Completion of structurally-incomplete matrices with reweighted low-rank and sparsity priors

Abstract

Most matrix completion methods impose a low-rank prior or its variants to well pose the problem. However, the rank minimization is problematic to handle matrices with structural missing. To remedy this, this paper introduces a new matrix completion method using double priors on the latent matrix, named Reweighted Low-rank and Sparsity Priors. In the proposed model, the matrix is regularized by a low-rank prior to exploit the inter-column (row) correlations, and its columns (rows) are regularized by a sparsity prior under a dictionary to exploit intra-column (row) correlations. Both the low-rank and sparse priors are reweighted on the fly to promote low-rankness and sparsity, respectively. Numerical algorithm to solve our model is derived via the alternating direction method under the augmented Lagrangian multiplier framework. Experimental results show that our model is quite effective in recovering matrices with highly-structural missing, complementing the classic matrix completion models that handle random missing only.