mixer (version 0.2)

mixer: Mixture of Erdös-Rényi Random Graphs

Description

Estimate the parameters and hidden class variable of a Mixture of Erdös Rényi Random Graphs. The estimation is performed for a Bernoulli Mixture

Usage

mixer(x,qmin=2,qmax=NULL,method="variational",nbiter=10,improve=FALSE)

Arguments

x

Adjacency matrix or a matrix of egdes (each column gives the nodes defining an edge) or spm filename (a .spm file describes the network as a sparse matrix

qmin

Number of classes estimated (if used alone, it is the minimum number of classes which will be tested)

qmax

Maximimum number of classes (use with qmin)

method

strategy used for the estimation: "classification", "variational", or "bayesian"

nbiter

Number of EM iterations for the E step (Default: 10)

improve

Flag to choose between improved or basic strategies for chosing the model

Value

• mixer returns an object of class mixer, which is basically a list of item, each item containing the result of the estimation for a given number of class q. It has the following fields
• ICL
  Integrated Classification Likelihood, which is the criterion used for model selection
• alphas
  The vector of proportion, whose length is the number of component
• Pis
  The connectivity matrix
• Taus
  The matrix of posterior probabilities (of the hidden color knowing the graph structure)

Details

mixer is a R wrapper for the c++ software package mixnet developped by Vincent Miele (2006).

Erdös-Rényi Mixture Model for Graph (MixNet), which has been proposed by Daudin et. al (2008) with an associated EM estimation algorithm, and is not to be confused with Exponential Random Graph Models for Network Data (ERGM) which consider distributions ensuing from the exponential family to model the edge distribution. The MixNet model allows to capture the structure of a network and in particular to detect communities.

There exists a strong connection between Mixnet and block clustering.. Block clustering searches for homogeneous blocks in a data matrix by simultaneous clustering of rows and columns.

The proposed estimation strategies deals with undirected graphs. They are of two type:

• variational

{ which refers to the paper of Daudin et. al (2008). It is the default method. } classification{ which implements the method described in Zanghi et. al (2008). This method is faster than the variational approach and is able to deal with bigger network but can produce biased estimates.} bayesian{ which implements the method described in Latouche et. al (2008). It improves over variational and classification strategies when dealing with small networks (less than 50 nodes). It should not be used with networks having more than 100 nodes. }

References

Jean-Jacques Daudin, Franck Picard and Stephane Robin June (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 Erdös-Rényi mixture. Pattern Recognition, 41, 3592-3599.

Hugo Zanghi, Franck Picard, Vincent Miele, and Christophe Ambroise (2008), Strategies for Online Inference of Network Mixture, http://genome.jouy.inra.fr/ssb/preprint/AMPZ07-SSBpreprint.pdf

Pierre Latouche, Etienne Birmele, and Christophe Ambroise (2008), Bayesian methods for graph clustering, http://genome.jouy.inra.fr/ssb/preprint/SSB-RR-17.bayesianMixNet.pdf

Vincent Miele. MixNet C++ package, http://stat.genopole.cnrs.fr/sg/software/mixer/.

Examples

graph.affiliation(n=100,c(1/3,1/3,1/3),0.8,0.2)->g
mixer(g$x,qmin=2,qmax=6)->xout
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
plot(xout)

plot(xout)
data(blog)
mixer(x=blog$links,qmin=2,qmax=12)->xout
plot(xout)