Document Detail

Fast and Accurate Matrix Completion via Truncated Nuclear Norm Regularization.
MedLine Citation:
PMID:  23868774     Owner:  NLM     Status:  In-Data-Review    
Recovering a large matrix from a small subset of its entries is a challenging problem arising in many real applications, such as image inpainting and recommender systems. Many existing approaches formulate this problem as a general low-rank matrix approximation problem. Since the rank operator is nonconvex and discontinuous, most of the recent theoretical studies use the nuclear norm as a convex relaxation. One major limitation of the existing approaches based on nuclear norm minimization is that all the singular values are simultaneously minimized, and thus the rank may not be well approximated in practice. In this paper, we propose to achieve a better approximation to the rank of matrix by truncated nuclear norm, which is given by the nuclear norm subtracted by the sum of the largest few singular values. In addition, we develop a novel matrix completion algorithm by minimizing the Truncated Nuclear Norm. We further develop three efficient iterative procedures, TNNR-ADMM, TNNR-APGL, and TNNR-ADMMAP, to solve the optimization problem. TNNR-ADMM utilizes the alternating direction method of multipliers (ADMM), while TNNR-AGPL applies the accelerated proximal gradient line search method (APGL) for the final optimization. For TNNR-ADMMAP, we make use of an adaptive penalty according to a novel update rule for ADMM to achieve a faster convergence rate. Our empirical study shows encouraging results of the proposed algorithms in comparison to the state-of-the-art matrix completion algorithms on both synthetic and real visual datasets.
Yao Hu; Debing Zhang; Jieping Ye; Xuelong Li; Xiaofei He
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Publication Detail:
Type:  Journal Article    
Journal Detail:
Title:  IEEE transactions on pattern analysis and machine intelligence     Volume:  35     ISSN:  1939-3539     ISO Abbreviation:  IEEE Trans Pattern Anal Mach Intell     Publication Date:  2013 Sep 
Date Detail:
Created Date:  2013-07-22     Completed Date:  -     Revised Date:  -    
Medline Journal Info:
Nlm Unique ID:  9885960     Medline TA:  IEEE Trans Pattern Anal Mach Intell     Country:  United States    
Other Details:
Languages:  eng     Pagination:  2117-30     Citation Subset:  IM    
Zhejiang University, Hangzhou.
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