NAC (version 0.1.0)

Net_based: 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)

Value

estall

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

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.

References

Joseph, A., & Yu, B. (2016). Impact of Regularization on Spectral Clustering. The Annals of Statistics, 44(4), 1765-1791.
tools:::Rd_expr_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)