Abstract: The classical Nonsmooth Nonnegative Matrix Factorization(nsNMF) method discovers only the global statistical information of data and fails in dealing with nonlinear distributed data,while the manifold learning algorithms show great power in exploring the faithful intrinsic geometry structures of high dimensional data set．To address this issue,based on manifold regularization,we developed a novel algorithm called Manifold Regularized-based Nonsmooth Nonnegative Matrix Factorization(MRnsNMF)．It not only considers the geometric structure in the data representation,but also introduces sparseness constraint to both coding coefficient and basis matrix simultaneously,and integrates them into one single objective function．An efficient multiplicative updating procedure was produced along with its theoretic justification of the algorithmic convergence．The feasibility and effectiveness of MRnsNMF were verified on several standard data sets with promising results.

Key words: Non-negative matrix,Nonsmooth,Manifold regularization