  In this paper, we propose two new algorithms for transduction with Matrix
Completion (MC) problem. The joint MC and prediction tasks are addressed
simultaneously to enhance the accuracy, i.e., the label matrix is concatenated
to the data matrix forming a stacked matrix. Assuming the data matrix is of low
rank, we propose new recommendation methods by posing the problem as a
constrained minimization of the Smoothed Rank Function (SRF). We provide
convergence analysis for the proposed algorithms. The simulations are conducted
on real datasets in two different scenarios of randomly missing pattern with
and without block loss. The results confirm that the accuracy of our proposed
methods outperforms those of state-of-the-art methods even up to 10% in low
observation rates for the scenario without block loss. Our accuracy in the
latter scenario, is comparable to state-of-the-art methods while the complexity
of the proposed algorithms are reduced up to 4 times.
