nd.extremal | R Documentation |
k
eigenvaluesExtremal distance (nd.extremal
) is a type of spectral distance measures on two graphs' graph Laplacian,
L := D-A
where A
is an adjacency matrix and D_{ii}=\sum_j A_{ij}
. It takes top-k
eigenvalues from
graph Laplacian matrices and take normalized sum of squared differences as metric. Note that it is
1. non-negative, 2. separated, 3. symmetric, and satisfies 4. triangle inequality in that
it is indeed a metric.
nd.extremal(A, out.dist = TRUE, k = ceiling(nrow(A)/5))
A |
a list of length |
out.dist |
a logical; |
k |
the number of largest eigenvalues to be used. |
a named list containing
an (N\times N)
matrix or dist
object containing pairwise distance measures.
an (N\times k)
matrix where each row is top-k
Laplacian eigenvalues.
jakobson_extremal_2002NetworkDistance
## load data
data(graph20)
## compute distance matrix
output = nd.extremal(graph20, out.dist=FALSE, k=2)
## visualize
opar = par(no.readonly=TRUE)
par(pty="s")
image(output$D[,20:1], main="two group case", col=gray(0:32/32), axes=FALSE)
par(opar)
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