A Markov random field-regulated Pitman–Yor process prior for spatially constrained data clustering

In this work, we propose a Markov random field-regulated Pitman–Yor process (MRF-PYP) prior for nonparametric clustering of data with spatial interdependencies. The MRF-PYP is constructed by imposing a Pitman–Yor process over the distribution of the latent variables that allocate data points to clusters (model states), the discount hyperparameter of which is regulated by an additionally postulated simplified (pointwise) Markov random field (Gibbsian) distribution with a countably infinite number of states. Further, based on the stick-breaking construction of the Pitman–Yor process, we derive an efficient truncated variational Bayesian algorithm for model inference. We examine the efficacy of our approach by considering an unsupervised image segmentation application using a real-world dataset. We show that our approach completely outperforms related methods from the field of Bayesian nonparametrics, including the recently proposed infinite hidden Markov random field model and the Dirichlet process prior.