Learning robust principal components from L1-norm maximization

Ding-cheng FENG; Feng CHEN; Wen-li XU

doi:10.1631/jzus.C1200180

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Learning robust principal components from L1-norm maximization

计算机与自动化 | Updated：2022-12-09

- Learning robust principal components from L1-norm maximization
- Learning robust principal components from L1-norm maximization
- 信息与电子工程前沿（英文） 2012年13卷第12期页码：901-908
- Affiliations：
  
  1.Tsinghua National Laboratory for Information Science and Technology, Tsinghua University, Beijing 100084, China
  2.Department of Automation, Tsinghua University, Beijing 100084, China
- Author bio：
  
  [ "Ding-cheng FENG, fdc08@mails.tsinghua.edu.cn" ]
  Feng CHEN, E-mail: fdc08@mails.tsinghua.edu.cn
  [ "Wen-li XU, xuwl@tsinghua.edu.cn" ]
- Funds：
  
  Project supported by the National Natural Science Foundation of China (Nos. 61071131 and 61271388), the Beijing Natural Sci ence Foundation (No. 4122040), the Research Project of Tsinghua University (No. 2012Z01011), and the United Technologies Re search Center (UTRC)
- DOI：10.1631/jzus.C1200180
  中图分类号： TP391.4
- 收稿：2012-06-11，
  
  修回：2012-11-12，
  
  纸质出版：2012-12
- Accepted：
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Learning robust principal components from L1-norm maximization[J]. 信息与电子工程前沿（英文）, 2012,13(12):901-908.

Ding-cheng FENG, Feng CHEN, Wen-li XU. Learning robust principal components from L1-norm maximization[J]. Frontiers of Information Technology & Electronic Engineering, 2012, 13(12): 901-908.
Learning robust principal components from L1-norm maximization[J]. 信息与电子工程前沿（英文）, 2012,13(12):901-908. DOI： 10.1631/jzus.C1200180.

Ding-cheng FENG, Feng CHEN, Wen-li XU. Learning robust principal components from L1-norm maximization[J]. Frontiers of Information Technology & Electronic Engineering, 2012, 13(12): 901-908. DOI： 10.1631/jzus.C1200180.

摘要

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.

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references

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