modelSelection_Q function

Selects the number of groups with ICL

Selects the number of groups with Integrated Classification Likelihood Criterion

modelSelection_Q(data, n, Qmin = 1, Qmax, directed = TRUE, sparse = FALSE,
  sol.hist.sauv)

Arguments

• data: List with 2 components:

  • $Time - [0,data$Time] is the total time interval of observation
  • $Nijk - data matrix with the statistics per process$N_{ij}$and sub-intervals$k$

• n: Total number of nodes $n$

• Qmin: Minimum number of groups

• Qmax: Maximum number of groups

• directed: Boolean for directed (TRUE) or undirected (FALSE) case

• sparse: Boolean for sparse (TRUE) or not sparse (FALSE) case

• sol.hist.sauv: List of size Qmax-Qmin+1 obtained from running mainVEM(data,n,Qmin,Qmax,method='hist')

Examples

# load data of a synthetic graph with 50 individuals and 3 clusters
n <- 50

# compute data matrix with precision d_max=3
Dmax <- 2^3
data <- list(Nijk=statistics(generated_Q3$data,n,Dmax,directed=FALSE),
    Time=generated_Q3$data$Time)

# ICL-model selection
sol.selec_Q <- modelSelection_Q(data,n,Qmin=1,Qmax=4,directed=FALSE,
    sparse=FALSE,generated_sol_hist)

# best number Q of clusters:
sol.selec_Q$Qbest

References

BIERNACKI, C., CELEUX, G. & GOVAERT, G. (2000). Assessing a mixture model for clustering with the integrated completed likelihood. IEEE Trans. Pattern Anal. Machine Intel. 22, 719–725.

CORNELI, M., LATOUCHE, P. & ROSSI, F. (2016). Exact ICL maximization in a non-stationary temporal extension of the stochastic block model for dynamic networks. Neurocomputing 192, 81 – 91.

DAUDIN, J.-J., PICARD, F. & ROBIN, S. (2008). A mixture model for random graphs. Statist. Comput. 18, 173–183.

MATIAS, C., REBAFKA, T. & VILLERS, F. (2018). A semiparametric extension of the stochastic block model for longitudinal networks. Biometrika.