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Sparse Subspace Clustering with Missing and Corrupted Data

Abstract: 

In many settings, we can accurately model high-dimensional data as lying in a union of subspaces. Subspace clustering is the process of inferring the subspaces and determining which point belongs to each subspace. In this paper we study a ro- bust variant of sparse subspace clustering (SSC). While SSC is well-understood when there is little or no noise, less is known about SSC under significant noise or missing en- tries. We establish clustering guarantees in the presence of corrupted or missing entries. We give explicit bounds on the amount of additive noise and the number of missing entries the algorithm can tolerate, both in deterministic settings and in a random generative model. Our analysis shows that this method can tolerate up to O(n/d) missing entries per column instead of O(n/d2) as previous analyses show, where we have d-dimensional subspaces in an n-dimensional ambient space. Moreover, our method and analysis work by simply filling in the missing entries with zeros and do not need to know the location of missing entries.

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Paper Details

Authors:
Amin Jalali, Rebecca Willett
Submitted On:
31 May 2018 - 6:30pm
Short Link:
Type:
Presentation Slides
Event:
Presenter's Name:
Zachary Charles
Paper Code:
DSW18001
Document Year:
2018
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sparse_subpsace_clustering_with_missing_and_corrupted_data.pdf

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[1] Amin Jalali, Rebecca Willett, "Sparse Subspace Clustering with Missing and Corrupted Data", IEEE SigPort, 2018. [Online]. Available: http://sigport.org/3227. Accessed: Aug. 21, 2018.
@article{3227-18,
url = {http://sigport.org/3227},
author = {Amin Jalali; Rebecca Willett },
publisher = {IEEE SigPort},
title = {Sparse Subspace Clustering with Missing and Corrupted Data},
year = {2018} }
TY - EJOUR
T1 - Sparse Subspace Clustering with Missing and Corrupted Data
AU - Amin Jalali; Rebecca Willett
PY - 2018
PB - IEEE SigPort
UR - http://sigport.org/3227
ER -
Amin Jalali, Rebecca Willett. (2018). Sparse Subspace Clustering with Missing and Corrupted Data. IEEE SigPort. http://sigport.org/3227
Amin Jalali, Rebecca Willett, 2018. Sparse Subspace Clustering with Missing and Corrupted Data. Available at: http://sigport.org/3227.
Amin Jalali, Rebecca Willett. (2018). "Sparse Subspace Clustering with Missing and Corrupted Data." Web.
1. Amin Jalali, Rebecca Willett. Sparse Subspace Clustering with Missing and Corrupted Data [Internet]. IEEE SigPort; 2018. Available from : http://sigport.org/3227