Class-Based Deep Non-Negative Matrix Factorization Algorithm for Facial Image Representation

Deep non-negative matrix factorizations (DNMF) are the promising multi-layer non-negativity feature extraction methods for image data representation and have been successfully applied to image data clustering and recognition tasks. However, most of the DNMF methods do not utilize the information of class labels which is more important for classification. Also, they have high computational complexity. To address the problems of DNMF methods, this paper proposes a novel class-based deep non-negative matrix factorization (CDNMF) approach. Under the non-negativity constraint, our CDNMF method recursively decomposes the basis matrix of each class and makes the basis vectors from different classes are orthogonal at the same layer. The CDNMF algorithm is shown to be convergent using the auxiliary function technique. Compared with the state-of-the-art deep NMF algorithms on face recognition, experimental results demonstrate that the proposed CDNMF algorithm has superior classification performance and higher computational efficiency.