Adjacent graph-based block kernel nonnegative matrix factorization

Abstract

Using block technique and graph theory, we present a variant of nonnegative matrix factorization (NMF) with high performance for face recognition. We establish a novel objective function in kernel space by the class label information and local scatter information. The class label information is implied in the block decomposition technique and intra-class covariance matrix, while the local scatter information is determined by the adjacent graph matrix. We theoretically construct an auxiliary function related to the objective function and then derive the iterative formulae of our method by solving the stable point of the auxiliary function. The property of auxiliary function shows that our algorithm is convergent. Finally, empirical results show that our method is effective.