Robust sparse principal component analysis

The model for improving the robustness of sparse principal component analysis（PCA） is proposed in this paper. Instead of the l2-norm variance utilized in the conventional sparse PCA model,the proposed model maximizes the l1-norm variance,which is less sensitive to noise and outlier. To ensure sparsi...

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Bibliographic Details
Published inScience China. Information sciences Vol. 57; no. 9; pp. 171 - 184
Main Authors Zhao, Qian, Meng, DeYu, Xu, ZongBen
Format Journal Article
LanguageEnglish
Published Heidelberg Science China Press 01.09.2014
Springer Nature B.V
Subjects
Algorithms
Computer Science
Information Systems and Communication Service
L1范数
L2范数
Noise sensitivity
Outliers (statistics)
P-范数
PCA方法
PCA模型
Principal components analysis
Research Paper
Robustness
主成分分析
健壮
稀疏
noise
outlier
robustness
sparsity
principal component analysis
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Summary:The model for improving the robustness of sparse principal component analysis（PCA） is proposed in this paper. Instead of the l2-norm variance utilized in the conventional sparse PCA model,the proposed model maximizes the l1-norm variance,which is less sensitive to noise and outlier. To ensure sparsity,lp-norm（0 p 1） constraint,which is more general and effective than l1-norm,is considered. A simple yet efficient algorithm is developed against the proposed model. The complexity of the algorithm approximately linearly increases with both of the size and the dimensionality of the given data,which is comparable to or better than the current sparse PCA methods. The proposed algorithm is also proved to converge to a reasonable local optimum of the model. The efficiency and robustness of the algorithm is verified by a series of experiments on both synthetic and digit number image data.
Bibliography:11-5847/TP
noise; outlier; principal component analysis; robustness; sparsity
The model for improving the robustness of sparse principal component analysis（PCA） is proposed in this paper. Instead of the l2-norm variance utilized in the conventional sparse PCA model,the proposed model maximizes the l1-norm variance,which is less sensitive to noise and outlier. To ensure sparsity,lp-norm（0 p 1） constraint,which is more general and effective than l1-norm,is considered. A simple yet efficient algorithm is developed against the proposed model. The complexity of the algorithm approximately linearly increases with both of the size and the dimensionality of the given data,which is comparable to or better than the current sparse PCA methods. The proposed algorithm is also proved to converge to a reasonable local optimum of the model. The efficiency and robustness of the algorithm is verified by a series of experiments on both synthetic and digit number image data.
ISSN:1674-733X
1869-1919
DOI:10.1007/s11432-013-4970-y