Class-Cone Based Nonnegative Matrix Factorization for Face Recognition

Nonnegative matrix factorization (NMF) is an effectively parts-based feature representation approach and has achieved good performance in different tasks such as computer vision, clustering and so on. To enhance the discriminative power of NMF in nonnegative feature space, this paper proposes a novel supervised matrix decomposition method, called Class-Cone based Nonnegative Matrix Factorization (CCNMF). We establish a loss function with class-cone regularization which contains the volumes of class-cones and the quantity of between class-cones. To minimize the objective function will leads to small class-cones and large distance between class-cones. This good property is beneficial to the performance of NMF algorithm. We solve the optimization problem using KKT conditions and obtain the updating rules of CCNMF. Our approach is experimentally shown to be convergence and successfully applied to face recognition. Experimental results demonstrate the effectiveness of the proposed CCNMF algorithm.