Exact Subspace Segmentation and Outlier Detection by Low-Rank Representation

Guangcan Liu, Huan Xu, Shuicheng Yan
Proceedings of the Fifteenth International Conference on Artificial Intelligence and Statistics, PMLR 22:703-711, 2012.

Abstract

In this work, we address the following matrix recovery problem: suppose we are given a set of data points containing two parts, one part consists of samples drawn from a union of multiple subspaces and the other part consists of outliers. We do not know which data points are outliers, or how many outliers there are. The rank and number of the subspaces are unknown either. Can we detect the outliers and segment the samples into their right subspaces, efficiently and exactly? We utilize a so-called Low-Rank Representation (LRR) method to solve this problem, and prove that under mild technical conditions, any solution to LRR exactly recover the row space of the samples and detect the outliers as well. Since the subspace membership is provably determined by the row space, this further implies that LRR can perform exact subspace segmentation and outlier detection, in an efficient way.

Cite this Paper

BibTeX
@InProceedings{pmlr-v22-liu12a, title = {Exact Subspace Segmentation and Outlier Detection by Low-Rank Representation}, author = {Liu, Guangcan and Xu, Huan and Yan, Shuicheng}, booktitle = {Proceedings of the Fifteenth International Conference on Artificial Intelligence and Statistics}, pages = {703--711}, year = {2012}, editor = {Lawrence, Neil D. and Girolami, Mark}, volume = {22}, series = {Proceedings of Machine Learning Research}, address = {La Palma, Canary Islands}, month = {21--23 Apr}, publisher = {PMLR}, pdf = {http://proceedings.mlr.press/v22/liu12a/liu12a.pdf}, url = {https://proceedings.mlr.press/v22/liu12a.html}, abstract = {In this work, we address the following matrix recovery problem: suppose we are given a set of data points containing two parts, one part consists of samples drawn from a union of multiple subspaces and the other part consists of outliers. We do not know which data points are outliers, or how many outliers there are. The rank and number of the subspaces are unknown either. Can we detect the outliers and segment the samples into their right subspaces, efficiently and exactly? We utilize a so-called Low-Rank Representation (LRR) method to solve this problem, and prove that under mild technical conditions, any solution to LRR exactly recover the row space of the samples and detect the outliers as well. Since the subspace membership is provably determined by the row space, this further implies that LRR can perform exact subspace segmentation and outlier detection, in an efficient way.} }
Endnote
%0 Conference Paper %T Exact Subspace Segmentation and Outlier Detection by Low-Rank Representation %A Guangcan Liu %A Huan Xu %A Shuicheng Yan %B Proceedings of the Fifteenth International Conference on Artificial Intelligence and Statistics %C Proceedings of Machine Learning Research %D 2012 %E Neil D. Lawrence %E Mark Girolami %F pmlr-v22-liu12a %I PMLR %P 703--711 %U https://proceedings.mlr.press/v22/liu12a.html %V 22 %X In this work, we address the following matrix recovery problem: suppose we are given a set of data points containing two parts, one part consists of samples drawn from a union of multiple subspaces and the other part consists of outliers. We do not know which data points are outliers, or how many outliers there are. The rank and number of the subspaces are unknown either. Can we detect the outliers and segment the samples into their right subspaces, efficiently and exactly? We utilize a so-called Low-Rank Representation (LRR) method to solve this problem, and prove that under mild technical conditions, any solution to LRR exactly recover the row space of the samples and detect the outliers as well. Since the subspace membership is provably determined by the row space, this further implies that LRR can perform exact subspace segmentation and outlier detection, in an efficient way.
RIS
TY - CPAPER TI - Exact Subspace Segmentation and Outlier Detection by Low-Rank Representation AU - Guangcan Liu AU - Huan Xu AU - Shuicheng Yan BT - Proceedings of the Fifteenth International Conference on Artificial Intelligence and Statistics DA - 2012/03/21 ED - Neil D. Lawrence ED - Mark Girolami ID - pmlr-v22-liu12a PB - PMLR DP - Proceedings of Machine Learning Research VL - 22 SP - 703 EP - 711 L1 - http://proceedings.mlr.press/v22/liu12a/liu12a.pdf UR - https://proceedings.mlr.press/v22/liu12a.html AB - In this work, we address the following matrix recovery problem: suppose we are given a set of data points containing two parts, one part consists of samples drawn from a union of multiple subspaces and the other part consists of outliers. We do not know which data points are outliers, or how many outliers there are. The rank and number of the subspaces are unknown either. Can we detect the outliers and segment the samples into their right subspaces, efficiently and exactly? We utilize a so-called Low-Rank Representation (LRR) method to solve this problem, and prove that under mild technical conditions, any solution to LRR exactly recover the row space of the samples and detect the outliers as well. Since the subspace membership is provably determined by the row space, this further implies that LRR can perform exact subspace segmentation and outlier detection, in an efficient way. ER -
APA
Liu, G., Xu, H. & Yan, S.. (2012). Exact Subspace Segmentation and Outlier Detection by Low-Rank Representation. Proceedings of the Fifteenth International Conference on Artificial Intelligence and Statistics, in Proceedings of Machine Learning Research 22:703-711 Available from https://proceedings.mlr.press/v22/liu12a.html.

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