Journal
ANNALS OF STATISTICS
Volume 41, Issue 2, Pages 772-801Publisher
INST MATHEMATICAL STATISTICS
DOI: 10.1214/13-AOS1097
Keywords
Dimension reduction; high-dimensional statistics; principal component analysis; principal subspace; sparsity; spiked covariance model; thresholding
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Funding
- Division Of Mathematical Sciences
- Direct For Mathematical & Physical Scien [0906812] Funding Source: National Science Foundation
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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.
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