nd_moments function

Log Moments Distance

For a graph with an adjacency matrix $A$, graph moment is defined as [REMOVE_ME]$\rho_m (A) = tr(A/n)^m [REMOVE_ME_2]$

where $n$ is the number of vertices and $m$ is an order of the moment. nd.moments computes pairwise distances based on log of graph moments from $m=1$ to $m=k$.

nd.moments(
  A,
  k = 3,
  metric = c("euclidean", "maximum", "manhattan", "canberra", "binary", "minkowski"),
  out.dist = TRUE
)

Arguments

• A: a list of length $N$ containing $(M\times M)$ adjacency matrices.
• k: the integer order of moments. If $k$ is too large, it may incur numerical overflow.
• metric: type of distance measures for log-moment features. See dist for more details.
• out.dist: a logical; TRUE for computed distance matrix as a dist object.

Returns

a named list containing

• D: an $(N\times N)$ matrix or dist object containing pairwise distance measures.

Description

For a graph with an adjacency matrix $A$, graph moment is defined as

where $n$ is the number of vertices and $m$ is an order of the moment. nd.moments computes pairwise distances based on log of graph moments from $m=1$ to $m=k$.

Examples

## load example data
data(graph20)

## compute distance based on different k's.
out3 <- nd.moments(graph20, k=3, out.dist=FALSE)
out5 <- nd.moments(graph20, k=5, out.dist=FALSE)
out7 <- nd.moments(graph20, k=7, out.dist=FALSE)
out9 <- nd.moments(graph20, k=9, out.dist=FALSE)

## visualize
opar = par(no.readonly=TRUE)
par(mfrow=c(2,2), pty="s")
image(out3$D[,20:1], col=gray(0:32/32), axes=FALSE, main="k=3")
image(out5$D[,20:1], col=gray(0:32/32), axes=FALSE, main="k=5")
image(out7$D[,20:1], col=gray(0:32/32), axes=FALSE, main="k=7")
image(out9$D[,20:1], col=gray(0:32/32), axes=FALSE, main="k=9")
par(opar)

References

Rdpack::insert_ref(key="mukherjee_clustering_2017",package="NetworkDistance")