Paper Info
Title
On the Optimal Solution of Weighted Nuclear Norm Minimization.
Abstract
In recent years, the nuclear norm minimization (NNM) problem has been attracting much attention in computer vision and machine learning. The NNM problem is capitalized on its convexity and it can be solved efficiently. The standard nuclear norm regularizes all singular values equally, which is however not flexible enough to fit real scenarios. Weighted nuclear norm minimization (WNNM) is a natural extension and generalization of NNM. By assigning properly different weights to different singular values, WNNM can lead to state-of-the-art results in applications such as image denoising. Nevertheless, so far the global optimal solution of WNNM problem is not completely solved yet due to its non-convexity in general cases. In this article, we study the theoretical properties of WNNM and prove that WNNM can be equivalently transformed into a quadratic programming problem with linear constraints. This implies that WNNM is equivalent to a convex problem and its global optimum can be readily achieved by off-the-shelf convex optimization solvers. We further show that when the weights are non-descending, the globally optimal solution of WNNM can be obtained in closed-form.
Year
Venue
Field
2014
CoRR
Mathematical optimization,Convexity,Nuclear norm minimization,Singular value,Global optimum,Matrix norm,Image denoising,Quadratic programming,Convex optimization,Mathematics
DocType
Volume
Citations 
Journal
abs/1405.6012
4
PageRank 
References 
Authors
0.40
2
7
Name
Order
Citations
PageRank
Qi Xie131219.42
Deyu Meng22025105.31
Shuhang Gu370128.25
Lei Zhang416326543.99
Wangmeng Zuo53833173.11
Xiangchu Feng6742.38
Zongben Xu73203198.88