TY - JOUR
T1 - Robust recovery of subspace structures by low-rank representation
AU - Liu, Guangcan
AU - Lin, Zhouchen
AU - Yan, Shuicheng
AU - Sun, Ju
AU - Yu, Yong
AU - Ma, Yi
PY - 2013
Y1 - 2013
N2 - 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.
AB - 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.
KW - Low-rank representation
KW - outlier detection
KW - segmentation
KW - subspace clustering
UR - http://www.scopus.com/inward/record.url?scp=84870197517&partnerID=8YFLogxK
UR - http://www.scopus.com/inward/citedby.url?scp=84870197517&partnerID=8YFLogxK
U2 - 10.1109/TPAMI.2012.88
DO - 10.1109/TPAMI.2012.88
M3 - Article
C2 - 22487984
AN - SCOPUS:84870197517
SN - 0162-8828
VL - 35
SP - 171
EP - 184
JO - IEEE Transactions on Pattern Analysis and Machine Intelligence
JF - IEEE Transactions on Pattern Analysis and Machine Intelligence
IS - 1
M1 - 6180173
ER -