Transductive multi-label learning from missing data using smoothed rank function

In this paper, we propose two new algorithms for transductive multi-label learning from missing data. In transductive matrix completion (MC), the challenge is prediction while the data matrix is partially observed. The joint MC and prediction tasks are addressed simultaneously to enhance accuracy in comparison with separate tackling of each. In this setting, the labels to be predicted are modeled as missing entries inside a stacked matrix along the feature-instance data. Assuming the data matrix is of low rank, we propose a new recommendation method for transductive MC by posing the problem as a minimization of the smoothed rank function with non-affine constraints, rather than its convex surrogate. We provide convergence analysis for the proposed algorithms and illustrate their low computational complexity and robustness in comparison with other methods. The simulations are conducted on well-known real datasets in two different scenarios of randomly missing pattern with and without block-loss. The simulations reveal our methods accuracy is superior to state-of-the-art methods up to 10% in low observation rates for the scenario without block-loss. The accuracy of the proposed methods in the scenario with block-loss is comparable to the state-of-the-art while the complexity is reduced up to four times.