Cov_based {NAC}

Covariates-based Spectral Clustering.

Description

Covariates-based Spectral Clustering is a spectral clustering method that focuses solely on the covariates structure, i.e., the XX^{\prime} where X is the covariates matrix, as introduced in Lee et al. (2010).

Usage

Cov_based(Covariate, K, itermax = 100, startn = 10)

Arguments

Covariate

An n \times p covariate matrix. The rows correspond to nodes and the columns correspond to covariates.

K

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

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

Lee, A. B., Luca, D., Klei, L., Devlin, B., & Roeder, K. (2010). Discovering genetic ancestry using spectral graph theory. Genetic Epidemiology: The Official Publication of the International Genetic Epidemiology Society, 34(1), 51-59.
doi:10.1002/gepi.20434

Examples

# Simulate the Covariate Matrix
n = 10; p = 5; K = 2; prob1 = 0.9;
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
}
Q = 0.1*matrix(sign(runif(p*K) - 0.5), nrow = p);
for(i in 1:K){
  Q[(i-1)*(p/K)+(1:(p/K)), i] = 0.3; #remark. has a change here
}
W = matrix(0, nrow = n, ncol = K);
for(jj in 1:n) {
  pp = rep(1/(K-1), K); pp[l[jj]] = 0;
  if(runif(1) <= prob1) {W[jj, 1:K] = Pi[jj, ];}
  else
  W[jj, sample(K, 1, prob = pp)] = 1;
  }
W = t(W)
D0 = Q %*% W
D = matrix(0, n, p)
for (i in 1:n){
  D[i,] = rnorm(p, mean = D0[,i], sd = 1);
}
Cov_based(D, 2)