ABSTRACT
The goal of matrix completion is to impute missing values of a possibly low-rank matrix with only partial entries observed. This problem arises in online recommendation systems, computer vision, etc. In real-world applications, the matrix to be recovered might be contaminated by noise or outliers, where robust techniques are needed. In this chapter, we introduce a robust matrix completion model, where the robustness benefits from a nonconvex loss function. Efficient algorithms are proposed to solve the introduced robust matrix completion model. Experiments are carried out on synthetic as well as real datasets to validate the efficiency and effectiveness of the proposed models and algorithms. The problem of matrix completion aims at recovering a matrix from a sampling of its entries, which has arisen from a variety of real-world applications including online recommendation systems [26, 30], image impainting [1, 20], computer vision, and video denoising [17]. The problem itself could be an ill-posed problem without further constraints since we have fewer samples than entries. However, in many applications including those mentioned-above, it is common that the matrix that we are going to recover has some special structures; for example, low-rank or approximately low-rank, which makes it possible to search within all possible completions.
