Signal-Noise Separation in Random Matrices by using Eigenvalue
Spectrum Analysis
An algorithm which can be used to determine an objective threshold for signal-noise separation in large random matrices (correlation matrices, mutual information matrices, network adjacency matrices) is provided. The package makes use of the results of Random Matrix Theory (RMT). The algorithm increments a suppositional threshold monotonically, thereby recording the eigenvalue spacing distribution of the matrix. According to RMT, that distribution undergoes a characteristic change when the threshold properly separates signal from noise. By using the algorithm, the modular structure of a matrix - or of the corresponding network - can be unraveled.

Distributions and Statistics from Random Matrix Theory
Patrick O. Perry <patperry@gmail.com>, with contributions from
Iain M. Johnstone, Zongming Ma, and Morteza Shahram.
Functions for working with the Tracy-Widom laws and other
distributions related to the eigenvalues of large Wishart
matrices.

The tables for computing the Tracy-Widom densities and distribution
functions were computed by Momar Dieng's MATLAB package
"RMLab", which is available on his homepage at
http://math.arizona.edu/~momar/research.htm

This package is part of a collaboration between Iain Johnstone,
Zongming Ma, Patrick Perry, and Morteza Shahram.  It will soon
be replaced by a package with more accuracy and built-in
support for relevant statistical tests.

Distributions, Statistics and Tests derived from Random Matrix
Theory
Iain M. Johnstone, Zongming Ma, Patrick O. Perry and Morteza
Shahram.

Distributions, Statistics and Tests Derived from Random Matrix
Theory
Iain M. Johnstone, Zongming Ma, Patrick O. Perry, Morteza Shahram, and Evan Biederstedt
Functions for working with the Tracy-Widom laws and other distributions
related to the eigenvalues of large Wishart matrices.
The tables for computing the Tracy-Widom densities and distribution
functions were computed by functions were computed by Momar Dieng's MATLAB package "RMLab". This package is part of a collaboration between Iain Johnstone, Zongming Ma, Patrick Perry, and Morteza Shahram.