A new method based on the manifold-alternative approximating for low-rank matrix completion

In this paper, a new method is proposed for low-rank matrix completion which is based on the least squares approximating to the known elements in the manifold formed by the singular vectors of the partial singular value decomposition alternatively. The method can achieve a reduction of the rank of the manifold by gradually reducing the number of the singular value of the thresholding and get the optimal low-rank matrix. It is proven that the manifold-alternative approximating method is convergent under some conditions. Furthermore, compared with the augmented Lagrange multiplier and the orthogonal rank-one matrix pursuit algorithms by random experiments, it is more effective as regards the CPU time and the low-rank property.