mlvsbm_estimate_network function

Infer a multilevel network (MLVSBM object), the original object is modified

The inference use a greedy algorithm to navigate between model size. For a given model size, the inference is done via a variational EM algorithm. The returned model is the one with the highest ICL criterion among all visited models.

By default the algorithm fits a single level SBM for each level, before inferring the multilevel network. This step can be skipped by specifying an initial clustering with the init_clustering. Also, a given model size can be force by setting the parameters nb_clusters to a given value.

mlvsbm_estimate_network(
  mlv,
  nb_clusters = NULL,
  init_clustering = NULL,
  nb_cores = NULL,
  init_method = "hierarchical"
)

Arguments

• mlv: A MLVSBM object, the network to be inferred.

• nb_clusters: A list of 2 integers, the model size. If left to NULL, the algorithm will navigate freely. Otherwise it will navigate between the specified model size and its neighbors.

• init_clustering: A list of 2 vectors of integers of the same length as the number of node of each level. If specified, the algorithm will start from this clustering, then navigate freely.

• nb_cores: An integer, the number of cores to use. Default to 1

  for Windows and detectCores()/2 for Linux and MacOS

• init_method: One of "hierarchical" (the default) or "spectral", "spectral" might be more efficient but can lead to some numeric errors. Not used when int_clustering is given.

Returns

A FitMLVSBM object, the best inference of the network

Examples

my_mlvsbm <- MLVSBM::mlvsbm_simulate_network(
  n = list(I = 10, O = 20), # Number of nodes for the lower level and the upper level
  Q = list(I = 2, O = 2), # Number of blocks for the lower level and the upper level
  pi = c(.3, .7), # Block proportion for the upper level, must sum to one
  gamma = matrix(c(.9, .2,   # Block proportion for the lower level,
                   .1, .8), # each column must sum to one
                 nrow = 2, ncol = 2, byrow = TRUE),
  alpha = list(I = matrix(c(.8, .2,
                            .2, .1),
                          nrow = 2, ncol = 2, byrow = TRUE), # Connection matrix
               O = matrix(c(.99, .3,
                            .3, .1),
                          nrow = 2, ncol = 2, byrow = TRUE)),# between blocks
  directed = list(I = FALSE, O = FALSE), # Are the upper and lower level directed or not ?
  affiliation = "preferential") # How the affiliation matrix is generated
fit <- MLVSBM::mlvsbm_estimate_network(mlv = my_mlvsbm, nb_cores = 1)