Discriminant non-negative graph embedding for face recognition

Non-negative Matrix Factorization (NMF) is an unsupervised algorithm for low-rank approximation of non-negative data and has been widely used in many fields, but its performance in feature extraction is not satisfactory. The main reason is that the model of NMF and its variants did not take into account the label information of the samples, which can add the discriminant ability of the methods. In this paper, we proposed a novel method, called discriminant non-negative graph embedding (DNGE) algorithm in which the label information of the samples and the local geometric structure are all integrated in the objective function. Furthermore, we incorporated the between-class graph and within-class graph into the objective functions to indicate that we not only used the local separability but also used the whole separability of the samples. To guarantee convergence, we use the KKT condition to calculate the non-negative solution of the DNGE. A convergent multiplicative non-negative updating rule is then derived to learn the transformation matrix. Experiments are conducted on the CMU PIE, ORL, Yale, FERET and AR database. The results show that the DNGE algorithm provides better facial representation and achieves higher recognition rates than naïve Non-Negative Matrix Factorization and its extension methods.