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arXiv · 1112.2432

Sparse principal component analysis and iterative thresholding

Zongming Ma
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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.

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Zongming Ma. 2013-05-24. Sparse principal component analysis and iterative thresholding. https://doi.org/10.1214/13-aos1097

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