gen.int function

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

The function generating the initial values.

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.

Returns

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.

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

References

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

Author(s)

Mingyang Ren.