Matrix Completion via Successive Low-rank Matrix Approximation

In this paper, a successive low-rank matrix approximation algorithm is presented for the matrix completion (MC) based on hard thresholding method, which approximate the optimal low-rank matrix from rank-one matrix step by step. The algorithm enables the distance between the matrix with the observed elements and the projection on low-rank manifold to be minimum. The optimal low-rank matrix with observed elements is obtained when the distance is zero. In theory, convergence and convergent error of the new algorithm are analyzed in detail. Furthermore, some numerical experiments show that the algorithm is more effective in CPU time and precision than the orthogonal rank-one matrix pursuit(OR1MP) algorithm and the augmented Lagrange multiplier (ALM) method when the sampling rate is low.