Model-based clustering of probability density functions

In this paper, we propose a method to group a set of probability density functions (pdfs) into homogeneous clusters, provided that the pdfs have to be estimated nonparametrically from the data. Since elements belonging to the same cluster are naturally thought of as samples from the same probability model, the idea is to tackle the clustering problem by defining and estimating a proper mixture model on the space of probability densities. The issue of model building is challenging, because of the infinite-dimensionality and the Riemannian geometry of the domain space. By adopting a proper representation for the elements in the space, the task is accomplished using mixture models for hyper-spherical data. The proposed solution is illustrated on a real data set.