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Article

Optimal mean robust principal component analysis

Authors:

Heng HuangAuthors Info & Claims

ICML'14: Proceedings of the 31st International Conference on International Conference on Machine Learning - Volume 32

Pages II-1062 - II-1070

Published: 21 June 2014 Publication History

Abstract

Principal Component Analysis (PCA) is the most widely used unsupervised dimensionality reduction approach. In recent research, several robust PCA algorithms were presented to enhance the robustness of PCA model. However, the existing robust PCA methods incorrectly center the data using the l₂-norm distance to calculate the mean, which actually is not the optimal mean due to the l₁-norm used in the objective functions. In this paper, we propose novel robust PCA objective functions with removing optimal mean automatically. Both theoretical analysis and empirical studies demonstrate our new methods can more effectively reduce data dimensionality than previous robust PCA methods.

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Cited By

Tian LNie FWang RLi XLarochelle HRanzato MHadsell RBalcan MLin H(2020)Learning feature sparse principal subspaceProceedings of the 34th International Conference on Neural Information Processing Systems10.5555/3495724.3496981(14997-15008)Online publication date: 6-Dec-2020
https://dl.acm.org/doi/10.5555/3495724.3496981
Zhang RTong HWallach HLarochelle HBeygelzimer Ad'Alché-Buc FFox E(2019)Robust principal component analysis with adaptive neighborsProceedings of the 33rd International Conference on Neural Information Processing Systems10.5555/3454287.3454912(6961-6969)Online publication date: 8-Dec-2019
https://dl.acm.org/doi/10.5555/3454287.3454912
Dan CWang HZhang HZhou YRavikumar PWallach HLarochelle HBeygelzimer Ad'Alché-Buc FFox E(2019)Optimal analysis of subset-selection based ℓ low-rank approximationProceedings of the 33rd International Conference on Neural Information Processing Systems10.5555/3454287.3454515(2541-2552)Online publication date: 8-Dec-2019
https://dl.acm.org/doi/10.5555/3454287.3454515
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Optimal mean robust principal component analysis
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ICML'14: Proceedings of the 31st International Conference on International Conference on Machine Learning - Volume 32

June 2014

2786 pages

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JMLR.org

Publication History

Published: 21 June 2014

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Cited By

Tian LNie FWang RLi XLarochelle HRanzato MHadsell RBalcan MLin H(2020)Learning feature sparse principal subspaceProceedings of the 34th International Conference on Neural Information Processing Systems10.5555/3495724.3496981(14997-15008)Online publication date: 6-Dec-2020
https://dl.acm.org/doi/10.5555/3495724.3496981
Zhang RTong HWallach HLarochelle HBeygelzimer Ad'Alché-Buc FFox E(2019)Robust principal component analysis with adaptive neighborsProceedings of the 33rd International Conference on Neural Information Processing Systems10.5555/3454287.3454912(6961-6969)Online publication date: 8-Dec-2019
https://dl.acm.org/doi/10.5555/3454287.3454912
Dan CWang HZhang HZhou YRavikumar PWallach HLarochelle HBeygelzimer Ad'Alché-Buc FFox E(2019)Optimal analysis of subset-selection based ℓ low-rank approximationProceedings of the 33rd International Conference on Neural Information Processing Systems10.5555/3454287.3454515(2541-2552)Online publication date: 8-Dec-2019
https://dl.acm.org/doi/10.5555/3454287.3454515
Ban FBhattiprolu VBringmann KKolev PLee EWoodruff DChan T(2019)A PTAS for ℓ-low rank approximationProceedings of the Thirtieth Annual ACM-SIAM Symposium on Discrete Algorithms10.5555/3310435.3310482(747-766)Online publication date: 6-Jan-2019
https://dl.acm.org/doi/10.5555/3310435.3310482
Huang CAbeo TShen X(2019)Manifold Alignment with Multi-graph EmbeddingProceedings of the 1st ACM International Conference on Multimedia in Asia10.1145/3338533.3366588(1-6)Online publication date: 15-Dec-2019
https://dl.acm.org/doi/10.1145/3338533.3366588
Mi JZhu QLu J(2019)Principal component analysis based on block-norm minimizationApplied Intelligence10.1007/s10489-018-1382-049:6(2169-2177)Online publication date: 1-Jun-2019
https://dl.acm.org/doi/10.1007/s10489-018-1382-0
Wan MYang GSun CLiu M(2019)Sparse two-dimensional discriminant locality-preserving projection (S2DDLPP) for feature extractionSoft Computing - A Fusion of Foundations, Methodologies and Applications10.1007/s00500-018-3207-923:14(5511-5518)Online publication date: 1-Jul-2019
https://dl.acm.org/doi/10.1007/s00500-018-3207-9
Zhu XLei CYu HLi YGan JZhang S(2018)Robust graph dimensionality reductionProceedings of the 27th International Joint Conference on Artificial Intelligence10.5555/3304889.3305113(3257-3263)Online publication date: 13-Jul-2018
https://dl.acm.org/doi/10.5555/3304889.3305113
Fang YLi YLei CLi YDeng X(2018)Hypergraph expressing low-rank feature selection algorithmMultimedia Tools and Applications10.5555/3288251.328828977:22(29551-29572)Online publication date: 1-Nov-2018
https://dl.acm.org/doi/10.5555/3288251.3288289
Lu GLi BYang WYin J(2018)Unsupervised feature selection with graph learning via low-rank constraintMultimedia Tools and Applications10.5555/3288251.328828777:22(29531-29549)Online publication date: 1-Nov-2018
https://dl.acm.org/doi/10.5555/3288251.3288287
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