Noisy Sparse Subspace Clustering

Yu-Xiang Wang, Huan Xu
; Proceedings of the 30th International Conference on Machine Learning, PMLR 28(1):89-97, 2013.

Abstract

This paper considers the problem of subspace clustering under noise. Specifically, we study the behavior of Sparse Subspace Clustering (SSC) when either adversarial or random noise is added to the unlabelled input data points, which are assumed to lie in a union of low-dimensional subspaces. We show that a modified version of SSC is \emphprovably effective in correctly identifying the underlying subspaces, even with noisy data. This extends theoretical guarantee of this algorithm to the practical setting and provides justification to the success of SSC in a class of real applications.

Cite this Paper


BibTeX
@InProceedings{pmlr-v28-wang13, title = {Noisy Sparse Subspace Clustering}, author = {Yu-Xiang Wang and Huan Xu}, booktitle = {Proceedings of the 30th International Conference on Machine Learning}, pages = {89--97}, year = {2013}, editor = {Sanjoy Dasgupta and David McAllester}, volume = {28}, number = {1}, series = {Proceedings of Machine Learning Research}, address = {Atlanta, Georgia, USA}, month = {17--19 Jun}, publisher = {PMLR}, pdf = {http://proceedings.mlr.press/v28/wang13.pdf}, url = {http://proceedings.mlr.press/v28/wang13.html}, abstract = {This paper considers the problem of subspace clustering under noise. Specifically, we study the behavior of Sparse Subspace Clustering (SSC) when either adversarial or random noise is added to the unlabelled input data points, which are assumed to lie in a union of low-dimensional subspaces. We show that a modified version of SSC is \emphprovably effective in correctly identifying the underlying subspaces, even with noisy data. This extends theoretical guarantee of this algorithm to the practical setting and provides justification to the success of SSC in a class of real applications.} }
Endnote
%0 Conference Paper %T Noisy Sparse Subspace Clustering %A Yu-Xiang Wang %A Huan Xu %B Proceedings of the 30th International Conference on Machine Learning %C Proceedings of Machine Learning Research %D 2013 %E Sanjoy Dasgupta %E David McAllester %F pmlr-v28-wang13 %I PMLR %J Proceedings of Machine Learning Research %P 89--97 %U http://proceedings.mlr.press %V 28 %N 1 %W PMLR %X This paper considers the problem of subspace clustering under noise. Specifically, we study the behavior of Sparse Subspace Clustering (SSC) when either adversarial or random noise is added to the unlabelled input data points, which are assumed to lie in a union of low-dimensional subspaces. We show that a modified version of SSC is \emphprovably effective in correctly identifying the underlying subspaces, even with noisy data. This extends theoretical guarantee of this algorithm to the practical setting and provides justification to the success of SSC in a class of real applications.
RIS
TY - CPAPER TI - Noisy Sparse Subspace Clustering AU - Yu-Xiang Wang AU - Huan Xu BT - Proceedings of the 30th International Conference on Machine Learning PY - 2013/02/13 DA - 2013/02/13 ED - Sanjoy Dasgupta ED - David McAllester ID - pmlr-v28-wang13 PB - PMLR SP - 89 DP - PMLR EP - 97 L1 - http://proceedings.mlr.press/v28/wang13.pdf UR - http://proceedings.mlr.press/v28/wang13.html AB - This paper considers the problem of subspace clustering under noise. Specifically, we study the behavior of Sparse Subspace Clustering (SSC) when either adversarial or random noise is added to the unlabelled input data points, which are assumed to lie in a union of low-dimensional subspaces. We show that a modified version of SSC is \emphprovably effective in correctly identifying the underlying subspaces, even with noisy data. This extends theoretical guarantee of this algorithm to the practical setting and provides justification to the success of SSC in a class of real applications. ER -
APA
Wang, Y. & Xu, H.. (2013). Noisy Sparse Subspace Clustering. Proceedings of the 30th International Conference on Machine Learning, in PMLR 28(1):89-97

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