Net_based {NAC}

Network-based Regularized Spectral Clustering.

Description

Network-based Regularized Spectral Clustering is a spectral clustering with regularized Laplacian method, fully established in fully established in Impact of Regularization on Spectral Clustering of Joseph & Yu (2016).

Usage

Net_based(Adj, K, tau = NULL, itermax = 100, startn = 10)

Arguments

Adj

An n \times n symmetric adjacency matrix with diagonals being 0 and positive entries being 1.

K

A positive positive integer which is no larger than n. This is the predefined number of communities.

tau

An optional tuning parameter to add J to the adjacency matrix A, where J is a constant matrix with all entries equal to 1/n. The default value is the mean of nodes' degrees.

itermax

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

startn

k-means parameter. The number of times the algorithm should be run with different initial centroids. The default value is 10.

Value

estall

A factor indicating nodes' labels. Items sharing the same label are in the same community.

References

Joseph, A., & Yu, B. (2016). Impact of Regularization on Spectral Clustering. The Annals of Statistics, 44(4), 1765-1791.
doi:10.1214/16-AOS1447

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)]
Net_based(Adj, 2)