Graph regularized discriminative non-negative matrix factorization for face recognition

Non-negative matrix factorization (NMF) has been widely employed in computer vision and pattern recognition fields since the learned bases can be interpreted as a natural parts-based representation of the input space, which is consistent with the psychological intuition of combining parts to form a whole. In this paper, we propose a novel constrained nonnegative matrix factorization algorithm, called the graph regularized discriminative non-negative matrix factorization (GDNMF), to incorporate into the NMF model both intrinsic geometrical structure and discriminative information which have been essentially ignored in prior works. Specifically, both the graph Laplacian and supervised label information are jointly utilized to learn the projection matrix in the new model. Further we provide the corresponding multiplicative update solutions for the optimization framework, together with the convergence proof. A series of experiments are conducted over several benchmark face datasets to demonstrate the efficacy of our proposed GDNMF.