make_psd,matrix-method: Adjust network matrix to be positive semi-definite
Description
Adjust network matrix to be positive semi-definite
Usage
# S4 method for matrix
make_psd(x, eps = sqrt(.Machine$double.eps))
Arguments
x
A matrix specifying the network adjacency matrix.
eps
A numeric value, setting the tolance for smallest
eigenvalue adjustment
Value
The matrixx, if it is positive definite and the closest
positive semi-definite matrix if x is not positive semi-definite.
Details
For a matrix N, the closest positive semi-definite matrix is
calculated as N* = rho*N + (1+rho)*I, where I is the identity matrix
and rho = 1/(1 - lambda) with lambda the smallest eigenvalue of N.
For more details check the references.
References
Freytag S, Manitz J, Schlather M, Kneib T, Amos CI, Risch A, Chang-Claude J, Heinrich J, Bickeboeller H: A network-based kernel machine test for the identification of risk pathways in genome-wide association studies. Hum Hered. 2013, 76(2):64-75.
# NOT RUN {set.seed(2345)
m <- matrix(data=sample(size=25, c(0,0,1), replace=TRUE),5,5)
m <- m + t(m)
min(eigen(m, only.values = TRUE, symmetric = TRUE)$values)
round(make_psd(m),2)
# }