Title: Looking at Bayesian nonparametric clustering from a community detection point of view
Authors: Stefano Tonellato - Ca' Foscari University of Venice (Italy) [presenting]
Abstract: It is well-known that a wide class of Bayesian nonparametric priors leads to the representation of the distribution of the observables as a mixture density with an infinite number of components, and that such a representation induces a clustering structure in the observations. However, cluster identification is not straightforward a posteriori and some post-processing of the MCMC output is usually required. It has been proven that pairwise posterior similarity successfully allows to either apply classical clustering algorithms or estimate the underlying partition by minimising a suitable loss function. We show how it can be used to map sample items on a weighted undirected graph, where each node represents an individual and edge weights are given by the posterior pairwise similarities. A community detection algorithm, known as infomap, can be applied to such a network, providing a minimum description length unsupervised classification. A relevant feature of this method is that it allows for the quantification of the posterior uncertainty of the clustering. The same approach can be easily extended to the unsupervised classification of time series.