Title: An exact sinΘ formula for matrix perturbation analysis and its applications.
Abstract: In this paper, we establish a useful set of formulae for the $\sin\Theta$ distance between the original and the perturbed singular subspaces. These formulae explicitly show that how the perturbation of the original matrix propagates into singular vectors and singular subspaces, thus providing a direct way of analyzing them. Following this, we derive a collection of new results on SVD perturbation related problems, including a tighter bound on the $\ell_{2,\infty}$ norm of the singular vector perturbation errors under Gaussian noise, a new stability analysis of the Principal Component Analysis and an error bound on the singular value thresholding operator. For the latter two, we consider the most general rectangular matrices with full matrix rank.
Publication Year: 2020
Publication Date: 2020-11-16
Language: en
Type: preprint
Access and Citation
Cited By Count: 2
AI Researcher Chatbot
Get quick answers to your questions about the article from our AI researcher chatbot