自动化学报2017，Vol.43Issue(1)：142-151,10.DOI:10.16383/j.aas.2017.c150512
鲁棒的稀疏Lp-模主成分分析
Robust Sparse Lp-norm Principal Component Analysis
摘要
Abstract
Principle component analysis (PCA) is a widely applied dimensionality reduction method. However, the construction of classical PCA is based on L2-norm, which leads to its sensitivity to outliers and noises, as well as sparsity. To solve this problem, the paper proposes a sparse principal component analysis method based on Lp-norm for dimensionality reduction (LpSPCA). In particular, LpSPCA maximizes the Lp-norm variance with sparse regularization term, which ensures the sparseness and robustness while reducing dimensions. LpSPCA can be solved by a simple iterative algorithm, and its convergence is theoretically guaranteed when p≥1. Besides, by choosing a different p, LpSPCA can be used for more types of data sets. Experimental results on both synthetic and human face data sets demonstrate that the proposed LpSPCA not only has better dimensionality reduction ability but also has strong anti-noise property.关键词
主成分分析/稀疏性/鲁棒性/降维/Lp-模Key words
Principal component analysis (PCA)/sparseness/robustness/dimensionality reduction/Lp-norm引用本文复制引用
李春娜,陈伟杰,邵元海..鲁棒的稀疏Lp-模主成分分析[J].自动化学报,2017,43(1):142-151,10.基金项目
Manuscript received August 27,2015 （）
accepted July 11,2016国家自然科学基金(11201426,11371365,11426200,11426202,61603338),浙江省自然科学基金(LQ13F030010, LQ17F030003, LY15 F030013),浙江省教育厅基金(Y201432746)资助Supported by National Natural Science Foundation of China (11201426,11371365,11426200,11426202,61603338), Zhejiang Provincial Natural Science Foundation (LQ13F030010, LQ17F030003, LY15F030013), and Scientific Research Fund of Zhejiang Provincial Education Department (Y201432746) （11201426,11371365,11426200,11426202,61603338）
