R 1-PCA: Rotational invariant L 1-norm principal component analysis for robust subspace factorization

Chris Ding; Ding Zhou; Xiaofeng He; Hongyuan Zha

R ₁-PCA: Rotational invariant L ₁-norm principal component analysis for robust subspace factorization

Chris Ding^*
, Ding Zhou
, Xiaofeng He
, Hongyuan Zha

^*Corresponding author for this work

Lawrence Berkeley National Laboratory
Pennsylvania State University

Research output: Chapter in Book/Report/Conference proceeding › Conference contribution › peer-review

241 Scopus citations

Abstract

Principal component analysis (PCA) minimizes the sum of squared errors (L ₂-norm) and is sensitive to the presence of outliers. We propose a rotational invariant L ₁-norm PCA (R ₁-PCA). R ₁-PCA is similar to PCA in that (1) it has a unique global solution, (2) the solution are principal eigenvectors of a robust covariance matrix (re-weighted to soften the effects of outliers), (3) the solution is rotational invariant. These properties are not shared by the Li-norm PCA. A new subspace iteration algorithm is given to compute R ₁-PCA efficiently. Experiments on several real-life datasets show R ₁-PCA can effectively handle outliers. We extend R ₁-norm to K-means clustering and show that L ₁-norm K-means leads to poor results while R ₁-K-means outperforms standard K-means.

Original language	English
Title of host publication	ICML 2006 - Proceedings of the 23rd International Conference on Machine Learning
Pages	281-288
Number of pages	8
State	Published - 2006
Externally published	Yes
Event	ICML 2006: 23rd International Conference on Machine Learning - Pittsburgh, PA, United States Duration: 25 Jun 2006 → 29 Jun 2006

Publication series

Name	ICML 2006 - Proceedings of the 23rd International Conference on Machine Learning
Volume	2006

Conference

Conference	ICML 2006: 23rd International Conference on Machine Learning
Country/Territory	United States
City	Pittsburgh, PA
Period	25/06/06 → 29/06/06

Cite this

@inproceedings{3cfd0a9fc7cd4a859899d84743ee55bb,

title = "R 1-PCA: Rotational invariant L 1-norm principal component analysis for robust subspace factorization",

abstract = "Principal component analysis (PCA) minimizes the sum of squared errors (L 2-norm) and is sensitive to the presence of outliers. We propose a rotational invariant L 1-norm PCA (R 1-PCA). R 1-PCA is similar to PCA in that (1) it has a unique global solution, (2) the solution are principal eigenvectors of a robust covariance matrix (re-weighted to soften the effects of outliers), (3) the solution is rotational invariant. These properties are not shared by the Li-norm PCA. A new subspace iteration algorithm is given to compute R 1-PCA efficiently. Experiments on several real-life datasets show R 1-PCA can effectively handle outliers. We extend R 1-norm to K-means clustering and show that L 1-norm K-means leads to poor results while R 1-K-means outperforms standard K-means.",

author = "Chris Ding and Ding Zhou and Xiaofeng He and Hongyuan Zha",

year = "2006",

language = "英语",

isbn = "1595933832",

series = "ICML 2006 - Proceedings of the 23rd International Conference on Machine Learning",

pages = "281--288",

booktitle = "ICML 2006 - Proceedings of the 23rd International Conference on Machine Learning",

note = "ICML 2006: 23rd International Conference on Machine Learning ; Conference date: 25-06-2006 Through 29-06-2006",

}

Ding, C, Zhou, D, He, X & Zha, H 2006, R ₁-PCA: Rotational invariant L ₁-norm principal component analysis for robust subspace factorization. in ICML 2006 - Proceedings of the 23rd International Conference on Machine Learning. ICML 2006 - Proceedings of the 23rd International Conference on Machine Learning, vol. 2006, pp. 281-288, ICML 2006: 23rd International Conference on Machine Learning, Pittsburgh, PA, United States, 25/06/06.

R ₁-PCA: Rotational invariant L ₁-norm principal component analysis for robust subspace factorization. / Ding, Chris; Zhou, Ding; He, Xiaofeng et al.
ICML 2006 - Proceedings of the 23rd International Conference on Machine Learning. 2006. p. 281-288 (ICML 2006 - Proceedings of the 23rd International Conference on Machine Learning; Vol. 2006).

Research output: Chapter in Book/Report/Conference proceeding › Conference contribution › peer-review

TY - GEN

T1 - R 1-PCA

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AU - Ding, Chris

AU - Zhou, Ding

AU - He, Xiaofeng

AU - Zha, Hongyuan

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N2 - Principal component analysis (PCA) minimizes the sum of squared errors (L 2-norm) and is sensitive to the presence of outliers. We propose a rotational invariant L 1-norm PCA (R 1-PCA). R 1-PCA is similar to PCA in that (1) it has a unique global solution, (2) the solution are principal eigenvectors of a robust covariance matrix (re-weighted to soften the effects of outliers), (3) the solution is rotational invariant. These properties are not shared by the Li-norm PCA. A new subspace iteration algorithm is given to compute R 1-PCA efficiently. Experiments on several real-life datasets show R 1-PCA can effectively handle outliers. We extend R 1-norm to K-means clustering and show that L 1-norm K-means leads to poor results while R 1-K-means outperforms standard K-means.

AB - Principal component analysis (PCA) minimizes the sum of squared errors (L 2-norm) and is sensitive to the presence of outliers. We propose a rotational invariant L 1-norm PCA (R 1-PCA). R 1-PCA is similar to PCA in that (1) it has a unique global solution, (2) the solution are principal eigenvectors of a robust covariance matrix (re-weighted to soften the effects of outliers), (3) the solution is rotational invariant. These properties are not shared by the Li-norm PCA. A new subspace iteration algorithm is given to compute R 1-PCA efficiently. Experiments on several real-life datasets show R 1-PCA can effectively handle outliers. We extend R 1-norm to K-means clustering and show that L 1-norm K-means leads to poor results while R 1-K-means outperforms standard K-means.

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SN - 1595933832

SN - 9781595933836

T3 - ICML 2006 - Proceedings of the 23rd International Conference on Machine Learning

SP - 281

EP - 288

BT - ICML 2006 - Proceedings of the 23rd International Conference on Machine Learning

Y2 - 25 June 2006 through 29 June 2006

ER -

R ₁-PCA: Rotational invariant L ₁-norm principal component analysis for robust subspace factorization

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