Clustering of variables defined on the hypersphere: a comparison of methods

Abstract

We discuss the identi cation of a mixture of Watson distributions de ned on the hypersphere using the dynamic clusters algorithm and the EM algorithm (Estimation-Maximization). The identi cation of the mixture allows us to obtain homogeneous groups of variables, such that each group is associated with a privileged direction, whose maximum likelihood estimate corresponds to the rst principal component of the group and is associated with a parameter that measures the concentration around the privileged direction. Our aim is to compare the two algorithms used in the identi cation of the mixture by analyzing simulated and real data.