ELASTIC-NET REGULARIZATION FOR LOW-RANK MATRIX RECOVERY

Abstract

This paper considers the problem of recovering a low-rank matrix from a small number of measurements consisting of linear combinations of the matrix entries. We extend the elastic-net regularization in compressive sensing to a more general setting, the matrix recovery setting, and consider the elastic-net regularization scheme for matrix recovery. To investigate on the statistical properties of this scheme and in particular on its convergence properties, we set up a suitable mathematic framework. We characterize some properties of the estimator and construct a natural iterative procedure to compute it. The convergence analysis shows that the sequence of iterates converges, which then underlies successful applications of the matrix elastic-net regularization algorithm. In addition, the error bounds of the proposed algorithm for low-rank matrix and even for full-rank matrix are presented in this paper.