Transduction with Matrix Completion Using Smoothed Rank Function
This work addresses matrix completion for recommendation systems, offering improved accuracy and reduced complexity, though it appears incremental as it builds on existing low-rank and smoothed rank function approaches.
The paper tackles the transduction with matrix completion problem by proposing two new algorithms that jointly handle matrix completion and prediction tasks, achieving up to 10% higher accuracy than state-of-the-art methods in low observation rates without block loss.
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.