Nonnegative matrix factorization by joint locality-constrained and a"" 2,1-norm regularization

Nonnegative matrix factorization has been widely applied recently. The nonnegativity constraints result in parts-based, sparse representations which can be more robust than global, non-sparse features. However, existing techniques could not accurately dominate the sparseness. To address this issue, we present a unified criterion, called Nonnegative Matrix Factorization by Joint Locality-constrained and a"" (2,1)-norm Regularization(NMF2L), which is designed to simultaneously perform nonnegative matrix factorization and locality constraint as well as to obtain the row sparsity. We reformulate the nonnegative local coordinate factorization problem and use a"" (2,1)-norm on the coefficient matrix to obtain row sparsity, which results in selecting relevant features. An efficient updating rule is proposed, and its convergence is theoretically guaranteed. Experiments on benchmark face datasets demonstrate the effectiveness of our presented method in comparison to the state-of-the-art methods.