A spatially-constrained normalized Gamma process prior

Authors:
Sotirios P. Chatzis;Dimitrios Korkinof;Yiannis Demiris
Affiliations:
Department of Electrical Engineering, Computer Engineering and Informatics, Cyprus University of Technology, 33 Saripolou Street, Limassol, Cyprus;Department of Electrical Engineering, Computer Engineering and Informatics, Cyprus University of Technology, 33 Saripolou Street, Limassol, Cyprus;Department of Electrical Engineering, Computer Engineering and Informatics, Cyprus University of Technology, 33 Saripolou Street, Limassol, Cyprus
Venue:
Expert Systems with Applications: An International Journal
Year:
2012

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Abstract

In this work, we propose a novel nonparametric Bayesian method for clustering of data with spatial interdependencies. Specifically, we devise a novel normalized Gamma process, regulated by a simplified (pointwise) Markov random field (Gibbsian) distribution with a countably infinite number of states. As a result of its construction, the proposed model allows for introducing spatial dependencies in the clustering mechanics of the normalized Gamma process, thus yielding a novel nonparametric Bayesian method for spatial data clustering. We derive an efficient truncated variational Bayesian algorithm for model inference. We examine the efficacy of our approach by considering an image segmentation application using a real-world dataset. We show that our approach outperforms related methods from the field of Bayesian nonparametrics, including the infinite hidden Markov random field model, and the Dirichlet process prior.