Student or educator? Sign up with your school email and get 6 months of Pro free.
CoChat
Sign Up
Cited by 3,594

The DOI matches its Crossref record; 2 of the 2 references it cites were found in a registry or an index.

Robust Recovery of Subspace Structures by Low-Rank Representation

Open access
Liu, Guangcan, Lin, Zhouchen, Yan, Shuicheng, Sun, Ju, Yu, Yong, Ma, Yi·2013·IEEE Transactions on Pattern Analysis and Machine Intelligence
DOI 10.1109/tpami.2012.88
Open this paper in CoChat — free account

Abstract

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.

Overview

The claims and statistics of this paper haven’t been checked yet.

Run the check — free, no account needed. It reads the open-access text and checks the sources it cites.

A few free checks a day · papers already verified open instantly · results are public

Integrity signals

Registry

Crossref · 10.1109/tpami.2012.88

Cites

2 of 2 references verified0 citation errors · 0 not checkable

Statistics

Verification

Claims the paper makes

The claims and statistics of this paper haven’t been checked yet.

Run the check — free, no account needed. It reads the open-access text and checks the sources it cites.

A few free checks a day · papers already verified open instantly · results are public

Self-check

Percentages, sums and reported differences re-computed from the paper’s own numbers.

The self-check needs the paper’s full text.

Citations

Cites

Research works printed but not linked: 50

  1. 10.1023/A:1008026310903 · doi:10.1023/a:1008026310903
  2. 10.1007/11744085_8 · DOI · Paper page
  3. 10.1109/TPAMI.2009.191 · doi:10.1109/tpami.2009.191
  4. 10.1109/ICCV.2011.6126422 · DOI · Paper page
  5. 10.1109/TPAMI.2007.1085 · DOI · Paper page
  6. 10.1109/JPROC.2009.2035722 · DOI · Paper page
  7. Candès, 2009, Robust Principal Component Analysis?”, J. ACM
  8. 10.1109/CVPR.2003.1211332 · DOI · Paper page
  9. 10.1109/TPAMI.2009.40 · DOI
  10. 10.1016/j.automatica.2005.04.010 · doi:10.1016/j.automatica.2005.04.010
  11. 10.1023/A:1008000628999 · DOI · Paper page
  12. 10.1109/CVPR.2009.5206547 · DOI · Paper page
  13. Liu, Robust Subspace Segmentation by Low-Rank Representation, 663
  14. Soltanolkotabi, 2011, A Geometric Analysis of Subspace Clustering with Outliers, arXiv:1112.4258v2 · arXiv
  15. Xu, 2010, Robust PCA via Outlier Pursuit, Systems Advances in Neural Information Processing Systems, 23, 2496
  16. Fazel, 2002, Matrix Rank Minimization with Applications
  17. 10.1109/ICCV.2011.6126528 · DOI · Paper page
  18. 10.1109/TIP.2011.2169274 · DOI · Paper page
  19. 10.1109/TIT.2009.2030471 · DOI · Paper page
  20. 10.1109/CVPR.2004.1315101 · doi:10.1109/cvpr.2004.1315101
  21. 10.1109/ICCVW.2009.5457695 · DOI
  22. 10.1109/CVPRW.2006.178 · DOI
  23. 10.1137/060655523 · DOI · Paper page
  24. 10.1007/s11263-009-0314-1 · doi:10.1007/s11263-009-0314-1
  25. 10.1109/34.868688 · DOI · Paper page
  26. 10.1007/s11263-008-0178-9 · doi:10.1007/s11263-008-0178-9
  27. 10.1007/s10208-009-9043-7 · doi:10.1007/s10208-009-9043-7
  28. Zhang, 2011, Hybrid Linear Modeling via Local Best-Fit Flats, arXiv:1010.3460 · arXiv
  29. 10.1214/11-EJS651 · DOI
  30. 10.1109/ICCV.2009.5459173 · doi:10.1109/iccv.2009.5459173
  31. 10.1002/cpa.20132 · DOI · Paper page
  32. 10.1109/CVPR.2011.5995679 · doi:10.1109/cvpr.2011.5995679
  33. Lerman, 2011, Robust Recovery of Multiple Subspaces by Geometric $\ell_p$ Minimization, arXiv:1104.3770 · arXiv
  34. Zhang, TILT: Transform Invariant Low-Rank Textures, 10.1007/978-3-642-19318-7_25 · DOI
  35. Lin, 2009, The Augmented Lagrange Multiplier Method for Exact Recovery of Corrupted Low-Rank Matrices
  36. Bertsekas, 1982, Constrained Optimization and Lagrange Multiplier Methods
  37. 10.1137/080738970 · DOI · Paper page
  38. 10.1137/080730421 · DOI · Paper page
  39. Zhang, 2010, Recent Advances in Alternating Direction Methods: Practice and Theory, tutorial
  40. 10.1007/BF01581204 · DOI · Paper page
  41. Wei, 2010, Analysis and Improvement of Low Rank Representation for Subspace Segmentation, arXiv:1107.1561 · arXiv
  42. Liu, Exact Subspace Segmentation and Outlier Detection by Low-Rank Representation
  43. 10.1109/CVPR.2004.1315075 · doi:10.1109/cvpr.2004.1315075
  44. 10.1109/CVPR.2004.1315223 · doi:10.1109/cvpr.2004.1315223
  45. 10.1109/CVPR.2007.382974 · DOI · Paper page
  46. 10.1109/TPAMI.2005.92 · DOI · Paper page
  47. 10.1109/CVPR.2004.383 · DOI · Paper page
  48. Sugaya, 2004, Multi-Stage Unsupervised Learning for Multi-Body Motion Segmentation, IEICE Trans. Information Systems, 1935
  49. 10.1109/CVPR.2007.383235 · DOI · Paper page
  50. 10.1109/CVPR.2011.5995365 · doi:10.1109/cvpr.2011.5995365

Cited by

See all 3,594

Metadata

Authors
Liu, G., Lin, Z., Yan, S., Sun, J., Yu, Y., & Ma, Y.
Venue
IEEE Transactions on Pattern Analysis and Machine Intelligence
Publisher
Institute of Electrical and Electronics Engineers (IEEE)
Published
2013-01
Volume
35
Issue
1
Pages
171-184
ISSN
  • 0162-8828 (ISSN-L)
  • 2160-9292
DOI
10.1109/tpami.2012.88
OpenAlex
W1997201895
Cited by
3,594
References
2
FWCI
128.87
Type
journal article
Language
en
Open access
green
Licence
ieeexplore.ieee.org/Xplorehelp/downloads/license-information/IEEE.html (vor)

About these checks

Registry, retraction, Cites and statistics results are computed, not judged, with one exception: a printed reference that no index lists is read once by a model before it counts as a citation error. Claims are extracted by a model and kept only when their quote appears verbatim in the text; each cited source is then checked, with a model’s help, for whether it says what the claim relies on. Those verdicts can be wrong — read the claim’s quote and the cited source before relying on one.

Statistics and arithmetic are recomputed, not judged.

Confidence bands are shown only for fields calibrated on our annotated test set. None is calibrated yet, so no band is shown.

What counts as a claim ›How we measure confidence ›How we check this ›

Are you an author, or do you see a problem with this page? Request a review

Data sources

Bibliographic data: Semantic Scholar, OpenAlex, Crossref.

Contains information from the Semantic Scholar Academic Graph Datasets, made available under the ODC Attribution License (ODC-BY 1.0).

Semantic Scholar’s data is described in: Kinney, R., et al. (2023). The Semantic Scholar Open Data Platform. arXiv:2301.10140.