Greedy Matrix Completion with Fitting Error and Rank Iterative Minimization

A novel matrix completion algorithm which iteratively minimizes the fitting error and the matrix rank is presented. Unlike conventional matrix completion algorithms, which usually require some relaxation technique to cope with the low rank constraints, the proposed algorithm does not require any such techniques, thus making the selection of the parameter q of the matrix q-norm (0 < q ≤1) or the regularization parameter unnecessary. Simulation results of the random generated data and Jester joke data set verify our algorithm's effectiveness and superiority over the reported algorithms in literature.