A data-driven selection of the number of clusters in the Dirichlet allocation model via Bayesian mixture modelling. Issue 15 (13th October 2019)

• Record Type: Journal Article
• Authors: Saraiva, E. F.; Pereira, C. A. B.; Suzuki, A. K.
• Is Part Of: Journal of statistical computation and simulation. Volume 89:Issue 15(2019)
• Page Start: 2848
• Page End: 2870
• Publication Date: 2019-10-13
• Subjects: Mixture model -- Bayesian approach -- Gibbs sampling -- Metropolis–Hastings -- split-merge update -- Kullback–Leibler divergence; 62M05; Mathematical statistics -- Data processing -- Periodicals; Digital computer simulation -- Periodicals; 519.5028505
• DOI: 10.1080/00949655.2019.1643345
• Languages: English
• ISSNs: 0094-9655

Abstract

ABSTRACT: In this paper, we consider a Bayesian mixture model that allows us to integrate out the weights of the mixture in order to obtain a procedure in which the number of clusters is an unknown quantity. To determine clusters and estimate parameters of interest, we develop an MCMC algorithm denominated by sequential data-driven allocation sampler. In this algorithm, a single observation has a non-null probability to create a new cluster and a set of observations may create a new cluster through the split-merge movements. The split-merge movements are developed using a sequential allocation procedure based in allocation probabilities that are calculated according to the Kullback–Leibler divergence between the posterior distribution using the observations previously allocated and the posterior distribution including a 'new' observation. We verified the performance of the proposed algorithm on the simulated data and then we illustrate its use on three publicly available real data sets.