CASCORE (version 0.1.2)

SCORE: Spectral Clustering On Ratios-of-Eigenvectors.

Description

Using ratios-of-eigenvectors to detect underlying communities.

Usage

SCORE(G, K, itermax = NULL, startn = NULL)

Value

estall

A lavel vector.

Arguments

G

A 0/1 adjacency matrix of a connected graph.

K

A positive integer, indicating the number of underlying communities in graph G.

itermax

k-means parameter, indicating the maximum number of iterations allowed. The default value is 100.

startn

k-means parameter. If centers is a number, how many random sets should be chosen? The default value is 10.

Details

SCORE is fully established in Fast community detection by SCORE of Jin (2015). SCORE uses the entry-wise ratios between the first leading eigenvector and each of the other \(K-1\) leading eigenvectors for clustering. It is noteworthy that SCORE only works on connected graphs, in other words, it does not allow for isolated vertices.

References

Jin, J. (2015). Fast community detection by score. The Annals of Statistics 43 (1), 57–89.
tools:::Rd_expr_doi("10.1214/14-AOS1265")

Examples

# Simulate the Network
n = 10; K = 2;
theta = 0.4 + (0.45-0.05)*(seq(1:n)/n)^2; Theta = diag(theta);
P  = matrix(c(0.8, 0.2, 0.2, 0.8), byrow = TRUE, nrow = K)
set.seed(2022)
l = sample(1:K, n, replace=TRUE); # node labels
Pi = matrix(0, n, K) # label matrix
for (k in 1:K){
  Pi[l == k, k] = 1
}
Omega = Theta %*% Pi %*% P %*% t(Pi) %*% Theta;
Adj = matrix(runif(n*n, 0, 1), nrow = n);
Adj = Omega - Adj;
Adj = 1*(Adj >= 0)
diag(Adj) = 0
Adj[lower.tri(Adj)] = t(Adj)[lower.tri(Adj)]
library(igraph)
is.igraph(Adj) # [1] FALSE
ix = components(graph.adjacency(Adj))
componentLabel = ix$membership
giantLabel = which(componentLabel == which.max(ix$csize))
Giant = Adj[giantLabel, giantLabel]
SCORE(Giant, 2)