make_psd-matrix-method function

Adjust network matrix to be positive semi-definite

## S4 method for signature '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

Returns

The matrix x, 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.

Examples

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)

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.

Author(s)

Juliane Manitz, Saskia Freytag, Stefanie Friedrichs