Analysis of singular subspaces under random perturbations

arXiv:2403.09170v1 Announce Type: cross
Abstract: We present a comprehensive analysis of singular vector and singular subspace perturbations in the context of the signal plus random Gaussian noise matrix model. Assuming a low-rank signal matrix, we extend the Wedin-Davis-Kahan theorem in a fully generalized manner, applicable to any unitarily invariant matrix norm, extending previous results of O'Rourke, Vu and the author. We also obtain the fine-grained results, which encompass the $\ell_\infty$ analysis of singular vectors, the $\ell_{2, \infty}$ analysis of singular …

abstract analysis arxiv context cs.na davis generalized low math.na math.pr math.st matrix noise norm random signal singular stat.ml stat.th theorem type vector