Multi-Label Ranking Loss Minimization for Matrix Completion

The common matrix completion methods minimize the rank of the matrix to be completed in addition to the Hamming loss between the incomplete and completed matrices. The rank of matrix measures the linear relation among the vectors of matrix, which may introduce ambiguity for data recovery. To cope with this issue, we extend multi-label ranking loss into matrix completion, and employ multi-label ranking loss minimization (MLRM) in this paper to exploit the relative correlation among matrix vectors. In MLRM, the original incomplete matrix is converted into a pairwise ranking matrix, and the approximation on this newly generated matrix can be viewed as a surrogate of multi-label ranking loss to replace the Hamming loss pattern in the existing methods. Extensive experiments demonstrate that MLRM outperforms the state-of-the-art matrix completion methods in varies of applications, including movie recommendation, drug-target interaction prediction and multi-label learning.