Generalized Newton methods for graph signal matrix completion

Abstract

The matrix completion problem can be found in many applications such as classification, image inpainting and collaborative filtering. In recent years, the emerging field of graph signal processing (GSP) has shed new light on this problem, deriving the graph signal matrix completion problem which incorporates the correlation of data elements. The nuclear-norm based methods possess satisfactory recovery performance, while they suffer from high computational cost and usually have slow convergence rate. In this paper, we propose two new iterative algorithms for solving the nuclear-norm regularization based graph signal matrix completion (NRGSMC) problem. By adopting approximate diagonalization approaches to estimate singular value decomposition (SVD), we obtain two generalized Newton algorithms, the generalized Newton with truncated Jacobi method (GNTJM) and the generalized Newton with parallel truncated Jacobi method (GNPTJM). The proposed methods are with low complexity and fast convergence by using the second-order information associated with the problem. Numerical results on three real-world data sets demonstrate that our schemes have evidently faster convergence rate than the gradient method with exact SVD, while maintain the similar completion performance.