Clustering of Variables Based on Watson Distribution on Hypersphere: A Comparison of Algorithms

Abstract

We consider n individuals described by p variables, represented by points of the surface of unit hypersphere. We suppose that the individuals are fixed and the set of variables comes from a mixture of bipolar Watson distributions. For the mixture identification, we use EM and dynamic clusters algorithms, which enable us to obtain a partition of the set of variables into clusters of variables.Our aim is to evaluate the clusters obtained in these algorithms, using measures of within-groups variability and between-groups variability and compare these clusters with those obtained in other clustering approaches, by analyzing simulated and real data.