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SSC Seminar Series - Raffaele Argiento

Friday, June 27, 2014, 03:00pm - 04:00pm



“Bayesian Principal Curve Clustering by Normalized Generalized Gamma 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. First of all we will define a new class of random probability measures, approximating the well-known normalized generalized gamma (NGG) process. Our approximation relies on the representation of NGG process as discrete measures where the weights are obtained by normalization of the jumps of a Poisson process. In our approximation only unnormalized jumps larger than a threshold $epsilon$ will be considered; as a consequence the number of jumps of this new prior, called $epsilon$-NG process, is a.s. finite. We will assume the $epsilon$-NGG process as the mixing measure in a mixture model for density and cluster estimation. Moreover, as kernel of our mixture, we will consider 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 Tibshirani~1992 into a Bayesian framework. As an application we will consider the detection of seismic faults using data coming from Italian earthquake catalogues.

This is a joint work with Alessandra Guglielmi from Politecnico of Milano

Location : GDC 7.402