Spatially correlated nonnegative matrix factorization

Low rank approximation of matrices has been frequently applied in information processing tasks, and in recent years, Nonnegative Matrix Factorization (NMF) has received considerable attentions for its straightforward interpretability and superior performance. When applied to image processing, ordinary NMF merely views a p"1xp"2 image as a vector in p"1xp"2-dimensional space and the pixels of the image are considered as independent. It fails to consider the fact that an image displayed in the plane is intrinsically a matrix, and pixels spatially close to each other may probably be correlated. Even though we have p"1xp"2 pixels per image, this spatial correlation suggests that the real number of freedom is far less. In this paper, we introduce a Spatially Correlated Nonnegative Matrix Factorization algorithm, which explicitly models the spatial correlation between neighboring pixels in the parts-based image representation. A multiplicative updating algorithm is also proposed to solve the corresponding optimization problem. Experimental results on benchmark image data sets demonstrate the effectiveness of the proposed method.