A deep discriminative and robust nonnegative matrix factorization network method with soft label constraint

In order to obtain a discriminative, compact and robust data representation, a discriminative and robust nonnegative matrix factorization method with soft label constraint (DRNMF_SLC) is proposed. By minimizing the objective function, the data representation after learning soft label constraint is obtained. To further acquire a more hierarchical and discriminative data representation, a deep discriminative and robust nonnegative matrix factorization network method with soft label constraint (Deep DRNMFN_SLC) is constructed. In order to improve the feature expression ability of deep neural network (DNN), a deep discriminative and robust nonnegative matrix factorization network method with soft label constraint based on DNN (Deep DRNMFN_SLC_DNN) is proposed, which could obtain a more discriminative, robust and generalized feature representation, and meanwhile greatly reduce the dimension of data features. Furthermore, the objective function of DRNMF_SLC is constructed by introducing both the global loss function and the central loss function of soft label constraint matrix, and the optimization solution and convergence proof of objective function are given simultaneously. When the proposed DRNMF_SLC method and Deep DRNMFN_SLC_DNN method are, respectively, applied to the face recognition under occlusions and illumination variations, the frameworks, Algorithm 1 and Algorithm 2 are given. The extensive and adequate experiments demonstrate the effectiveness of the proposed method.