Bayesian nonparametric clustering as a community detection problem

It is well known that a wide class of bayesian nonparametric priors lead to the representation of the distribution of the observable variables 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 is usually required. In order to circumvent label switching, pairwise posterior similarity has been introduced, and it has been used in order to either apply classical clustering algorithms or estimate the underlying partition by minimising a suitable loss function. This paper proposes to map observations on a weighted undirected graph, where each node represents a sample item and edge weights are given by the posterior pairwise similarities. It will be shown how, after building a particular random walk on such a graph, it is possible to apply a community detection algorithm, known as map equation method, by optimising the description length of the partition. A relevant feature of this method is that it allows for both the quantification of the posterior uncertainty of the classification and the selection of variables to be used for classification purposes.