Mixture of Multilayer Integrator SBM (mimiSBM)

mimiSBM is a model that allows both clustering of individuals and grouping of views by component. This Bayesian model estimates the probability of individuals belonging to each cluster (cluster crossing all views) and the membership component for all views. In addition, the connectivity tensor between classes, conditional on the components, is also estimated.

mimiSBM(
  A,
  Kset,
  Qset,
  beta_0 = 1/2,
  theta_0 = 1/2,
  eta_0 = 1/2,
  xi_0 = 1/2,
  criterion = "ILVB",
  tol = 0.001,
  iter_max = 10,
  n_init = 1,
  alternate = F,
  Verbose = F,
  eps_conv = 1e-04,
  type_init = "SBM"
)

Arguments

A

an array of dim=c(N,N,V)

Kset

Set of number of clusters

Qset

Set of number of components

beta_0

hyperparameters for beta

theta_0

hyperparameters for theta

eta_0

hyperparameters for eta

xi_0

hyperparameters for xi

criterion

model selection criterion, criterion=c("ILVB","ICL_approx","ICL_variationnel","ICL_exact")

tol

convergence parameter on ELBO

iter_max

maximal number of iteration of mimiSBM

n_init

number of initialization of the mimi algorithm.

alternate

boolean indicated if we put an M-step after each part of the E-step, after u optimization and after tau optimization. If not, we optimize u and tau and after the M-step is made.

Verbose

boolean for information on model fitting

eps_conv

parameter of convergence for tau.

type_init

select the type of initialization type_init=c("SBM","Kmeans","random")

Value

The best model, conditionnally to the criterion, and its parameters.

Examples

set.seed(42)
K = c(2,3); pi_k = rep(1/4,4) ; rho = rep(1/2,2)
res <- rSMB_partition(N = 50,V = 5,K = K ,pi_k = pi_k ,rho = rho,p_switch = 0.1)
A = res$simulation$A ; Kset = 4 ; Qset = 2
model <- mimiSBM(A,Kset,Qset,n_init = 1, Verbose=FALSE)
#> initialization of network1
#> 

#> 





#> initialization of network2
#> 

#> 





#> initialization of network3
#> 

#> 





#> initialization of network4
#> 

#> 








#> initialization of network5
#> 

#> 








#> Components verification