SCORE {CASCORE}

Spectral Clustering On Ratios-of-Eigenvectors.

Description

Using ratios-of-eigenvectors to detect underlying communities.

Usage

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

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.

Value

estall

A lavel vector.

References

Jin, J. (2015). Fast community detection by score. The Annals of Statistics 43 (1), 57–89.
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)