ergmclust: Model-Based Clustering of Large Networks Through ERGMs.
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) using Variational Expectation-Maximization algorithm.

1	ergmclust(adjmat, K, 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.
`K`	Number of clusters in the mixed membership Exponential-Family Random Graph Models (ERGMs).
`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 is an R implementation for the model-based clustering through the mixed membership Exponential-Family Random Graph Models (ERGMs) with undirected and directed network data. It uses the Variational Expectation-Maximization algorithm to solve the approximate maximum likelihood estimation.

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

`coefficients`	An object of class vector of size (K x 1) containing the canonical network parameters in Exponential-Family Random Graph Models (ERGMs).
`probability`	An object of class matrix of size (N x K) containing the mixed membership probabilities of the model for N nodes distributed in K clusters.
`clust.labels`	An object of class vector of size (N x 1) containing the cluster membership labels in {1, ..., K} for N nodes.
`ICL`	Integrated Classification Likelihood (ICL) score calculated from completed data log-likelihood and penalty terms.

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

Maintainer: Amal Agarwal <amalag.19@gmail.com>

Agarwal, A. and Xue, L. (2019) Model-Based Clustering of Nonparametric Weighted Networks With Application to Water Pollution Analysis, Technometrics, to appear

https://amstat.tandfonline.com/doi/abs/10.1080/00401706.2019.1623076

Blei, D. M. , Kucukelbir, A., and McAuliffe, J. D. (2017), Variational Inference: A Review for Statisticians, Journal of the American Statistical Association, Vol. 112(518), 859-877

https://www.tandfonline.com/doi/full/10.1080/01621459.2017.1285773

Lee, K. H., Xue, L, and Hunter, D. R. (2017) Model-Based Clustering of Time-Evolving Networks through Temporal Exponential-Family Random Graph Models, Journal of Multivariate Analysis, to appear

https://arxiv.org/abs/1712.07325

Vu D. Q., Hunter, D. R., and Schweinberger, M. (2013) Model-based Clustering of Large Networks, The Annals of Applied Statistics, Vol. 7(2), 1010-1039

https://projecteuclid.org/euclid.aoas/1372338477

## undirected network:
data(tradenet)
## clustering and estimation for K = 2 groups
ergmclust(adjmat = tradenet, K = 2, directed = FALSE, 
thresh = 1e-06, iter.max = 120, coef.init = NULL)

## directed network:
data(armsnet)
## clustering and estimation for K = 2 groups
ergmclust(adjmat = armsnet, K = 2, directed = TRUE, 
thresh = 1e-06, iter.max = 120, coef.init = NULL)