Threshold associated to a given number of edges.

Description

Computes the threshold for the correlation matrix in order to obtain an adjacency matrix with a given number of edges.

Usage

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choose.thresh.nbedges(cor.mat,  var.ind.mat = 0, n.ind = 0,  thresh = 0.05,  
                       nb.edges = 405, test.method = "gaussian",  
                       proc.length = 518, num.levels, use.tanh = FALSE, 
                       max.iter = 10)

Arguments

cor.mat

matrix containing the correlation values. (must be diagonal with 1 on the diagonal)

var.ind.mat

matrix containing the variance inter individuals of the correlation. Only used with test.method="t.test". (default not used)

n.ind

number of individuals to take into account in the test. Only used with test.method="t.test". (default not used)

thresh

indicates the rate at which the FDR procedure is controlled. (default 0.05)

nb.edges

indicates the exact number of edges that the final graph should contain.

test.method

name of the method to be applied. "gaussian" assumes a gaussian law for the estimator. "t.test" implements a t.test for computing the p-value. (default "gaussian")

proc.length

specifies the length of the original processes using to construct the cor.mat

num.levels

specifies the number of the wavelet scale to take into account in the hypothesis test. Only used with test.method="gaussian"

use.tanh

logical. If FALSE take the atanh of the correlation values before applying the hypothesis test, in order to use the Fisher approximation

max.iter

indicates the number of maximum iteration to compute before stopping the loop

Details

In order to compare graphs, the best way to do it is to make sure that all the graphs have the same number of edges!

Value

Real number corresponding to the threshold value.

Note

only in version 2 and higher

Author(s)

S. Achard

References

S. Achard, R. Salvador, B. Whitcher, J. Suckling, Ed Bullmore (2006) A Resilient, Low-Frequency, Small-World Human Brain Functional Network with Highly Connected Association Cortical Hubs. Journal of Neuroscience, Vol. 26, N. 1, pages 63-72.

Examples

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data(brain)
brain<-as.matrix(brain)
# WARNING : To process only the first five regions
brain<-brain[,1:5]

#Construction of the correlation matrices for each level of the wavelet decomposition
wave.cor.list<-const.cor.list(brain, method = "modwt" ,wf = "la8", n.levels = 6,
                               boundary = "periodic", p.corr = 0.975)

#Construction of the adjacency matrice for scale 4

adj.mat.4<-const.adj.mat(wave.cor.list[[4]], sup = 0.44,proc.length=dim(brain)[1], 
                          num.levels=4)
nb.edges<-sum(adj.mat.4)/2

sup.thresh<-choose.thresh.nbedges(wave.cor.list[[4]],nb.edges=nb.edges,
                         proc.length=dim(brain)[1],num.levels=4)