Sparse principal component analysis and iterative thresholding
The Annals of Statistics · 2013 · Volume 41 · Issue 2
Abstract
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.
Keywords
62G20, 62H12, 62H25, Dimension reduction, High-dimensional statistics, Principal Component Analysis, principal subspace, Sparsity, spiked covariance model, thresholding
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