NDLI: Matrix completion by Truncated Nuclear Norm Regularization

Content Provider	IEEE Xplore Digital Library
Author	Debing Zhang Yao Hu Jieping Ye Xuelong Li Xiaofei He
Copyright Year	2012
Description	Author affiliation: Arizona University Tempe, AZ 85287 (Jieping Ye) \|\| Center for OPTical IMagery Analysis and Learning (OPTIMAL), State Key Laboratory of Transient Optics and Photonics, Xi'an Institute of Optics and Precision Mechanics, Chinese Academy of Sciences, Xi'an 710119, Shaanxi, China (Xuelong Li) \|\| State Key Lab of CAD&CG, Zhejiang University, Hangzhou, China (Debing Zhang; Yao Hu; Xiaofei He)
Abstract	Estimating missing values in visual data is a challenging problem in computer vision, which can be considered as a low rank matrix approximation problem. Most of the recent studies use the nuclear norm as a convex relaxation of the rank operator. However, by minimizing the nuclear norm, all the singular values are simultaneously minimized, and thus the rank can not be well approximated in practice. In this paper, we propose a novel matrix completion algorithm based on the Truncated Nuclear Norm Regularization (TNNR) by only minimizing the smallest N-r singular values, where N is the number of singular values and r is the rank of the matrix. In this way, the rank of the matrix can be better approximated than the nuclear norm. We further develop an efficient iterative procedure to solve the optimization problem by using the alternating direction method of multipliers and the accelerated proximal gradient line search method. Experimental results in a wide range of applications demonstrate the effectiveness of our proposed approach.
Starting Page	2192
Ending Page	2199
File Size	382724
Page Count	8
File Format	PDF
ISBN	9781467312264
ISSN	10636919
e-ISBN	9781467312288
e-ISBN	9781467312271
DOI	10.1109/CVPR.2012.6247927
Language	English
Publisher	Institute of Electrical and Electronics Engineers, Inc. (IEEE)
Publisher Date	2012-06-16
Publisher Place	USA
Access Restriction	Subscribed
Rights Holder	Institute of Electrical and Electronics Engineers, Inc. (IEEE)
Subject Keyword	Optimization Approximation methods Educational institutions Minimization Convergence Visualization Acceleration
Content Type	Text
Resource Type	Article
Subject	Computer Vision and Pattern Recognition Software

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