We propose a second-order accurate method to estimate the eigenvectors of
extremely large matrices thereby addressing a problem of relevance to
statisticians working in the analysis of very large datasets. More
specifically, we show that averaging eigenvectors of randomly subsampled
matrices efficiently approximates the true eigenvectors of the original matrix
under certain conditions on the incoherence of the spectral decomposition. This
incoherence assumption is typically milder than those made in matrix completion
and allows eigenvectors to be sparse. We discuss applications to spectral
methods in dimensionality reduction and information retrieval.Comment: Complete proofs are included on averaging performanc