numerical experiments with an artificial data set, the characteristics of each method are presented.