nd.csd {NetworkDistance}

L_2 Distance of Continuous Spectral Densities

Description

The method employs spectral density of eigenvalues from Laplacian in that for each, we have corresponding spectral density \rho(w) as a sum of narrow Lorentz distributions with bandwidth parameter. Since it involves integration of a function over the non-compact domain, it may blow up to infinity and the code automatically aborts the process.

Usage

nd.csd(A, out.dist = TRUE, bandwidth = 1)

Arguments

A

a list of length N containing (M\times M) adjacency matrices.

out.dist

a logical; TRUE for computed distance matrix as a dist object.

bandwidth

common bandwidth of positive real number.

Value

a named list containing

D

an (N\times N) matrix or dist object containing pairwise distance measures.

spectra

an (N\times M-1) matrix where each row is top-M-1 vibrational spectra.

References

Ipsen M, Mikhailov AS (2002). “Evolutionary reconstruction of networks.” Physical Review E, 66(4). ISSN 1063-651X, 1095-3787.

Examples

## load example data
data(graph20)

## compute distance matrix
output = nd.csd(graph20, out.dist=FALSE, bandwidth=1.0)

## visualize
opar = par(no.readonly=TRUE)
par(pty="s")
image(output$D[,20:1], main="two group case", axes=FALSE, col=gray(0:32/32))
par(opar)