Clustering using the fisher-rao distance

In this paper we consider the Fisher-Rao distance in the space of the multivariate diagonal Gaussian distributions for clustering methods. Centroids in this space are derived and used to introduce two clustering algorithms for diagonal Gaussian mixture models associated to this metric: the k-means and the hierarchical clustering. These algorithms allow to reduce the number of components of such mixture models in the context of image segmentation. The algorithms presented here are compared with the Bregman hard and hierarchical clustering algorithms regarding the advantages of each method in different situations.