oPCA {CASCORE} R Documentation

## 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);