nd_dsd function

Discrete Spectral Distance

Discrete Spectral Distance (DSD) is defined as the Euclidean distance between the spectra of various matrices, such as adjacency matrix $A$("Adj"), (unnormalized) Laplacian matrix $L=D-A$("Lap"), signless Laplacian matrix $|L|=D+A$("SLap"), or normalized Laplacian matrix $\tilde{L}=D^{-1/2}LD^{-1/2}$.

nd.dsd(A, out.dist = TRUE, type = c("Lap", "SLap", "NLap", "Adj"))

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.
• type: type of target structure. One of "Lap","SLap","NLap","Adj" as defined above.

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 and extract only a few
data(graph20)
gr.small = graph20[c(1:5,11:15)]

## compute distance matrix
output <- nd.dsd(gr.small, out.dist=FALSE)

## visualize
opar <- par(no.readonly=TRUE)
par(pty="s")
image(output$D[,10:1], main="two group case", axes=FALSE, col=gray(0:32/32))
par(opar)

References

Rdpack::insert_ref(key="wilson_study_2008",package="NetworkDistance")