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	Generalized Nonconvex Nonsmooth Low-Rank Minimization
	Lu, Canyi ; Tang, Jinhui ; Yan, Shuicheng ; Lin, Zhouchen
	2014
英文摘要	As surrogate functions of L-0-norm, many nonconvex penalty functions have been proposed to enhance the sparse vector recovery. It is easy to extend these nonconvex penalty functions on singular values of a matrix to enhance low-rank matrix recovery. However, different from convex optimization, solving the nonconvex low-rank minimization problem is much more challenging than the nonconvex sparse minimization problem. We observe that all the existing nonconvex penalty functions are concave and monotonically increasing on [0, infinity. Thus their gradients are decreasing functions. Based on this property, we propose an Iteratively Reweighted Nuclear Norm (IRNN) algorithm to solve the nonconvex nonsmooth low-rank minimization problem. IRNN iteratively solves a Weighted Singular Value Thresholding (WSVT) problem. By setting the weight vector as the gradient of the concave penalty function, the WSVT problem has a closed form solution. In theory, we prove that IRNN decreases the objective function value monotonically, and any limit point is a stationary point. Extensive experiments on both synthetic data and real images demonstrate that IRNN enhances the low-rank matrix recovery compared with state-of-the-art convex algorithms.; CPCI-S(ISTP); canyilu@gmail.com; jinhuitang@mail.njust.edu.cn; eleyans@nus.edu.sg; zlin@pku.edu.cn; 4130-4137
语种	英语
出处	2014 IEEE CONFERENCE ON COMPUTER VISION AND PATTERN RECOGNITION (CVPR)
DOI标识	10.1109/CVPR.2014.526
内容类型	其他
源URL	[http://ir.pku.edu.cn/handle/20.500.11897/424325]
专题	信息科学技术学院
推荐引用方式 GB/T 7714	Lu, Canyi,Tang, Jinhui,Yan, Shuicheng,et al. Generalized Nonconvex Nonsmooth Low-Rank Minimization. 2014-01-01.

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