  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.
