Analysis of singular subspaces under random perturbations

Kavli Affiliate: Ke Wang

| First 5 Authors: Ke Wang, , , ,

| Summary:

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 subspaces, as
well as the exploration of linear and bilinear functions related to the
singular vectors. Moreover, we explore the practical implications of these
findings, in the context of the Gaussian mixture model and the submatrix
localization problem.

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