nd_csd function

$L_2$ Distance of Continuous Spectral Densities

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.

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.

Returns

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.

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)

References

Rdpack::insert_ref(key="ipsen_evolutionary_2002",package="NetworkDistance")