Robust Recovery of Subspace Structures by Low-Rank Representation

doi:10.1109/TPAMI.2012.88

CORC > 北京大学 > 信息科学技术学院

	Robust Recovery of Subspace Structures by Low-Rank Representation
	Liu, Guangcan ; Lin, Zhouchen ; Yan, Shuicheng ; Sun, Ju ; Yu, Yong ; Ma, Yi
刊名	ieee模式分析与机器智能汇刊
	2013
关键词	Low-rank representation subspace clustering segmentation outlier detection MOTION SEGMENTATION MULTIBODY FACTORIZATION MATRIX COMPLETION GPCA ALGORITHM MIXED DATA OBJECTS
DOI	10.1109/TPAMI.2012.88
英文摘要	In this paper, we address the subspace clustering problem. Given a set of data samples (vectors) approximately drawn from a union of multiple subspaces, our goal is to cluster the samples into their respective subspaces and remove possible outliers as well. To this end, we propose a novel objective function named Low-Rank Representation (LRR), which seeks the lowest rank representation among all the candidates that can represent the data samples as linear combinations of the bases in a given dictionary. It is shown that the convex program associated with LRR solves the subspace clustering problem in the following sense: When the data is clean, we prove that LRR exactly recovers the true subspace structures; when the data are contaminated by outliers, we prove that under certain conditions LRR can exactly recover the row space of the original data and detect the outlier as well; for data corrupted by arbitrary sparse errors, LRR can also approximately recover the row space with theoretical guarantees. Since the subspace membership is provably determined by the row space, these further imply that LRR can perform robust subspace clustering and error correction in an efficient and effective way.; Computer Science, Artificial Intelligence; Engineering, Electrical & Electronic; SCI(E); 101; ARTICLE; 1; 171-184; 35
语种	英语
内容类型	期刊论文
源URL	[http://ir.pku.edu.cn/handle/20.500.11897/228310]
专题	信息科学技术学院
推荐引用方式 GB/T 7714	Liu, Guangcan,Lin, Zhouchen,Yan, Shuicheng,et al. Robust Recovery of Subspace Structures by Low-Rank Representation[J]. ieee模式分析与机器智能汇刊,2013.
APA	Liu, Guangcan,Lin, Zhouchen,Yan, Shuicheng,Sun, Ju,Yu, Yong,&Ma, Yi.(2013).Robust Recovery of Subspace Structures by Low-Rank Representation.ieee模式分析与机器智能汇刊.
MLA	Liu, Guangcan,et al."Robust Recovery of Subspace Structures by Low-Rank Representation".ieee模式分析与机器智能汇刊 (2013).