Feature and Nuclear Norm Minimization for Matrix Completion

Matrix completion, whose goal is to recover a matrix from a few entries observed, is a fundamental model behind many applications. Our study shows that, in many applications, the to-be-complete matrix can be represented as the sum of a low-rank matrix and a sparse matrix associating with side information matrices. The low-rank matrix depicts the global patterns while the sparse matrix characterizes the local patterns, which are often described by the side information. Accordingly, to achieve high-quality matrix completion, we propose a Feature and Nuclear Norm Minimization (FNNM) model. The rationale of FNNM is to employ transductive completion to generalize the global pattern and inductive completion to recover the local pattern. Alternative minimization algorithm based on fixed-point iteration is developed to numerically solve the FNNM model. FNNM has demonstrated promising results on a variety of applications, including movie recommendation, drug-target interaction prediction, and multi-label learning, consistently outperforming the state-of-the-art matrix completion algorithms.