منابع مشابه
A Unified Convex Surrogate for the Schatten-p Norm
The Schatten-p norm (0 < p < 1) has been widely used to replace the nuclear norm for better approximating the rank function. However, existing methods are either 1) not scalable for large scale problems due to relying on singular value decomposition (SVD) in every iteration, or 2) specific to some p values, e.g., 1/2, and 2/3. In this paper, we show that for any p, p1, and p2 > 0 satisfying 1/p...
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The low-rank matrix completion problem is a fundamental machine learning and data mining problem with many important applications. The standard low-rank matrix completion methods relax the rank minimization problem by the trace norm minimization. However, this relaxation may make the solution seriously deviate from the original solution. Meanwhile, most completion methods minimize the squared p...
متن کاملLow-Rank Matrix Recovery via Efficient Schatten p-Norm Minimization
As an emerging machine learning and information retrieval technique, the matrix completion has been successfully applied to solve many scientific applications, such as collaborative prediction in information retrieval, video completion in computer vision, etc. The matrix completion is to recover a low-rank matrix with a fraction of its entries arbitrarily corrupted. Instead of solving the popul...
متن کاملVisual Processing by a Unified Schatten-p Norm and ℓq Norm Regularized Principal Component Pursuit
In this paper, we propose a non-convex formulation to recover the authentic structure from the corrupted real data. Typically, the specific structure is assumed to be low rank, which holds for a wide range of data, such as images and videos. Meanwhile, the corruption is assumed to be sparse. In the literature, such a problem is known as Robust Principal Component Analysis (RPCA), which usually ...
متن کاملWeighted Schatten $p$-Norm Minimization for Image Denoising with Local and Nonlocal Regularization
This paper presents a patch-wise low-rank based image denoising method with constrained variational model involving local and nonlocal regularization. On one hand, recent patch-wise methods can be represented as a low-rank matrix approximation problem whose convex relaxation usually depends on nuclear norm minimization (NNM). Here, we extend the NNM to the nonconvex schatten p-norm minimization...
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ژورنال
عنوان ژورنال: Glasgow Mathematical Journal
سال: 1987
ISSN: 0017-0895,1469-509X
DOI: 10.1017/s0017089500006716