Second order accurate distributed eigenvector computation for extremely large matrices

TL;DR

This paper introduces a second-order accurate distributed method for estimating eigenvectors of large matrices, leveraging averaging of subsampled eigenvectors under mild incoherence conditions, with applications in spectral analysis.

Contribution

It presents a novel second-order accurate approach that efficiently approximates eigenvectors of large matrices using subsampling and averaging, applicable to sparse eigenvectors.

Findings

Averaging eigenvectors of subsampled matrices approximates true eigenvectors.

Method works under mild incoherence conditions, allowing for sparse eigenvectors.

Applicable to spectral methods in dimensionality reduction and information retrieval.

Abstract

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.