SINGULAR VECTOR PERTURBATION UNDER GAUSSIAN NOISE

被引：21
|
作者：
Wang, Rongrong [1 ]
机构：
[1] Univ British Columbia, Dept Math, Vancouver, BC V6T 1Z2, Canada
来源：
SIAM JOURNAL ON MATRIX ANALYSIS AND APPLICATIONS | 2015年 / 36卷 / 01期
关键词：
singular value decomposition; singular vector; Gaussian noise; nonasymptotic analysis; MODULATION CLASSIFICATION;
D O I：
10.1137/130938177
中图分类号：
O29 [应用数学];
学科分类号：
070104 ;
摘要：
We perform a nonasymptotic analysis on the singular vector distribution under Gaussian noise. In particular, we provide sufficient conditions on a matrix for its first few singular vectors to have near normal distribution. Our result can be used to facilitate the error analysis in linear dimension reduction.
引用
收藏
页码：158 / 177
页数：20
相关论文
共 50 条
  • [1] Perturbation of Linear Forms of Singular Vectors Under Gaussian Noise
    Koltchinskii, Vladimir
    Xia, Dong
    HIGH DIMENSIONAL PROBABILITY VII: THE CARGESE VOLUME, 2016, 71 : 397 - 423
  • [2] Matrices With Gaussian Noise: Optimal Estimates for Singular Subspace Perturbation
    O'Rourke, Sean
    Vu, Van
    Wang, Ke
    IEEE TRANSACTIONS ON INFORMATION THEORY, 2024, 70 (03) : 1978 - 2002
  • [3] Optimality of singular vector perturbation under maximum norm
    Liu, Youming
    Qi, Xinyu
    MATHEMATICAL METHODS IN THE APPLIED SCIENCES, 2020, 43 (08) : 5010 - 5018
  • [4] Renormalization group method for singular perturbation system with additive fractional Gaussian noise
    Guo, Lihong
    Qu, Shiduo
    Shi, Shaoyun
    STOCHASTIC ANALYSIS AND APPLICATIONS, 2025, 43 (01) : 48 - 76
  • [5] On Estimating the Norm of a Gaussian Vector Under Additive White Gaussian Noise
    Dytso, Alex
    Cardone, Martina
    Poor, H. Vincent
    IEEE SIGNAL PROCESSING LETTERS, 2019, 26 (09) : 1325 - 1329
  • [6] Characterizing the Dynamics of the Watt Governor System Under Harmonic Perturbation and Gaussian Noise
    Rosa, Lucas A. S.
    Prebianca, Flavio
    Hoff, Anderson
    Manchein, Cesar
    Albuquerque, Holokx A.
    INTERNATIONAL JOURNAL OF BIFURCATION AND CHAOS, 2020, 30 (01):
  • [7] Geometric singular perturbation theory with real noise
    Li, Ji
    Lu, Kening
    Bates, Peter W.
    JOURNAL OF DIFFERENTIAL EQUATIONS, 2015, 259 (10) : 5137 - 5167
  • [8] ON THE PRODUCT OF A SINGULAR WISHART MATRIX AND A SINGULAR GAUSSIAN VECTOR IN HIGH DIMENSION
    Bodnar, T.
    Mazur, S.
    Muhinyuza, S.
    Parolya, N.
    THEORY OF PROBABILITY AND MATHEMATICAL STATISTICS, 2018, 99 : 37 - 50
  • [9] Singular Vectors Under Random Perturbation
    Vu, Van
    RANDOM STRUCTURES & ALGORITHMS, 2011, 39 (04) : 526 - 538
  • [10] SINGULAR PERTURBATION OF NONLINEAR VECTOR BOUNDARY VALUE PROBLEM
    康盛亮
    陈琪
    Applied Mathematics and Mechanics(English Edition), 1988, (09) : 873 - 880
12345