Co-Regularized Collective Matrix Factorization for Joint Matrix Completion

Collective matrix factorization (CMF) is a popular technique for joint matrix completion. However, it relies on a strong assumption that matrices share a common low-rank structure, which may not be easily satisfied in practice. To lift this limitation, this paper introduces a novel joint matrix completion method based on a relaxed assumption. Specifically, we allow the matrix structures to be different, but assume their induced subspaces lie close to each other. Then, we propose a method that penalizes the distance between these subspaces while learning different factorization models for different matrices. Compared with the state-of-art solution, our solution has lower model complexity and hence suffers less from over-fitting. In experiment we demonstrate its effectiveness.