|
Activity Number:
|
373
- Recent Advances in Complex and High-Dimensional Data
|
|
Type:
|
Topic Contributed
|
|
Date/Time:
|
Wednesday, August 10, 2022 : 8:30 AM to 10:20 AM
|
|
Sponsor:
|
IMS
|
|
Abstract #322739
|
|
|
Title:
|
Leave-One-Out Singular Subspace Perturbation Analysis for Spectral Clustering
|
|
Author(s):
|
Harrison Zhou*
|
|
Companies:
|
Yale University
|
|
Keywords:
|
Spectral method;
clustering;
Leave-one-out;
minimax estimation;
Gaussian mixtures
|
|
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’sTheorem. Powered by this leave-one-out perturbation theory, we provide a deterministic entrywise analysis for the performance of the spectral clustering under mixture models. Our analysis leads to an explicit exponential error rate for the clustering of sub-Gaussian mixture models. For the mixture of isotropic Gaussians, the rate is optimal under a weaker signal-to-noise condition than that of Löffler et al. (2021).
|
Authors who are presenting talks have a * after their name.
Back to the full JSM 2022 program
|
