CASCORE {CASCORE}

Covariate Assisted Spectral Clustering on Ratios of Eigenvectors.

Description

Using ratios-of-eigenvectors to detect underlying communities in networks with node covariates.

Usage

CASCORE(
  Adj,
  Covariate,
  K,
  alpha = NULL,
  alphan = 5,
  itermax = 100,
  startn = 10
)

Arguments

Adj

A 0/1 adjacency matrix.

Covariate

A covariate matrix. The rows correspond to nodes and the columns correspond to covariates.

K

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

alpha

A numeric vector, each element of which is a tuning parameter to weigh the covariate matrix.

alphan

The number of candidates \alpha. The default number is 5.

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

CASCORE is fully established in Network-Adjusted Covariates for Community Detection of Hu & Wang (2023). CASCORE detects the latent community structure under the covariate assisted degree corrected stochastic block model (CADCSBM), and it allows the disagreement between the community structures indicated in the graph and the covariates, respectively. K-means is applied on the entry-wise ratios between first leading eigenvector and each of the other K leading eigenvectors of the combined matrix of the adjacency matrix and the covariate matrix, to reveal the underlying memberships.

Value

estall

A lavel vector

.

References

Hu, Y., & Wang, W. (2023) Network-AdjustedCovariatesforCommunity Detection,
https://arxiv.org/abs/2306.15616

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)]
caseno = 4; Nrange = 10; Nmin = 10; prob1 = 0.9; p = n*4;
Q = matrix(runif(p*K, 0, 1), nrow = p, ncol = K)
Q = sweep(Q,2,colSums(Q),`/`)
W = matrix(0, nrow = n, ncol = K);
for(jj in 1:n) {
  if(runif(1) <= prob1) {W[jj, 1:K] = Pi[jj, ];}
  else W[jj, sample(K, 1)] = 1;
}
W = t(W)
D0 = Q %*% W
X = matrix(0, n, p)
N = switch(caseno, rep(100, n), rep(100, n), round(runif(n)*Nrange+ Nmin),
  round(runif(n)* Nrange+Nmin))
for (i in 1: ncol(D0)){
  X[i, ] = rmultinom(1, N[i], D0[, i])
}
CASCORE(Adj, X, 2)