Nonnegative matrix factorization with gibbs random field modeling

In this paper, we present a Gibbs Random Field (GRF) modeling based Nonnegative Matrix Factorization (NMF) algorithm, called GRF-NMF. We propose to treat the component matrix of NMF as a Gibbs random field. Since each component presents a localized object part, as usually expected, we propose an energy function with the prior knowledge of smoothness and locality. This way of directly modeling on the structure of components makes the algorithm able to learn sparse, smooth, and localized object parts. Furthermore, we find that at each update iteration, the constrained term can be processed conveniently via local filtering on components. Finally we give a well established convergence proof for the derived algorithm. Experimental results on both synthesized and real image databases shows that the proposed GRF-NMF algorithm significantly outperforms other NMF related algorithms in sparsity, smoothness, and locality of the learned components.