Główne pojęcia
Comprehensive analysis of singular subspaces under random perturbations in the context of low-rank signal matrices and Gaussian noise.
Streszczenie
The content delves into the analysis of singular vectors and subspaces perturbed by random Gaussian noise, extending classical theorems. It explores perturbation bounds for spectral parameters, emphasizing unitarily invariant norms. The study focuses on low-rank signal matrices and random noise, presenting stochastic variants of established theorems. Applications to Gaussian Mixture Models and submatrix localization are discussed. Results include ℓ8 and ℓ2,8 analyses, linear and bilinear forms exploration, and practical implications for spectral algorithms.
Statystyki
Assuming a low-rank signal matrix A has rank r ≥ 1.
Denote SVD of A as A = UΣV^T.
Perturbation bounds quantify influence of small noise on spectral parameters.
Unitarily invariant matrix norms used for analysis.
Singular subspaces spanned by leading singular vectors are primary focus.
Cytaty
"The goal is to classify observed data into clusters using spectral methods."
"Results extend classical theorems to analyze perturbations in low-rank matrices."
"Applications to Gaussian Mixture Models showcase theoretical performance."