q of a MIXture of Erdös Rényi random graphs.
The estimation is performed for binary graphs
(edges are assumed to be drawn from Bernoulli distributions).
mixer( x, qmin=2, qmax=NULL, method="variational", directed = NULL,
nbiter=10, fpnbiter=5, improve=FALSE, verbose=TRUE).spm
file describes the network as a sparse matrix).NULL,
only q=qmin is considered).TRUE/FALSE for directed/undirected
graph.
Default is NULL, i.e. according to the input array x,
mixer identifies whether the graph is directed or undirected. FALSE).TRUE).mixer returns an object of class mixer. Below the main attributes of this
class:
qmax-qmin+1 items. Each item
contains the result of the estimation for a given number
of class q. Details of output field:mixer implements inference methods for the MixNet model (sometimes referred to as Erdös-Rényi mixture model for graphs) which is described in Daudin et. al (2008). Please note that the MixNet model is a special case of binary stochastic block models (Nowicki and Snijders, 2001). The inference allows to uncover clusters of vertices sharing homogeneous connection profiles. In particular, the package can be used to look for specific clusters, namely communities, where nodes of a community are more likely to connect to nodes of the same community.
MixNet must not be confused with Exponential Random Graph Models for network data (ERGM).
The mixer package implements three different estimation strategies
which were developed to deal with directed and undirected graphs:
The implementation of the two first methods consists of an R wrapper of
the c++ software package mixnet developed by Vincent Miele
(2006).
The mixer routine uses the estimation strategy described in
method and computes a model selection criterion for each value
of q (the number of classes) between qmin and
qmax. The ICL criterion is used for the variational and
classification methods. It corresponds to an asymptotic
approximation of the Integrated Classification Likelihood. The other
criterion, so called ILvb (Integrated Likelihood variational
Bayes), is used for the bayesian method. It is based on a variational
(non-asymptotic) approximation of the Integrated observed Likelihood.
mixer is an user-friendly package with a reduced number of functions.
For R-developers in statistical networks a more complete set, called
mixer-dev, is provided (see below).
Hugo Zanghi, Christophe Ambroise and Vincent Miele (2008), Fast online graph clustering via Erdös-Rényi mixture. Pattern Recognition, 41, 3592-3599.
Hugo Zanghi, Franck Picard, Vincent Miele and Christophe Ambroise (2010), Strategies for online inference of model-based clustering in large and growing networks. Annals of Applied Statistics, 4, 2, 687-714.
Pierre Latouche, Etienne Birmelé and Christophe Ambroise (2012), Variational Bayesian inference and complexity control for stochastic block models. Statistical Modelling, SAGE Publications, 12, 1, 93-115.
Vincent Miele, MixNet C++ package, http://stat.genopole.cnrs.fr/logiciels/mixnet.
mixer-dev tool: see http://ssbgroup.fr/mixnet/mixer.html
graph.affiliation(n=100,c(1/3,1/3,1/3),0.8,0.2)->g
mixer(g$x,qmin=2,qmax=6)->xout
## Not run: plot(xout)
##
graph.affiliation(n=50,c(1/3,1/3,1/3),0.8,0.2)->g
mixer(g$x,qmin=2,qmax=5, method="bayesian")->xout
## Not run: plot(xout)
##
data(blog)
## set the seed to replicate results
setSeed(777)
mixer(x=blog$links,qmin=2,qmax=12)->xout
## Not run: plot(xout)
##
## get best run
m <- getModel(xout)
## get run for q=5
m <- getModel(xout, q=5)
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