Bayesian principal curve clustering by species-sampling mixture models

In this work we are interested in clustering data whose support is "curved". For this purpose, we will follow a Bayesian nonparametric approach by considering a species sampling mixture model. Our first goal is to define a general/flexible class of distributions, such that they can model data from clusters with non standard shape. To this end, we extend the definition of principal curve given in [8] (Tibshirani 1992) into a Bayesian framework.We propose a new hierarchical model, where the data in each cluster are parametrically distributed around the Bayesian principal curve, and the prior cluster assignment is given on the latent variables at the second level of hierarchy according to a species sampling model. As an application we will consider the detection of seismic faults using data coming from Italian earthquake catalogues.