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Mathematical Problems in Engineering
Volume 2014, Article ID 439417, 10 pages
Research Article

Low-Rank Representation for Incomplete Data

1School of Science, Xi’an University of Architecture and Technology, Xi’an 710055, China
2School of Mathematics and Computer Science, Shaanxi University of Technology, Hanzhong 723001, China

Received 20 August 2014; Revised 25 November 2014; Accepted 19 December 2014; Published 31 December 2014

Academic Editor: Wanquan Liu

Copyright © 2014 Jiarong Shi et al. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.


Low-rank matrix recovery (LRMR) has been becoming an increasingly popular technique for analyzing data with missing entries, gross corruptions, and outliers. As a significant component of LRMR, the model of low-rank representation (LRR) seeks the lowest-rank representation among all samples and it is robust for recovering subspace structures. This paper attempts to solve the problem of LRR with partially observed entries. Firstly, we construct a nonconvex minimization by taking the low rankness, robustness, and incompletion into consideration. Then we employ the technique of augmented Lagrange multipliers to solve the proposed program. Finally, experimental results on synthetic and real-world datasets validate the feasibility and effectiveness of the proposed method.