A Simple Decomposition Alternating Direction Method for Matrix Completion

Matrix completion(MC), which is to recover a data matrix from a sampling of its entries, arises in many applications. In this work, we consider find the solutions of the MC problems by solving a series of fixed rank problems. For the fixed rank problems, variables are divided into two parts naturally based on matrix factorization and a simple alternative direction method framework is proposed. For each fixed rank problem, the solving process of each part of variables can be further converted into a series of relative small scale independent linear equations systems. Based on these observations, we design a decomposition alternative direction method for the MC problem. To test the performance of the new method, we implement our method in Matlab(with a few C/Mex functions) and compare it with several state-of-the-art solvers for the MC problem. Preliminary experimental results indeed demonstrate the effectiveness and efficiency of our method.