Description Usage Arguments Details Value Author(s) References Examples
Estimate the parameters, the clusters, as well as the
number of clusters q
of a (binary) stochastic block model.
1 2 |
x |
an adjacency matrix or a matrix of edges (each column gives
the two node indexes defining an edge) or a spm file name (a |
qmin |
minimum number of classes. |
qmax |
maximum number of classes (if |
method |
strategy used for the estimation: "variational", "classification", or "bayesian" |
directed |
|
nbiter |
maximum number of EM iterations (default: 10). |
fpnbiter |
maximum number of internal iterations for the E step (default: 5). |
improve |
selects between improved or basic strategies
(default: |
verbose |
display warning messages (default: |
mixer
implements inference methods for the MixNet model (sometimes referred to as Erd<c3><b6>s-R<c3><a9>nyi 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:
refers to the paper of Daudin et. al (2008). It is the default method.
implements the method described in Zanghi et. al (2008). This method is faster than the variational approach and is able to deal with bigger networks but can produce biased estimates.
implements the method described in Latouche et. al (2012).
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).
mixer
returns an object of class mixer. Below the main attributes of this
class:
nnodes |
number of connected nodes. |
map |
mapping from connected nodes to the whole set of nodes. |
edges |
edge list. |
qmin, qmax |
number of classes. |
output |
output list of |
output[[i]]$criterion |
ICL criterion or ILvb criterion used for model selection (see details section for more). |
output[[i]]$alphas |
vector of proportion, whose length is the number of component. |
output[[i]]$Pis |
class connectivity matrix. |
output[[i]]$a |
vector of Dirichlet parameters for the (approximated) posterior distribution of the class proportions. |
output[[i]]$eta |
matrix of Beta parameters for the (approximated) posterior distribution of the connectivity matrix. |
output[[i]]$zeta |
matrix of Beta parameters for the (approximated) posterior distribution of the connectivity matrix. |
output[[i]]$Taus |
matrix of posterior probabilities (of the hidden color knowing the graph structure). |
Christophe Ambroise, Gilles Grasseau, Mark Hoebeke, Pierre Latouche, Vincent Miele, Franck Picard
Jean-Jacques Daudin, Franck Picard and Stephane Robin (2008), A mixture model for random graphs. Statistics and Computing, 18, 2, 151-171.
Hugo Zanghi, Christophe Ambroise and Vincent Miele (2008), Fast online graph clustering via Erd??s-R??nyi mixture. Pattern Recognition, 41, 3592-3599.
Hugo Zanghi, Franck Picard, Vincent Miele and Christophe Ambroise (2010), Strategies for online inference of model-based clustering in large and growing networks. Annals of Applied Statistics, 4, 2, 687-714.
Pierre Latouche, Etienne Birmel?? and Christophe Ambroise (2012), Variational Bayesian inference and complexity control for stochastic block models. Statistical Modelling, SAGE Publications, 12, 1, 93-115.
Vincent Miele, MixNet C++ package,
http://www.math-evry.cnrs.fr/logiciels/mixnet.
mixer-dev
tool: see http://ssbgroup.fr/mixnet/mixer.html
1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 | graph.affiliation(n=100,c(1/3,1/3,1/3),0.8,0.2)->g
mixer(g$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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