B0490
Title: Leave-one-out singular subspace perturbation analysis for spectral clustering
Authors: Anderson Ye Zhang - University of Pennsylvania (United States) [presenting]
Abstract: The singular subspaces perturbation theory is of fundamental importance in probability and statistics. It has various applications across different fields. We consider two arbitrary matrices where one is a leave-one-column-out submatrix of the other one and establish a novel perturbation upper bound for the distance between two corresponding singular subspaces. It is well-suited for mixture models and results in a sharper and finer statistical analysis than classical perturbation bounds such as Wedin's Theorem. Powered by this leave-one-out perturbation theory, we provide a deterministic entrywise analysis for the performance of spectral clustering under mixture models. Our analysis leads to an explicit exponential error rate for the clustering of sub-Gaussian mixture models.
