Singular Vector Perturbation under Gaussian Noise

TL;DR

This paper analyzes how Gaussian noise affects the distribution of singular vectors in matrices, providing conditions for near-normality which aids in understanding errors in linear dimension reduction.

Contribution

It offers a non-asymptotic analysis with sufficient conditions for singular vectors to be approximately normally distributed under Gaussian noise.

Findings

Singular vectors can have near-normal distribution under certain conditions.

The analysis helps improve error estimation in linear dimension reduction.

Provides a framework for understanding singular vector behavior in noisy environments.

Abstract

We perform a non-asymptotic analysis on the singular vector distribution under Gaussian noise. In particular, we provide sufficient conditions on a matrix for its first few singular vectors to have near normal distribution. Our result can be used to facilitate the error analysis in linear dimension reduction.