Distributions of Singular Values for Some Random Matrices

1997/09/25 by Ashis SenGupta, A. M. Sengupta, Sengupta, A. M. +3 · 2 citations
Computer Science · Engineering · Mathematics · Physics and Astronomy · #Data Analysis #FOS: Physical sciences #Medical Image Segmentation Techniques #Sparse and Compressive Sensing Techniques #Statistical Mechanics (cond-mat.stat-mech) #Statistical and numerical algorithms #Statistics and Probability (physics.data-an) #cond-mat.stat-mech #physics.data-an

paper · pdf · doi:10.48550/arxiv.cond-mat/9709283

8 pages, Latex, uses psfig

arxiv created 1997/09/25 · openalex publication_date 1997/09/25 · arxiv updated 2009/11/30 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

The Singular Value Decomposition is a matrix decomposition technique widely used in the analysis of multivariate data, such as complex space-time images obtained in both physical and biological systems. In this paper, we examine the distribution of Singular Values of low rank matrices corrupted by additive noise. Past studies have been limited to uniform uncorrelated noise. Using diagrammatic and saddle point integration techniques, we extend these results to heterogeneous and correlated noise sources. We also provide perturbative estimates of error bars on the reconstructed low rank matrix obtained by truncating a Singular Value Decomposition.

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