A Singular Value Thresholding Algorithm for Matrix Completion

This paper introduces a novel algorithm to approximate the matrix with minimum nuclear norm among all matrices obeying a set of convex constraints. This problem may be understood as the convex relaxation of a rank minimization problem and arises in many important applications as in the task of recovering a large matrix from a small subset of its entries (the famous Netflix problem). The algorithm is iterative, produces a sequence of matrices ..., and at each step mainly performs a soft-thresholding operation on the singular values of the matrix ... On the theoretical side, the paper provides a convergence analysis showing that the sequence of iterates converges. On the practical side, it provides numerical examples in which 1,000 x 1,000 matrices are recovered in less than a minute on a modest desktop computer. (ProQuest: ... denotes formulae/symbols omitted.)