Correntropy supervised non-negative matrix factorization

Non-negative matrix factorization (NMF) is a powerful dimension reduction method and has been widely used in many pattern recognition and computer vision problems. However, conventional NMF methods are neither robust enough as their loss functions are sensitive to outliers, nor discriminative because they completely ignore labels in a dataset. In this paper, we proposed a correntropy supervised NMF (CSNMF) to simultaneously overcome aforementioned deficiencies. In particular, CSNMF maximizes the correntropy between the data matrix and its reconstruction in low-dimensional space to inhibit outliers during learning the subspace, and narrows the minimizes the distances between coefficients of any two samples with the same class labels to enhance the subsequent classification performance. To solve CSNMF, we developed a multiplicative update rules and theoretically proved its convergence. Experimental results on popular face image datasets verify the effectiveness of CSNMF comparing with NMF, its supervised variants, and its robustified variants.