oPCA {CASCORE}

Ordinary Principle Component Analysis.

Description

Ordinary Principle Component Analysis (oPCA), also known as spectral clustering on the adjacency matrix is a classical spectral clustering method that applies k-means on the first K leading (unit-norm) eigenvectors of the adjacency matrix of a graph.

Usage

oPCA(Adj, K, itermax = 100, startn = 10)

Arguments

Adj

A 0/1 adjacency matrix.

K

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

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.

Value

estall

A lavel vector.

References

Chung, F. R., & Graham, F. C. (1997). Spectral graph theory (Vol. 92). American Mathematical Soc..

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)]
oPCA(Adj, 2)