Signal-Noise Separation in Random Matrices by using Eigenvalue Spectrum Analysis
Add Gaussian noise to a matrix
Create a real-valued, symmetric random matrix
Create ordered list of largest matrix elements
Remove noise from a random matrix by applying a threshold
Discard rows and columns from a matrix that exclusively contain zero-v...
Create a density plot and a histogram of the eigenvalue distribution
Estimate an objective threshold for signal-noise separation in random ...
Validate input matrix prior to threshold computation
Display a sequence of plots on screen
Plot the empirical distribution of the eigenvalue spacings
Internal functions for the RMThreshold package
Signal-Noise Separation in Correlation Matrices by using Eigenvalue Sp...
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.