statGraph (version 0.5.1)

graph.cem: Clustering Expectation-Maximization for Graphs (graph.cem)

Description

graph.cem clusters graphs following an expectation-maximization algorithm based on the Kullback-Leibler divergence between the spectral densities of the graph and of the random graph model.

Usage

graph.cem(g, model, k, max_iter = 10, ncores = 1, bandwidth = "Sturges")

Value

a list containing three fields: labels a vector of the same length of g containing the clusterization labels; a vector containing the estimated parameters for the groups. It has the length equals to k;

Arguments

g

a list containing the graphs or their adjacency matrices to be clustered.

model

a string that indicates one of the following random graph models: "ER" (Erdos-Renyi random graph), "GRG" (geometric random graph), "KR" (k regular graph), "WS" (Watts-Strogatz model), and "BA" (Barabasi-Albert model).

k

an integer specifying the number of clusters.

max_iter

the maximum number of expectation-maximization steps to execute.

ncores

the number of cores to be used for the parallel processing. The default value is 1.

bandwidth

string showing which criterion is used to choose the bandwidth during the spectral density estimation. Choose between the following criteria: "Silverman" (default), "Sturges", "bcv", "ucv" and "SJ". "bcv" is an abbreviation of biased cross-validation, while "ucv" means unbiased cross-validation. "SJ" implements the methods of Sheather & Jones (1991) to select the bandwidth using pilot estimation of derivatives.

References

Celeux, Gilles, and Gerard Govaert. "Gaussian parsimonious clustering models." Pattern recognition 28.5 (1995): 781-793.

Sheather, S. J. and Jones, M. C. (1991). A reliable data-based bandwidth selection method for kernel density estimation. _Journal of the Royal Statistical Society series B_, 53, 683-690. http://www.jstor.org/stable/2345597.

Examples

 set.seed(42)
 g <- list()
 for(i in 1:2){
   g[[i]] <- igraph::sample_gnp(n=10, p=0.5)
 }
 for(i in 3:4){
   g[[i]] <- igraph::sample_gnp(n=10, p=1)
 }
 res <- graph.cem(g, model="ER", k=2, max_iter=1, ncores=1)
 res