Robust sparse principal component analysis  

作　　者：ZHAO Qian MENG DeYu XU ZongBen 

机构地区：[1]Institute for Information and System Sciences,School of Mathematics and Statistics,Xi'an Jiaotong University [2]Ministry of Education Key Lab for Intelligent Networks and Network Security,Xi'an Jiaotong University

出　　处：《Science China(Information Sciences)》2014年第9期171-184,共14页中国科学（信息科学）（英文版）

基　　金：supported by National Basic Research Program of China(973)(Grant No.2013CB329404);National Natural Science Foundation of China(Grant Nos.61373114,11131006)

摘　　要：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.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.

关 键 词：noise OUTLIER principal component analysis ROBUSTNESS SPARSITY 

分 类 号：TP274.2[自动化与计算机技术—检测技术与自动化装置]