Accelerated sparse nonnegative matrix factorization for unsupervised feature learning

•We improved SNMF with implicit sparse constraints which are the L1-norm of coefficient matrix and L2-norm of basis matrix.•A subproblem is transformed into a convex optimization model solved by DG, another one is equivalent to FISTA by Lip. Cond.•We obtain the closed-form iteration form of each sub-problem by ADMM and learn the cluster assignments by resulting features.•We analyzed the convergence of algorithm in theory and proved that the convergence point is KKT point of equivalent model.•We analyzed the algorithm complexity and presented the performance of running time, CA and MI under the SVD initialization.