SPARSE PRINCIPAL COMPONENT ANALYSIS AND ITERATIVE THRESHOLDING

被引:184
作者
Ma, Zongming [1 ]
机构
[1] Univ Penn, Wharton Sch, Dept Stat, Philadelphia, PA 19104 USA
基金
美国国家科学基金会;
关键词
Dimension reduction; high-dimensional statistics; principal component analysis; principal subspace; sparsity; spiked covariance model; thresholding; CONSISTENCY; ASYMPTOTICS;
D O I
10.1214/13-AOS1097
中图分类号
O21 [概率论与数理统计]; C8 [统计学];
学科分类号
020208 ; 070103 ; 0714 ;
摘要
Principal component analysis (PCA) is a classical dimension reduction method which projects data onto the principal subspace spanned by the leading eigenvectors of the covariance matrix. However, it behaves poorly when the number of features p is comparable to, or even much larger than, the sample size n. In this paper, we propose a new iterative thresholding approach for estimating principal subspaces in the setting where the leading eigenvectors are sparse. Under a spiked covariance model, we find that the new approach recovers the principal subspace and leading eigenvectors consistently, and even optimally, in a range of high-dimensional sparse settings. Simulated examples also demonstrate its competitive performance.
引用
收藏
页码:772 / 801
页数:30
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