A discriminant manifold non-negative matrix factorization algorithm for facial expression recognition

In this paper, a novel discriminant manifold nonnegative matrix factorization (DMNMF) algorithm is proposed. To exploit the spatial neighborhood structure and prior defined class-based discriminant properties, a constraint is adopted to the objective function. The constraint is constructed based on the manifold learning and graph embedding theory. Firstly, a neighbor graph is used which encodes the spatial geometric information in original face samples; secondly a penalty graph is added which considers the discriminant class information. By using the constraints, the obtained parts-based representations of DMNMF vary smoothly along the geodesics of the data manifold and they are more discriminant for recognition. To guarantee the stationarity, the project gradient method is used for the optimization. Experiments are conducted on the JAFFE database and the Cohn-Kanade database. The results on both databases demonstrate that DMNMF provides better facial expression representations and achieves better recognition performance, compared with NMF and some variant algorithms.