Sparse matrix factorization with L_2,1 norm for matrix completion

Matrix factorization is a popular matrix completion method, however, it is difficult to determine the ranks of the factor matrices. We propose two new sparse matrix factorization methods with l_2,1 norm to explicitly force the row sparseness of the factor matrices, where the rank of the factor matrices is adaptively controlled by the regularization coefficient. We further theoretically prove the convergence property of our algorithms. The experimental results on the simulation and the benchmark datasets show that our methods achieve superior performance than its counterparts. Moreover our proposed methods can attain comparable performance with the deep learning-based matrix completion methods.