gen.int {cencrne}

Consistent Estimation of the Number of Communities via Regularized Network Embedding.

Description

The function generating the initial values.

Usage

gen.int(A, R=8, K.max0=8,rand.seed=123,
               lambda3=0, a=3, kappa=1, alpha=1,
               eps = 1e-2, niter = 20, niter.Z=5)

Arguments

A

An observed n * n adjacency matrix of undirected graph.

R

Int, the relatively large dimension of embedding vectors given in advance.

K.max0

The relatively large upper bound of the number of communities given in advance to generate initial values of B.

rand.seed

The random seed of generating initial value.

lambda3

A float value, the tuning parameter for sparsity of Z.

a

A float value, regularization parameter in MCP, the default setting is 3.

kappa

A float value, the penalty parameter in ADMM algorithm, the default setting is 1.

alpha

A float value, the step size of coordinate descent algorithm updating Z, the default setting is 1.

eps

A float value, algorithm termination threshold.

niter

Int, maximum number of cycles of the overall ADMM algorithm.

niter.Z

Int, maximum number of cycles of coordinate descent algorithm updating Z.

Value

A list including all estimated parameters and the BIC values with all choices of given tuning parameters, and the selected optional parameters. Opt_Z: A n * r matrix, the estimated embedding vectors corresponding to n nodes; Opt_B: A n * r matrix, the estimated community centers corresponding to n nodes; Opt_K: Int, the estimated number of communities; Opt_member: A n-dimensional vector, describing the membership of n nodes; Opt_cluster.matrix: A n * n membership matrix, whose (i,j)-element is 1, if nodes i and j belong to the same community, and 0, otherwise.

Author(s)

Mingyang Ren.

References

Ren, M., Zhang S., Zhang Q. and Ma S. (2022). Consistent Estimation of the Number of Communities via Regularized Network Embedding.

Examples

library(cencrne)
data(example.data)
A                   = example.data$A
K.true              = example.data$K.true
Z.true              = example.data$Z.true
B.true              = example.data$B.true
P.true              = example.data$P.true
Theta.true          = example.data$Theta.true
cluster.matrix.true = example.data$cluster.matrix.true

n              = dim(A)[1]
sample.index.n = rbind(combn(n,2),1:(n*(n-1)/2))
int.list       = gen.int(A)
Z.int          = int.list$Z.int
B.int          = int.list$B.int