Random Matrix Theory and Gaussian Noise Thresholding

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This Demonstration shows an application of random matrix theory (RMT) to the problem of signal-from-noise separation in large real-valued symmetric random matrices that takes advantage of the RMT predictions about the nearest-neighbor spacing distribution (NNSD) between the eigenvalues of these matrices.
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Contributed by: Jessica Alfonsi (August 2020)
(Padova, Italy)
Open content licensed under CC BY-NC-SA
Snapshots
Details
Snapshot 1: structured block matrix with no Gaussian noise
Snapshot 2: eigenvalue spacing distribution computed from the matrix in Snapshot 1 following an exponential function
Snapshot 3: masked structured block matrix with superimposed Gaussian noise
Snapshot 4: eigenvalue spacing distribution computed from the matrix in Snapshot 3 following a Wigner surmise function (Gaussian orthogonal ensemble distribution)
This work was inspired by Uwe Menzel's introduction to his own authored R package detailed in [1, 2].
References
[1] U. Menzel. "RMThreshold: Signal-Noise Separation in Random Matrices by Using Eigenvalue Spectrum Analysis." (Aug 18, 2020) cran.r-project.org/web/packages/RMThreshold.
[2] U. Menzel. "RMThreshold: A Short Introduction." (Aug 18, 2020) www.matstat.org/content_en/RMT/RMThreshold_Intro.pdf.
Permanent Citation