ergmclust (version 1.0.0)

ergmclust.ICL: Model Selection Based On Integrated Classification Likelihood.

Description

Model-based clustering and cluster-specific parameter estimation through the mixed membership Exponential-Family Random Graph Models (ERGMs) for the different number of clusters. Model selection is based on maximum value of Integrated Classification Likelihood (ICL).

Usage

ergmclust.ICL(adjmat, Kmax = 5, directed = FALSE,
    thresh = 1e-06, iter.max = 200, coef.init = NULL)

Arguments

adjmat

An object of class matrix of dimension (N x N) containing the adjacency matrix, where N is the number of nodes in the network.

Kmax

Maximum number of clusters.

directed

If TRUE, the network is supposed to be directed (and therefore adjmat is must be asymmetric in general). By default, this is set as FALSE.

thresh

Optional user-supplied convergence threshold for relative error in the objective in Variational Expectation-Maximization (VEM) algorithm. The default value is set as 1e-06.

iter.max

The maximum number of iterations after which the algorithm is terminated. The default value is set as 200.

coef.init

Optional user-supplied network canonical parameter vector (K-dimensional). Default is NULL, and ergmclust chooses a random perturbation around zero vector.

Value

Returns a list of ergmclust object. Each object of class ergmclust is a list with the following components:

Kselect

Optimum number of clusters chosen after model selection through Integrated Classification Likelihood (ICL).

coefficients

An object of class vector of size (Kselect x 1) containing the canonical network parameters of the model.

probability

An object of class matrix of size (N x Kselect) containing the mixed membership probabilities of the model for N nodes distributed in Kselect clusters.

clust.labels

An object of class vector of size (N x 1) containing the cluster membership labels in {1, ..., Kselect} for N nodes.

ICL

Integrated Classification Likelihood (ICL) score calculated from completed data log-likelihood and penalty terms.

Details

ergmclust.ICL is an R implementation for the model selection for an appropriate number of clusters in the mixed membership Exponential-Family Random Graph Models (ERGMs). The Integrated Classification Likelihood (ICL) was proposed by Biernacki et al. (2000) and Daudin, et. al. (2008) to assess the model-based clustering.

References

Biernacki, C., Celeux, G., and Govaert, G. (2000) Assessing a mixture model for clustering with the integrated completed likelihood, IEEE Transactions on Pattern Analysis and Machine Intelligence, Vol. 22(7), 719-725

https://ieeexplore.ieee.org/document/865189

Daudin, J. J., Picard, F., and Robin, S. (2008) A Mixture Model for Random Graphs, Statistics and Computing, Vol. 18(2), 173<U+2013>183

https://link.springer.com/article/10.1007/s11222-007-9046-7

Examples

# NOT RUN {
## undirected network:
data(tradenet)
## Model selection for Kmax = 3
ergmclust.ICL(adjmat = tradenet, Kmax = 3, directed = FALSE, 
thresh = 1e-06, iter.max = 120, coef.init = NULL)

## directed network:
data(armsnet)
## Model selection for Kmax = 3
ergmclust.ICL(adjmat = armsnet, Kmax = 3, directed = TRUE,
thresh = 1e-06, iter.max = 60, coef.init = NULL)
# }