NDLI: Generalized Nonconvex Nonsmooth Low-Rank Minimization

Content Provider	IEEE Xplore Digital Library
Author	Canyi Lu Jinhui Tang Shuicheng Yan Zhouchen Lin
Copyright Year	2014
Description	Author affiliation: Dept. of Electr. & Comput. Eng., Nat. Univ. of Singapore, Singapore, Singapore (Canyi Lu; Shuicheng Yan) \|\| Key Lab. of Machine Perception (MOE), Peking Univ., Beijing, China (Zhouchen Lin) \|\| Sch. of Comput. Sci., Nanjing Univ. of Sci. & Technol., Nanjing, China (Jinhui Tang)
Abstract	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, ∞). 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.
Starting Page	4130
Ending Page	4137
File Size	1169719
Page Count	8
File Format	PDF
ISBN	9781479951185
ISSN	10636919
DOI	10.1109/CVPR.2014.526
Language	English
Publisher	Institute of Electrical and Electronics Engineers, Inc. (IEEE)
Publisher Date	2014-06-23
Publisher Place	USA
Access Restriction	Subscribed
Rights Holder	Institute of Electrical and Electronics Engineers, Inc. (IEEE)
Subject Keyword	Minimization Educational institutions Convex functions Vectors Programming Convergence Algorithm design and analysis
Content Type	Text
Resource Type	Article
Subject	Computer Vision and Pattern Recognition Software

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