Non-negative enhanced discriminant matrix factorization method with sparsity regularization

Efficient low-rank representation of data plays a significant role in the field of computer vision and pattern recognition. In order to obtain a more discriminant and sparse low-dimensional representation, a novel non-negative enhanced discriminant matrix factorization method with sparsity regularization is proposed in this paper. Firstly, the local invariance and discriminant information of the low-dimensional representation are incorporated into the objective function to construct a new within-class encouragement constraint term, and the weighted coefficients are introduced to further enhance the compactness between the samples that belong to the same class in the new base space. Secondly, a new between-class penalty term is constructed to maximize the difference between different classes of samples, and meanwhile, the weighted coefficients are introduced to further enhance the discreteness and discriminativeness between classes. Finally, to learn the part-based representation of data better, the sparse constraint term is further introduced, and consequently, the sparseness of data representation, the local invariance, and the discriminativeness are integrated into a unified framework. Moreover, the optimization solution and the convergence proof of objective function are given. The extensive experiments demonstrate the strong robustness of the proposed method to face recognition and image classification under occlusions.