Graph-Preserving Sparse Nonnegative Matrix Factorization With Application to Facial Expression Recognition

In this paper, a novel graph-preserving sparse nonnegative matrix factorization (GSNMF) algorithm is proposed for facial expression recognition. The GSNMF algorithm is derived from the original NMF algorithm by exploiting both sparse and graph-preserving properties. The latter may contain the class information of the samples. Therefore, GSNMF can be conducted as an unsupervised or a supervised dimension reduction method. A sparse representation of the facial images is obtained by minimizing the l(1)-norm of the basis images. Furthermore, according to the graph embedding theory, the neighborhood of the samples is preserved by retaining the graph structure in the mapped space. The GSNMF decomposition transforms the high-dimensional facial expression images into a locality-preserving subspace with sparse representation. To guarantee convergence, we use the projected gradient method to calculate the nonnegative solution of GSNMF. Experiments are conducted on the JAFFE database and the Cohn-Kanade database with unoccluded and partially occluded facial images. The results show that the GSNMF algorithm provides better facial representations and achieves higher recognition rates than nonnegative matrix factorization. Moreover, GSNMF is also more robust to partial occlusions than other tested methods.