To overcome the disadvantage of projective non-negative matrix factorization (PNMF)

which fails to discover the intrinsic geometrical and discriminating structure

this paper proposes a novel graph embedding regularized projective non-negative matrix factorization (GEPNMF) method to extract face image features. First

this paper constructs two adjacent graphs to characterize the intrinsic geometrical structure of data subspace and interclass separability. Then

using the Laplacian matrices of the two adjacent graphs

this paper designs a graph embedding regularization incorporated with PNMF's objective function to construct the GEPNMF's objective function. Given that the graph embedding regularization is adopted by the objective function

the learned subspace of GEPNMF can preserve the geometrical structure of the data subspace

while it maximizes the margins between different classes. In addition

this paper introduces an orthogonal regularization into the objective function to ensure the learned bases to be parts-based. Finally

this paper deduces a multiplicative update rule to optimize the objective function and theoretically proves its convergence. The face recognition experiments are conducted on ORL

Yale

and CMU PIE face image datasets. The recognition rates reach 94.00%

66.43%

and 98.58%

respectively. Experimental results show that the face image features extracted by GEPNMF can achieve better face recognition performance.