Graph Matrix Completion in Presence of Outliers

Matrix completion problem has gathered a lot of attention in recent years. In the matrix completion problem, the goal is to recover a low-rank matrix from a subset of its entries. The graph matrix completion was introduced based on the fact that the relation between rows (or columns) of a matrix can be modeled as a graph structure. The graph matrix completion problem is formulated by adding the graph total variation term to the objective function of matrix completion problem. However; in practice, the observed data is noisy and contains outliers. Outlier data is defined as part of the observed that are different than other parts and are not consistent with the data structure. In this paper, we apply graph total variation based on the directed Laplacian and propose a new method for graph matrix completion. We introduce a new method called GMCO-DL for the case where both noise and outliers exist in observations. Simulation results show outstanding results for the proposed method in terms of estimation error.