Non-negative matrix factorization - A study on influence of matrix sparseness and subspace distance metrics on image object recognition

In recent years non-negative factorization (NMF) methods of a reduced image data representation attracted the attention of computer vision community. These methods are considered as a convenient part-based representation of image data for recognition tasks with occluded objects. In the paper two novel modifications of the NMF are proposed which utilize the matrix sparseness control used by Hoyer. We have analyzed the influence of sparseness on recognition rates (RR) for various dimensions of subspaces generated for two image databases. We have studied the behaviour of four types of distances between a projected unknown image object and feature vectors in NMF-subspaces generated for training data. For occluded ORL face data, Euclidean and diffusion distances perform better than Riemannian ones, not following the overall expactation that Euclidean metric is suitable only for orthogonal basis vectors. In the case of occluded USPS digit data, the RR obtained for the modified NMF algorithm show in comparison to the conventional NMF algorithms very close values for all four distances over all dimensions and sparseness constraints. In this case Riemannian distances provide higher RR than Euclidean and diffusion ones. The proposed modified NMF method has a relevant computational benefit, since it does not require calculation of feature vectors which are explicitly generated in the NMF optimization process.