Abstract
This paper studies the matrix completion problems when the entries are contaminated by non-Gaussian noise or outliers. The proposed approach employs a nonconvex loss function induced by the maximum correntropy criterion. With the help of this loss function, we develop a rank constrained, as well as a nuclear norm regularized model, which is resistant to non-Gaussian noise and outliers. However, its non-convexity also leads to certain difficulties. To tackle this problem, we use the simple iterative soft and hard thresholding strategies. We show that when extending to the general affine rank minimization problems, under proper conditions, certain recoverability results can be obtained for the proposed algorithms. Numerical experiments indicate the improved performance of our proposed approach.
Highlights
Arising from a variety of applications such as online recommendation systems [1,2], image inpainting [3,4] and video denoising [5], the matrix completion problem has drawn tremendous and continuous attention over recent years [6,7,8,9,10,11,12]
We extend the proposed models to deal with the affine rank minimization problem, which includes the matrix completion as a special case
Learning with correntropy-induced losses could be resistant to non-Gaussian noise and outliers while ensuring good prediction accuracy simultaneously with properly chosen parameter σ
Summary
Arising from a variety of applications such as online recommendation systems [1,2], image inpainting [3,4] and video denoising [5], the matrix completion problem has drawn tremendous and continuous attention over recent years [6,7,8,9,10,11,12]. Incorporated with the least squares loss, the nuclear norm regularization was proposed to solve (1) when the observed entries are contaminated by Gaussian noise [13,14,15,16]. We propose to use the correntropy-induced loss function in matrix completion problems when pursuing robustness. By employing the correntropy-induced losses, we propose a nonconvex relaxation approach to robust matrix completion. Based on this loss, a rank constraint, as well as a nuclear norm penalized model is proposed.
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