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CLC number: TP391.4

On-line Access: 2012-12-09

Received: 2012-06-11

Revision Accepted: 2012-11-12

Crosschecked: 2012-11-12

Cited: 2

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Journal of Zhejiang University SCIENCE C 2012 Vol.13 No.12 P.901-908

10.1631/jzus.C1200180


Learning robust principal components from L1-norm maximization


Author(s):  Ding-cheng Feng, Feng Chen, Wen-li Xu

Affiliation(s):  Tsinghua National Laboratory for Information Science and Technology, Tsinghua University, Beijing 100084, China; more

Corresponding email(s):   fdc08@mails.tsinghua.edu.cn, chenfeng@tsinghua.edu.cn, xuwl@tsinghua.edu.cn

Key Words:  Principal component analysis (PCA), Outliers, L1-norm, Greedy algorithms, Non-greedy algorithms


Ding-cheng Feng, Feng Chen, Wen-li Xu. Learning robust principal components from L1-norm maximization[J]. Journal of Zhejiang University Science C, 2012, 13(12): 901-908.

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Abstract: 
principal component analysis (PCA) is fundamental in many pattern recognition applications. Much research has been performed to minimize the reconstruction error in l1-norm based reconstruction error minimization (L1-PCA-REM) since conventional L2-norm based PCA (L2-PCA) is sensitive to outliers. Recently, the variance maximization formulation of PCA with l1-norm (L1-PCA-VM) has been proposed, where new greedy and non-greedy solutions are developed. Armed with the gradient ascent perspective for optimization, we show that the L1-PCA-VM formulation is problematic in learning principal components and that only a greedy solution can achieve robustness motivation, which are verified by experiments on synthetic and real-world datasets.

Darkslateblue:Affiliate; Royal Blue:Author; Turquoise:Article

Reference

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