ergmclust.ICL: Model Selection Based On Integrated Classification...
In ergmclust: ERGM-Based Network Clustering

Description Usage Arguments Details Value Author(s) References Examples

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).

1 2	ergmclust.ICL(adjmat, Kmax = 5, directed = FALSE, thresh = 1e-06, iter.max = 200, coef.init = NULL)

`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.

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.

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.

Authors: Amal Agarwal [aut, cre], Kevin Lee [aut], Lingzhou Xue [aut, cre], Anna Yinqi Zhang [cre]

Maintainer: Lingzhou Xue <lzxue@psu.edu>

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), 173–183

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

## 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)