Weighted hybrid truncated norm regularization method for low-rank matrix completion

Matrix completion is usually formulated as a low-rank matrix approximation problem. Several methods have been proposed to solve this problem, e.g., truncated nuclear norm regularization (TNNR) which performs well in recovery accuracy and convergence speed, and hybrid truncated norm regularization (HTNR) method which has better stability compared to TNNR. In this paper, a modified hybrid truncated norm regularization method, named WHTNR, is proposed to accelerate the convergence of the HTNR method. The proposed WHTNR method can preferentially restore rows with fewer missing elements in the matrix by assigning appropriate weights to the first r singular values. The presented experiments show empirical evidence on significant improvements of the proposed method over the closest four methods, both in convergence speed or in accuracy, it is robust to the parameter truncate singular values r.