RMThreshold (version 1.1)

RMThreshold-package: Signal-Noise Separation in Correlation Matrices by using Eigenvalue Spectrum Analysis

Description

The package provides an algorithm that can be used to determine an objective threshold for signal-noise separation in large random matrices.

Details

The package provides 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). 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. The modular structure of the matrix (or of the corresponding network) can be unraveled if such a threshold is found.

References

https://en.wikipedia.org/wiki/Random_matrix

Wigner, E. P. , Characteristic vectors of bordered matrices with infinite dimensions, Ann. Math. 62, 548-564, 1955.

Mehta, M., Random Matrices, 3nd edition. Academic Press, 2004.

Furht, B. and Escalante, A. (eds.), Handbook of Data Intensive Computing, Springer Science and Business Media, 2011.

Luo, F. et al., Constructing gene co-expression networks and predicting functions of unknown genes by random matrix theory. BMC Bioinformatics, 2007.

Examples

## Not run: 
#   set.seed(777)
#   random.mat <- create.rand.mat(size = 1000, distrib = "norm")$rand.matrix
#   res <- rm.matrix.validation(random.mat)	# ok
#   res <- rm.get.threshold(random.mat)		# threshold about 3.19	 			
#   rm.show.plots(res$comparison.plots) 							
#   cleaned.matrix <- rm.denoise.mat(random.mat, threshold = 3.2)	
#   cleaned.matrix <- rm.discard.zeros(cleaned.matrix)
# ## End(Not run)