,
Sophie Donnet [aut] ,
großBM team [ctb],
Pierre Barbillon [aut] | Title: | Stochastic Blockmodels |
|---|---|
| Description: | A collection of tools and functions to adjust a variety of stochastic blockmodels (SBM). Supports at the moment Simple, Bipartite, 'Multipartite' and Multiplex SBM (undirected or directed with Bernoulli, Poisson or Gaussian emission laws on the edges, and possibly covariate for Simple and Bipartite SBM). See Léger (2016) <doi:10.48550/arXiv.1602.07587>, 'Barbillon et al.' (2020) <doi:10.1111/rssa.12193> and 'Bar-Hen et al.' (2020) <doi:10.48550/arXiv.1807.10138>. |
| Authors: | Julien Chiquet [aut, cre] ,
Sophie Donnet [aut] ,
großBM team [ctb],
Pierre Barbillon [aut] |
| Maintainer: | Julien Chiquet <[email protected]> |
| License: | GPL (>= 3) |
| Version: | 0.4.7 |
| Built: | 2025-01-14 04:39:33 UTC |
| Source: | https://github.com/grosssbm/sbm |
R6 class for Bipartite SBM
R6 class for Bipartite SBM
sbm::SBM -> BipartiteSBM
dimLabelsvector of two characters giving the label of each connected dimension (row, col)
blockProplist of two vectors of block proportions (aka prior probabilities of each block)
connectParamparameters associated to the connectivity of the SBM, e.g. matrix of inter/inter block probabilities when model is Bernoulli
probMembershipsmatrix of estimated probabilities for block memberships for all nodes
nbBlocksvector of size 2: number of blocks (rows, columns)
nbDyadsnumber of dyads (potential edges in the network)
nbConnectParamnumber of parameter used for the connectivity
membershipslist of size 2: vector of memberships in row, in column.
indMembershipsmatrix for clustering memberships
new()
constructor for SBM
BipartiteSBM$new( model, nbNodes, blockProp, connectParam, dimLabels = c(row = "row", col = "col"), covarParam = numeric(length(covarList)), covarList = list() )
modelcharacter describing the type of model
nbNodesnumber of nodes in each dimension of the network
blockPropparameters for block proportions (vector of list of vectors)
connectParamlist of parameters for connectivity with a matrix of means 'mean' and an optional scalar for the variance 'var'. The dimensions of mu must match blockProp lengths
dimLabelsoptional labels of each dimension (in row, in column)
covarParamoptional vector of covariates effect
covarListoptional list of covariates data
rMemberships()
a method to sample new block memberships for the current SBM
BipartiteSBM$rMemberships(store = FALSE)
storeshould the sampled blocks be stored (and overwrite the existing data)? Default to FALSE
the sampled blocks
rEdges()
a method to sample a network data (edges) for the current SBM
BipartiteSBM$rEdges(store = FALSE)
storeshould the sampled edges be stored (and overwrite the existing data)? Default to FALSE
the sampled network
predict()
prediction under the current parameters
BipartiteSBM$predict(covarList = self$covarList, theta_p0 = 0)
covarLista list of covariates. By default, we use the covariates with which the model was estimated.
theta_p0double for thresholding...
show()
show method
BipartiteSBM$show(type = "Bipartite Stochastic Block Model")
typecharacter used to specify the type of SBM
plot()
basic matrix plot method for BipartiteSBM object or mesoscopic plot
BipartiteSBM$plot(
type = c("data", "expected", "meso"),
ordered = TRUE,
plotOptions = list()
)typecharacter for the type of plot: either 'data' (true connection), 'expected' (fitted connection) or 'meso' (mesoscopic view). Default to 'data'.
orderedlogical: should the rows and columns be reordered according to the clustering? Default to TRUE.
plotOptionslist with the parameters for the plot. See help of the corresponding S3 method for details.
a ggplot2 object for the 'data' and 'expected', a list with the igraph object g, the layout and the plotOptions for the 'meso'
clone()
The objects of this class are cloneable with this method.
BipartiteSBM$clone(deep = FALSE)
deepWhether to make a deep clone.
R6 Class definition of an Bipartite SBM fit
R6 Class definition of an Bipartite SBM fit
This class is designed to give a representation and adjust an LBM fitted with blockmodels.
sbm::SBM -> sbm::BipartiteSBM -> BipartiteSBM_fit
loglikdouble: approximation of the log-likelihood (variational lower bound) reached
ICLdouble: value of the integrated classification log-likelihood
penaltydouble, value of the penalty term in ICL
entropydouble, value of the entropy due to the clustering distribution
storedModelsdata.frame of all models fitted (and stored) during the optimization
new()
constructor for a Bipartite SBM fit
BipartiteSBM_fit$new( incidenceMatrix, model, dimLabels = c(row = "row", col = "col"), covarList = list() )
incidenceMatrixrectangular (weighted) matrix
modelcharacter ('bernoulli', 'poisson', 'gaussian')
dimLabelslabels of each dimension (in row, in columns)
covarListand optional list of covariates, each of whom must have the same dimension as incidenceMatrix
optimize()
function to perform optimization
BipartiteSBM_fit$optimize(estimOptions = list())
estimOptionsa list of parameters controlling the inference algorithm and model selection. See details.
setModel()
method to select a specific model among the ones fitted during the optimization. Fields of the current SBM_fit will be updated accordingly.
BipartiteSBM_fit$setModel(index)
indexinteger, the index of the model to be selected (row number in storedModels)
reorder()
permute group labels by order of decreasing probability
BipartiteSBM_fit$reorder()
show()
show method
BipartiteSBM_fit$show(type = "Fit of a Bipartite Stochastic Block Model")
typecharacter used to specify the type of SBM
clone()
The objects of this class are cloneable with this method.
BipartiteSBM_fit$clone(deep = FALSE)
deepWhether to make a deep clone.
Extracts model coefficients from objects with class SBM and children (SimpleSBM_fit,
BipartiteSBM_fit)
## S3 method for class 'SBM' coef(object, type = c("connectivity", "block", "covariates"), ...)## S3 method for class 'SBM' coef(object, type = c("connectivity", "block", "covariates"), ...)
object |
an R6 object inheriting from class SBM_fit (like SimpleSBM_fit or BipartiteSBM_fit) |
type |
type of parameter that should be extracted. Either 'block' for
, 'connectivity' for
, or "covariates" for
. Default is 'connectivity'. |
... |
additional parameters for S3 compatibility. Not used |
vector or list of parameters.
Define a network
defineSBM( netMat, model = "bernoulli", type = ifelse(ncol(netMat) == nrow(netMat), "simple", "bipartite"), directed = !isSymmetric(netMat), dimLabels = c(row = "row", col = "col"), covariates = list() )defineSBM( netMat, model = "bernoulli", type = ifelse(ncol(netMat) == nrow(netMat), "simple", "bipartite"), directed = !isSymmetric(netMat), dimLabels = c(row = "row", col = "col"), covariates = list() )
netMat |
a matrix describing the network: either an adjacency (square) or incidence matrix with possibly weighted entries. |
model |
character describing the model for the relation between nodes ( |
type |
Type of the matrix, choice between 'simple' and 'bipartite' |
directed |
logical: is the network directed or not? Only relevant when |
dimLabels |
an optional vector of labels for each dimension (in row, in column). Default value = c('row' = row,'col'= col) |
covariates |
a list of matrices with same dimension as mat describing covariates at the edge level. No covariate per Default. |
an object SimpleSBM or BipartiteSBM with the informations required to define a future multipartite network
A <- matrix(rbinom(100,1,.2), 10, 10) myNet <- defineSBM(A, "poisson", "simple", TRUE, "Actor")A <- matrix(rbinom(100,1,.2), 10, 10) myNet <- defineSBM(A, "poisson", "simple", TRUE, "Actor")
This function performs variational inference of bipartite Stochastic Block Models, with various model for the distribution of the edges: Bernoulli, Poisson, or Gaussian models.
estimateBipartiteSBM( netMat, model = "bernoulli", dimLabels = c(row = "row", col = "col"), covariates = list(), estimOptions = list() )estimateBipartiteSBM( netMat, model = "bernoulli", dimLabels = c(row = "row", col = "col"), covariates = list(), estimOptions = list() )
netMat |
a matrix describing the network: either an adjacency (square) or incidence matrix with possibly weighted entries. |
model |
character describing the model for the relation between nodes ( |
dimLabels |
an optional vector of labels for each dimension (in row, in column) |
covariates |
a list of matrices with same dimension as mat describing covariates at the edge level. No covariate per Default. |
estimOptions |
a list of parameters controlling the inference algorithm and model selection. See details. |
The list of parameters estimOptions essentially tunes the optimization process and the variational EM algorithm, with the following parameters
"nbCores integer for number of cores used. Default is 2
"verbosity" integer for verbosity (0, 1). Default is 1
"plot" boolean, should the ICL by dynamically plotted or not. Default is TRUE
"exploreFactor" control the exploration of the number of groups
"exploreMin" explore at least until exploreMin even if the exploration factor rule is achieved. Default 4. See the package blockmodels for details.
"exploreMax" Stop exploration at exploreMax even if the exploration factor rule is not achieved. Default Inf. See the package blockmodels for details.
"nbBlocksRange" minimal and maximal number or blocks explored
"fast" logical: should approximation be used for Bernoulli model with covariates. Default to TRUE
a list with the estimated parameters. See details...
### ======================================= ### BIPARTITE BINARY SBM (Bernoulli model) ## Graph parameters and Sampling nbNodes <- c(60, 80) blockProp <- list(c(.5, .5), c(1/3, 1/3, 1/3)) # group proportions means <- matrix(runif(6), 2, 3) # connectivity matrix # In Bernoulli SBM, parameters is a list with a # matrix of means 'mean' which are probabilities of connection connectParam <- list(mean = means) mySampler <- sampleBipartiteSBM(nbNodes, blockProp, connectParam, model = 'bernoulli') ## Estimation myBipartiteSBM <- estimateBipartiteSBM(mySampler$networkData, estimOptions = list(plot = FALSE)) plot(myBipartiteSBM, 'expected') ### ======================================= ### BIPARTITE POISSON SBM ## Graph parameters & Sampling nbNodes <- c(60, 80) blockProp <- list(c(.5, .5), c(1/3, 1/3, 1/3)) # group proportions means <- matrix(rbinom(6, 30, 0.25), 2, 3) # connectivity matrix connectParam <- list(mean = means) mySampler <- sampleBipartiteSBM(nbNodes, blockProp, connectParam, model = 'poisson') ## Estimation myBipartiteSBM <- estimateBipartiteSBM(mySampler$networkData, 'poisson', estimOptions = list(plot = FALSE)) plot(myBipartiteSBM, 'expected') ### ======================================= ### BIPARTITE GAUSSIAN SBM ## Graph parameters & sampling nbNodes <- c(60, 80) blockProp <- list(c(.5, .5), c(1/3, 1/3, 1/3)) # group proportions means <- 20 * matrix(runif(6), 2, 3) # connectivity matrix connectParam <- list(mean = means, var = 1) mySampler <- sampleBipartiteSBM(nbNodes, blockProp, connectParam, model = 'gaussian') ## Estimation myBipartiteSBM <- estimateBipartiteSBM(mySampler$networkData, 'gaussian', estimOptions = list(plot = FALSE)) plot(myBipartiteSBM, 'expected')### ======================================= ### BIPARTITE BINARY SBM (Bernoulli model) ## Graph parameters and Sampling nbNodes <- c(60, 80) blockProp <- list(c(.5, .5), c(1/3, 1/3, 1/3)) # group proportions means <- matrix(runif(6), 2, 3) # connectivity matrix # In Bernoulli SBM, parameters is a list with a # matrix of means 'mean' which are probabilities of connection connectParam <- list(mean = means) mySampler <- sampleBipartiteSBM(nbNodes, blockProp, connectParam, model = 'bernoulli') ## Estimation myBipartiteSBM <- estimateBipartiteSBM(mySampler$networkData, estimOptions = list(plot = FALSE)) plot(myBipartiteSBM, 'expected') ### ======================================= ### BIPARTITE POISSON SBM ## Graph parameters & Sampling nbNodes <- c(60, 80) blockProp <- list(c(.5, .5), c(1/3, 1/3, 1/3)) # group proportions means <- matrix(rbinom(6, 30, 0.25), 2, 3) # connectivity matrix connectParam <- list(mean = means) mySampler <- sampleBipartiteSBM(nbNodes, blockProp, connectParam, model = 'poisson') ## Estimation myBipartiteSBM <- estimateBipartiteSBM(mySampler$networkData, 'poisson', estimOptions = list(plot = FALSE)) plot(myBipartiteSBM, 'expected') ### ======================================= ### BIPARTITE GAUSSIAN SBM ## Graph parameters & sampling nbNodes <- c(60, 80) blockProp <- list(c(.5, .5), c(1/3, 1/3, 1/3)) # group proportions means <- 20 * matrix(runif(6), 2, 3) # connectivity matrix connectParam <- list(mean = means, var = 1) mySampler <- sampleBipartiteSBM(nbNodes, blockProp, connectParam, model = 'gaussian') ## Estimation myBipartiteSBM <- estimateBipartiteSBM(mySampler$networkData, 'gaussian', estimOptions = list(plot = FALSE)) plot(myBipartiteSBM, 'expected')
Estimation for multipartite SBM
estimateMultipartiteSBM(listSBM, estimOptions = list())estimateMultipartiteSBM(listSBM, estimOptions = list())
listSBM |
list of networks that were defined by the |
estimOptions |
options for the inference procedure |
The list of parameters estimOptions essentially tunes the optimization process and the variational EM algorithm, with the following parameters
"nbCores" integer for number of cores used. Default is 2
"verbosity" integer for verbosity (0, 1). Default is 1
"nbBlocksRange" List of length the number of functional groups, each element supplying the minimal and maximal number of blocks to be explored. The names of the list must be the names of the functional groups. Default value is from 1 to 10)
"initBM" Boolean. True if using simple and bipartite SBM as initialisations. Default value = TRUE
"maxiterVEM" Number of max. number of iterations in the VEM. Default value = 100
"maxiterVE" Number of max. number of iterations in the VE. Default value = 100
a MultipartiteSBM_fit object with the estimated parameters and the blocks in each Functional Group
## Not run: ## About the Parts/Functional Groups (FG) blockProp <- list(c(0.16 ,0.40 ,0.44),c(0.3,0.7)) # prop of blocks in each FG archiMultipartite <- rbind(c(1,2),c(2,2),c(1,1)) # architecture of the multipartite net. nbNodes <- c(60,50) ## About the connection matrices directed <- c(NA, TRUE, FALSE) # type of each network model <- c('gaussian','bernoulli','poisson') C1 <- list(mean = matrix(c(6.1, 8.9, 6.6, 9.8, 2.6, 1.0), 3, 2), var = matrix(c(1.6, 1.6, 1.8, 1.7 ,2.3, 1.5),3, 2)) C2 <- list(mean = matrix(c(0.7,1.0, 0.4, 0.6),2, 2)) m3 <- matrix(c(2.5, 2.6 ,2.2 ,2.2, 2.7 ,3.0 ,3.6, 3.5, 3.3),3,3 ) C3 <- list(mean = .5 * (m3 + t(m3))) connectParam <- list(C1, C2, C3) ## Graph Sampling mySampleMSBM <- sampleMultipartiteSBM(nbNodes, blockProp, archiMultipartite, connectParam, model, directed, dimLabels = c('A','B'), seed = 2) listSBM <- mySampleMSBM$listSBM estimOptions <- list(initBM = FALSE, nbCores = 2) myMSBM <- estimateMultipartiteSBM(listSBM, estimOptions) plot(myMSBM, type = "data") plot(myMSBM, type = "expected") plot(myMSBM, type = "meso") ## End(Not run)## Not run: ## About the Parts/Functional Groups (FG) blockProp <- list(c(0.16 ,0.40 ,0.44),c(0.3,0.7)) # prop of blocks in each FG archiMultipartite <- rbind(c(1,2),c(2,2),c(1,1)) # architecture of the multipartite net. nbNodes <- c(60,50) ## About the connection matrices directed <- c(NA, TRUE, FALSE) # type of each network model <- c('gaussian','bernoulli','poisson') C1 <- list(mean = matrix(c(6.1, 8.9, 6.6, 9.8, 2.6, 1.0), 3, 2), var = matrix(c(1.6, 1.6, 1.8, 1.7 ,2.3, 1.5),3, 2)) C2 <- list(mean = matrix(c(0.7,1.0, 0.4, 0.6),2, 2)) m3 <- matrix(c(2.5, 2.6 ,2.2 ,2.2, 2.7 ,3.0 ,3.6, 3.5, 3.3),3,3 ) C3 <- list(mean = .5 * (m3 + t(m3))) connectParam <- list(C1, C2, C3) ## Graph Sampling mySampleMSBM <- sampleMultipartiteSBM(nbNodes, blockProp, archiMultipartite, connectParam, model, directed, dimLabels = c('A','B'), seed = 2) listSBM <- mySampleMSBM$listSBM estimOptions <- list(initBM = FALSE, nbCores = 2) myMSBM <- estimateMultipartiteSBM(listSBM, estimOptions) plot(myMSBM, type = "data") plot(myMSBM, type = "expected") plot(myMSBM, type = "meso") ## End(Not run)
Estimation for Multiplex SBM
estimateMultiplexSBM(listSBM, dependent = FALSE, estimOptions = list())estimateMultiplexSBM(listSBM, dependent = FALSE, estimOptions = list())
listSBM |
list of networks that were defined by the |
dependent |
logical parameter indicating whether the networks in the multiplex structure are dependent beyond the latent variables, |
estimOptions |
options for the inference procedure |
The list of parameters estimOptions essentially tunes the optimization process and the variational EM algorithm, with the following parameters
"nbCores" integer for number of cores used. Default is 2
"verbosity" integer for verbosity (0, 1). Default is 1
"nbBlocksRange" List of length the number of functional groups, each element supplying the minimal and maximal number of blocks to be explored. The names of the list must be the names of the functional groups. Default value is from 1 to 10)
"initBM" Boolean. True if using simple and bipartite SBM as initialisations. Default value = TRUE
"maxiterVEM" Number of max. number of iterations in the VEM. Default value = 100
"maxiterVE" Number of max. number of iterations in the VE. Default value = 100
"plot" boolean, should the ICL by dynamically plotted or not. Default is TRUE. For dependent networks
"exploreFactor" control the exploration of the number of groups. For dependent networks
"exploreMin" explore at least until exploreMin even if the exploration factor rule is achieved. Default 4. See the package blockmodels for details. For dependent networks
"exploreMax" Stop exploration at exploreMax even if the exploration factor rule is not achieved. Default Inf. See the package blockmodels for details. For dependent networks
"nbBlocksRange" minimal and maximal number or blocks explored. For dependent networks
"fast" logical: should approximation be used for Bernoulli model with covariates. Default to TRUE. For dependent networks
a MultiplexSBM_fit object with the estimated parameters and the blocks
## Not run: ### ======================================= ### MULTIPLEX SBM without dependence between layers ## Nnodes <- 40 blockProp <- c(.4,.6) nbLayers <- 2 connectParam <- list(list(mean=matrix(rbeta(4,.5,.5),2,2)),list(mean=matrix(rexp(4,.5),2,2))) model <- c("bernoulli","poisson") type <- "directed" mySampleMultiplexSBM <- sampleMultiplexSBM( nbNodes = Nnodes, blockProp = blockProp, nbLayers = nbLayers, connectParam = connectParam, model=model, type=type) listSBM <- mySampleMultiplexSBM$listSBM estimOptions <- list(initBM = FALSE, nbCores = 2) myMultiplexSBM <- estimateMultiplexSBM(listSBM,estimOptions,dependent=FALSE) ### ======================================= ### MULTIPLEX SBM Gaussian with dependence ## Q <- 3 nbLayers <- 2 connectParam <- list() connectParam$mu <- vector("list",nbLayers) connectParam$mu[[1]] <- matrix(.1,Q,Q) + diag(1:Q) connectParam$mu[[2]] <- matrix(-2,Q,Q) + diag(rev(Q:1)) connectParam$Sigma <- matrix(c(2,1,1,4),nbLayers,nbLayers) model <- rep("gaussian",2) type <- "directed" Nnodes <- 80 blockProp <- c(.3,.3,.4) mySampleMultiplexSBM <- sampleMultiplexSBM( nbNodes = Nnodes, blockProp = blockProp, nbLayers = nbLayers, connectParam = connectParam, model=model, type="undirected", dependent=TRUE) listSBM <- mySampleMultiplexSBM$listSBM myMultiplexSBM <- estimateMultiplexSBM(listSBM,estimOptions,dependent=TRUE) ## MultiplexSBM Bernoulli with dependence Q <- 2 P00<-matrix(runif(Q*Q),Q,Q) P10<-matrix(runif(Q*Q),Q,Q) P01<-matrix(runif(Q*Q),Q,Q) P11<-matrix(runif(Q*Q),Q,Q) SumP<-P00+P10+P01+P11 P00<-P00/SumP P01<-P01/SumP P10<-P10/SumP P11<-P11/SumP connectParam <- list() connectParam$prob00 <- P00 connectParam$prob01 <- P01 connectParam$prob10 <- P10 connectParam$prob11 <- P11 model <- rep("bernoulli",2) type <- "directed" nbLayers <- 2 Nnodes <- 40 blockProp <- c(.6,.4) mySampleMultiplexSBM <- sampleMultiplexSBM( nbNodes = Nnodes, blockProp = blockProp, nbLayers = nbLayers, connectParam = connectParam, model=model, type=type, dependent=TRUE) listSBM <- mySampleMultiplexSBM$listSBM myMultiplexSBM <- estimateMultiplexSBM(listSBM,estimOptions,dependent=TRUE) ## End(Not run)## Not run: ### ======================================= ### MULTIPLEX SBM without dependence between layers ## Nnodes <- 40 blockProp <- c(.4,.6) nbLayers <- 2 connectParam <- list(list(mean=matrix(rbeta(4,.5,.5),2,2)),list(mean=matrix(rexp(4,.5),2,2))) model <- c("bernoulli","poisson") type <- "directed" mySampleMultiplexSBM <- sampleMultiplexSBM( nbNodes = Nnodes, blockProp = blockProp, nbLayers = nbLayers, connectParam = connectParam, model=model, type=type) listSBM <- mySampleMultiplexSBM$listSBM estimOptions <- list(initBM = FALSE, nbCores = 2) myMultiplexSBM <- estimateMultiplexSBM(listSBM,estimOptions,dependent=FALSE) ### ======================================= ### MULTIPLEX SBM Gaussian with dependence ## Q <- 3 nbLayers <- 2 connectParam <- list() connectParam$mu <- vector("list",nbLayers) connectParam$mu[[1]] <- matrix(.1,Q,Q) + diag(1:Q) connectParam$mu[[2]] <- matrix(-2,Q,Q) + diag(rev(Q:1)) connectParam$Sigma <- matrix(c(2,1,1,4),nbLayers,nbLayers) model <- rep("gaussian",2) type <- "directed" Nnodes <- 80 blockProp <- c(.3,.3,.4) mySampleMultiplexSBM <- sampleMultiplexSBM( nbNodes = Nnodes, blockProp = blockProp, nbLayers = nbLayers, connectParam = connectParam, model=model, type="undirected", dependent=TRUE) listSBM <- mySampleMultiplexSBM$listSBM myMultiplexSBM <- estimateMultiplexSBM(listSBM,estimOptions,dependent=TRUE) ## MultiplexSBM Bernoulli with dependence Q <- 2 P00<-matrix(runif(Q*Q),Q,Q) P10<-matrix(runif(Q*Q),Q,Q) P01<-matrix(runif(Q*Q),Q,Q) P11<-matrix(runif(Q*Q),Q,Q) SumP<-P00+P10+P01+P11 P00<-P00/SumP P01<-P01/SumP P10<-P10/SumP P11<-P11/SumP connectParam <- list() connectParam$prob00 <- P00 connectParam$prob01 <- P01 connectParam$prob10 <- P10 connectParam$prob11 <- P11 model <- rep("bernoulli",2) type <- "directed" nbLayers <- 2 Nnodes <- 40 blockProp <- c(.6,.4) mySampleMultiplexSBM <- sampleMultiplexSBM( nbNodes = Nnodes, blockProp = blockProp, nbLayers = nbLayers, connectParam = connectParam, model=model, type=type, dependent=TRUE) listSBM <- mySampleMultiplexSBM$listSBM myMultiplexSBM <- estimateMultiplexSBM(listSBM,estimOptions,dependent=TRUE) ## End(Not run)
This function performs variational inference of simple Stochastic Block Models, with various model for the distribution of the edges: Bernoulli, Poisson, or Gaussian models.
estimateSimpleSBM( netMat, model = "bernoulli", directed = !isSymmetric(netMat), dimLabels = c("node"), covariates = list(), estimOptions = list() )estimateSimpleSBM( netMat, model = "bernoulli", directed = !isSymmetric(netMat), dimLabels = c("node"), covariates = list(), estimOptions = list() )
netMat |
a matrix describing the network: either an adjacency (square) or incidence matrix with possibly weighted entries. |
model |
character describing the model for the relation between nodes ( |
directed |
logical: is the network directed or not? Only relevant when |
dimLabels |
an optional label for referring to the nodes |
covariates |
a list of matrices with same dimension as mat describing covariates at the edge level. No covariate per Default. |
estimOptions |
a list of parameters controlling the inference algorithm and model selection. See details. |
The list of parameters estimOptions essentially tunes the optimization process and the variational EM algorithm, with the following parameters
"nbCores integer for number of cores used. Default is 2
"verbosity" integer for verbosity (0, 1). Default is 1
"plot" boolean, should the ICL by dynamically plotted or not. Default is TRUE
"exploreFactor" control the exploration of the number of groups
"exploreMin" explore at least until exploreMin even if the exploration factor rule is achieved. Default 4. See the package blockmodels for details.
"exploreMax" Stop exploration at exploreMax even if the exploration factor rule is not achieved. Default Inf. See the package blockmodels for details.
"nbBlocksRange" minimal and maximal number or blocks explored
"fast" logical: should approximation be used for Bernoulli model with covariates. Default to TRUE
a list with the estimated parameters. See details...
### ======================================= ### SIMPLE BINARY SBM (Bernoulli model) ## Graph parameters & Sampling nbNodes <- 60 blockProp <- c(.5, .25, .25) # group proportions means <- diag(.4, 3) + 0.05 # connectivity matrix: affiliation network connectParam <- list(mean = means) mySampler <- sampleSimpleSBM(nbNodes, blockProp, connectParam) adjacencyMatrix <- mySampler$networkData ## Estimation mySimpleSBM <- estimateSimpleSBM(adjacencyMatrix, 'bernoulli', estimOptions = list(plot = FALSE)) plot(mySimpleSBM, 'data', ordered = FALSE) plot(mySimpleSBM, 'data') plot(mySimpleSBM, 'expected', ordered = FALSE) plot(mySimpleSBM, 'expected') plot(mySimpleSBM, 'meso') ### ======================================= ### SIMPLE POISSON SBM ## Graph parameters & Sampling nbNodes <- 60 blockProp <- c(.5, .25, .25) # group proportions means <- diag(15., 3) + 5 # connectivity matrix: affiliation network connectParam <- list(mean = means) mySampler <- sampleSimpleSBM(nbNodes, blockProp, list(mean = means), model = "poisson") adjacencyMatrix <- mySampler$networkData ## Estimation mySimpleSBM <- estimateSimpleSBM(adjacencyMatrix, 'poisson', estimOptions = list(plot = FALSE)) plot(mySimpleSBM, 'data', ordered = FALSE) plot(mySimpleSBM, 'data') plot(mySimpleSBM, 'expected', ordered = FALSE) plot(mySimpleSBM, 'expected') ### ======================================= ### SIMPLE GAUSSIAN SBM ## Graph parameters & Sampling nbNodes <- 60 blockProp <- c(.5, .25, .25) # group proportions means <- diag(15., 3) + 5 # connectivity matrix: affiliation network connectParam <- list(mean = means, var = 2) mySampler <- sampleSimpleSBM(nbNodes, blockProp, connectParam, model = "gaussian") ## Estimation mySimpleSBM <- estimateSimpleSBM(mySampler$networkData, 'gaussian', estimOptions = list(plot = FALSE)) plot(mySimpleSBM, 'data', ordered = FALSE) plot(mySimpleSBM, 'data') plot(mySimpleSBM, 'expected', ordered = FALSE) plot(mySimpleSBM, 'expected')### ======================================= ### SIMPLE BINARY SBM (Bernoulli model) ## Graph parameters & Sampling nbNodes <- 60 blockProp <- c(.5, .25, .25) # group proportions means <- diag(.4, 3) + 0.05 # connectivity matrix: affiliation network connectParam <- list(mean = means) mySampler <- sampleSimpleSBM(nbNodes, blockProp, connectParam) adjacencyMatrix <- mySampler$networkData ## Estimation mySimpleSBM <- estimateSimpleSBM(adjacencyMatrix, 'bernoulli', estimOptions = list(plot = FALSE)) plot(mySimpleSBM, 'data', ordered = FALSE) plot(mySimpleSBM, 'data') plot(mySimpleSBM, 'expected', ordered = FALSE) plot(mySimpleSBM, 'expected') plot(mySimpleSBM, 'meso') ### ======================================= ### SIMPLE POISSON SBM ## Graph parameters & Sampling nbNodes <- 60 blockProp <- c(.5, .25, .25) # group proportions means <- diag(15., 3) + 5 # connectivity matrix: affiliation network connectParam <- list(mean = means) mySampler <- sampleSimpleSBM(nbNodes, blockProp, list(mean = means), model = "poisson") adjacencyMatrix <- mySampler$networkData ## Estimation mySimpleSBM <- estimateSimpleSBM(adjacencyMatrix, 'poisson', estimOptions = list(plot = FALSE)) plot(mySimpleSBM, 'data', ordered = FALSE) plot(mySimpleSBM, 'data') plot(mySimpleSBM, 'expected', ordered = FALSE) plot(mySimpleSBM, 'expected') ### ======================================= ### SIMPLE GAUSSIAN SBM ## Graph parameters & Sampling nbNodes <- 60 blockProp <- c(.5, .25, .25) # group proportions means <- diag(15., 3) + 5 # connectivity matrix: affiliation network connectParam <- list(mean = means, var = 2) mySampler <- sampleSimpleSBM(nbNodes, blockProp, connectParam, model = "gaussian") ## Estimation mySimpleSBM <- estimateSimpleSBM(mySampler$networkData, 'gaussian', estimOptions = list(plot = FALSE)) plot(mySimpleSBM, 'data', ordered = FALSE) plot(mySimpleSBM, 'data') plot(mySimpleSBM, 'expected', ordered = FALSE) plot(mySimpleSBM, 'expected')
Extracts fitted values for object with class (SimpleSBM_fit,
BipartiteSBM_fit) or multipartitepartiteSBM_fit)
## S3 method for class 'SBM' fitted(object, ...)## S3 method for class 'SBM' fitted(object, ...)
object |
an R6 object inheriting from SimpleSBM_fit, BipartiteSBM_fit or MultipartiteSBM_fit |
... |
additional parameters for S3 compatibility. Not used |
a matrix of expected fitted values for each dyad
This data set provides information about $154$ fungi sampled on $51$ tree species.
fungusTreeNetworkfungusTreeNetwork
A list with the following entries:
fungi_list list of the fungus species names
tree_list list of the tree species names
fungus_tree binary fungus-tree interactions
tree_tree weighted tree-tree interactions (number of common fungal species two tree species host)
covar_tree covariates associated to pairs of trees (namely genetic, taxonomic and geographic distances)
Vacher, Corinne, Dominique Piou, and Marie-Laure Desprez-Loustau. "Architecture of an antagonistic tree/fungus network: the asymmetric influence of past evolutionary history." PloS one 3.3 (2008): e1740.
Auxiliary function to check the given class of an object
is_SBM(Robject)is_SBM(Robject)
Robject |
an R6 object inheriting from class SBM |
TRUE or FALSE
Multipartite network of mutualistic interactions between plants and pollinators, plants and birds and plants and ants.
multipartiteEcologicalNetworkmultipartiteEcologicalNetwork
A list a 3 binary incidence matrices
Inc_plant_ant Interactions between plants (rows) and ants (cols). Matrix with 141 rows and 30 columns
Inc_plant_bird Interactions between plants (rows) and birds (cols). Matrix with141 rows and 46 columns
Inc_plant_flovis Interactions between plants (rows) and pollinators (cols). Matrix with 141 rows and 173 columns
Dataset compiled and conducted at Centro de Investigaciones Costeras La Mancha (CICOLMA), located on the central coast of the Gulf of Mexico, Veracruz, Mexico. see doi:10.1098/rspb.2016.1564 and https://github.com/lucaspdmedeiros/multi-network_core_removal/tree/master/data
R6 Class definition of a Multipartite SBM
R6 Class definition of a Multipartite SBM
sbm::SBM -> MultipartiteSBM
dimLabelsvector of characters giving the label of each connected dimension
blockProplist of two vectors of block proportions (aka prior probabilities of each block)
connectParamparameters associated to the connectivity of the SBM, e.g. matrix of inter/inter block probabilities when model is Bernoulli
probMembershipsmatrix of estimated probabilities for block memberships for all nodes
nbBlocks: vector with the number of blocks in each FG
nbConnectParamnumber of parameter used for the connectivity
architectureorganization of the multipartite network
nbNetworksnumber of networks in the multipartite network
membershipslist of size 2: vector of memberships in all parts of the network
indMembershipsmatrix for clustering memberships
new()
constructor for Multipartite SBM
MultipartiteSBM$new( model = character(0), architecture = matrix(NA, 0, 2), directed = logical(0), nbNodes = numeric(0), dimLabels = character(0), blockProp = list(), connectParam = list() )
modelcharacter describing the type of model
architecturea 2-column matrix describing interactions between the networks
directedvector of logical: are the network directed or not?
nbNodesnumber of nodes in each dimension/part of the network
dimLabelslabels of each par of the network
blockPropparameters for block proportions (vector of list of vectors)
connectParamparameters of connectivity (vector of list of vectors)
show()
print method
MultipartiteSBM$show(type = "Multipartite Stochastic Block Model")
typecharacter to tune the displayed name
print()
print method
MultipartiteSBM$print()
plot()
plot Multipartite Network
MultipartiteSBM$plot(
type = c("data", "expected", "meso"),
ordered = TRUE,
plotOptions = list()
)typecharacter for the type of plot: either 'data' (true connection), 'expected' (fitted connection) or 'meso' (mesoscopic view). Default to 'data'.
orderedTRUE is the matrices are plotted after reorganization with the blocks. Default value = TRUE
plotOptionslist of plot options for the mesoscopic view or matrix view
clone()
The objects of this class are cloneable with this method.
MultipartiteSBM$clone(deep = FALSE)
deepWhether to make a deep clone.
R6 Class definition of a Multipartite SBM fit
R6 Class definition of a Multipartite SBM fit
This class is designed to give a representation and adjust a Multipartite SBM fitted with GREMLIN.
sbm::SBM -> sbm::MultipartiteSBM -> MultipartiteSBM_fit
loglikdouble: approximation of the log-likelihood (variational lower bound) reached
ICLdouble: value of the integrated classification log-likelihood
storedModelsdata.frame of all models fitted (and stored) during the optimization
new()
constructor for Multipartite SBM
MultipartiteSBM_fit$new(netList)
netListlist of SBM objects
optimize()
estimation of multipartiteSBM via GREMLINS
MultipartiteSBM_fit$optimize(estimOptions)
estimOptionsoptions for MultipartiteBM
predict()
prediction under the currently estimated model
MultipartiteSBM_fit$predict()
a list of matrices matrix of expected values for each dyad
setModel()
method to select a specific model among the ones fitted during the optimization. Fields of the current MultipartiteSBM_fit will be updated accordingly.
MultipartiteSBM_fit$setModel(index)
indexinteger, the index of the model to be selected (row number in storedModels)
show()
show method
MultipartiteSBM_fit$show(type = "Fit of a Multipartite Stochastic Block Model")
typecharacter used to specify the type of SBM
clone()
The objects of this class are cloneable with this method.
MultipartiteSBM_fit$clone(deep = FALSE)
deepWhether to make a deep clone.
R6 Class definition of a Multiplex SBM fit
R6 Class definition of a Multiplex SBM fit
This class is designed to give a representation and adjust a Multiplex SBM fitted with GREMLIN.
The list of parameters estimOptions essentially tunes the optimization process and the variational EM algorithm, with the following parameters
"nbCores" integer for number of cores used. Default is 2
"verbosity" integer for verbosity (0, 1). Default is 1
"nbBlocksRange" List of length the number of functional groups, each element supplying the minimal and maximal number of blocks to be explored. The names of the list must be the names of the functional groups. Default value is from 1 to 10)
"initBM" Boolean. True if using simple and bipartite SBM as initialisations. Default value = TRUE
"maxiterVEM" Number of max. number of iterations in the VEM. Default value = 100
"maxiterVE" Number of max. number of iterations in the VE. Default value = 100
sbm::SBM -> sbm::MultipartiteSBM -> sbm::MultipartiteSBM_fit -> MultiplexSBM_fit
nbBlocksvector of size 2: number of blocks (rows, columns)
dependentNetwork: connection parameters in each network
storedModelsdata.frame of all models fitted (and stored) during the optimization
namesLayers: names of the various Networks
new()
constructor for Multiplex SBM
MultiplexSBM_fit$new(netList, dependentNet = FALSE)
netListlist of SBM object with
dependentNetboolean indicating whether dependence is assumed between networks beyond the common dependence on the latent variables
optimize()
estimation of multipartiteSBM via GREMLINS
MultiplexSBM_fit$optimize(estimOptions)
estimOptionsoptions for MultipartiteBM
plot()
plot Multiplex Network
MultiplexSBM_fit$plot(
type = c("data", "expected"),
ordered = TRUE,
plotOptions = list()
)typecharacter for the type of plot: either 'data' (true connection), 'expected' (fitted connection). Default to 'data'.
orderedTRUE is the matrices are plotted after reorganization with the blocks. Default value = TRUE
plotOptionslist of plot options for the matrix view
show()
show method
MultiplexSBM_fit$show(type = "Fit of a Multiplex Stochastic Block Model")
typecharacter used to specify the type of SBM
predict()
prediction under the currently estimated model
MultiplexSBM_fit$predict()
a list of matrices matrix of expected values for each dyad
clone()
The objects of this class are cloneable with this method.
MultiplexSBM_fit$clone(deep = FALSE)
deepWhether to make a deep clone.
Basic matrix plot method for SBM object or mesoscopic view
## S3 method for class 'SBM' plot( x, type = c("data", "expected", "meso"), ordered = TRUE, plotOptions = list(), ... )## S3 method for class 'SBM' plot( x, type = c("data", "expected", "meso"), ordered = TRUE, plotOptions = list(), ... )
x |
an object inheriting from class SBM |
type |
character for the type of plot: either 'data' (true connection), 'expected' (fitted connection) or 'meso' (mesoscopic). Default to 'data'. |
ordered |
logical: should the rows and columns be ordered according to the clustering? Default to |
plotOptions |
list with parameters for 'meso' type plot and data type plot. Details are given below |
... |
additional parameters for S3 compatibility. Not used |
The list of parameters plotOptions for the mesoscopic plot is:
seed to control the layout
character string for the title. Default value is NULL
Default value = NULL
Default value is "salmon2"
Node border color.Default value is "black"
One of "none", "circle", "square", "csquare", "rectangle" "crectangle", "vrectangle", "pie", "raster", or "sphere". Default value = "circle"
Size of the node (default is 2)
The second size of the node (e.g. for a rectangle)
Names of the vertices. Default value is the label of the nodes
Default value is "black"
Default value is 2. Font: 1 plain, 2 bold, 3, italic, 4 bold italic, 5 symbol
Font size (multiplication factor, device-dependent).Default value is 0.9.
Distance between the label and the vertex. Default value is 0
The position of the label in relation to the vertex. default value is 0
Threshold under which the edge is not plotted. Default value is = -Inf
Default value is "gray"
Factor parameter. Default value is 10
Default value is 1
Default value is 2
Line type, could be 0 or "blank", 1 or "solid", 2 or "dashed", 3 or "dotted", 4 or "dotdash", 5 or "longdash", 6 or "twodash". Default value is "solid"
Default value is = 0.3.
For type = 'data' or 'expected plot', the list of parameters plotOptions is
Boolean. Set TRUE if you want to see the legend. Default value is FALSE
Boolean. Set TRUE if you want to print the title of the legend. Default value is FALSE
Position of the legend. Possible values are 'bottom', 'top','left,'right'. Default value is 'bottom'
Set true if the rownames must be plotted. Default value is FALSE
Set true if the colNames must be plotted. Default value is FALSE
Chain of character. The color of the lines to separate groups if a clustering is provided. Default value is red
Numeric. Width of the lines to separate groups. Default value is NULL, automatically chosen
Chain of character. Title of the plot. Default value is NULL
a ggplot2 object for the 'data' and 'expected', a list with the igraph object g and the layout for the 'meso'
Plot an alluvial plot between clusterings
plotAlluvial(listMemberships, plotOptions = list())plotAlluvial(listMemberships, plotOptions = list())
listMemberships |
: a list vectors containing the memberships |
plotOptions |
: a list containing the options for Alluvial plots |
The list of parameters plotOptions provides the following options
"curvy" numeric, controls the curvature of the alluvial. Default value = 0.3
"alpha numeric, vector of transparency of the stripes. Default value = 0.8
"gap.width" numeric, relative width of inter-category gaps. Default value = 0.1
"col" vector of colors of the stripes. Default value = "darkolivegreen3"
"border" vector of border colors for the stripes. Default is white
display the alluvial plot, returns the plotOptions as a list
listMemberships <- list(C1 = rep(c('A','B','C'),each=10),C2 = rep(c(1,2,4),10)) plotAlluvial(listMemberships)listMemberships <- list(C1 = rep(c('A','B','C'),each=10),C2 = rep(c(1,2,4),10)) plotAlluvial(listMemberships)
Plot an adjacency or incidence Matrix
plotMyMatrix( Mat, dimLabels = c(row = "row", col = "col"), clustering = NULL, plotOptions = NULL )plotMyMatrix( Mat, dimLabels = c(row = "row", col = "col"), clustering = NULL, plotOptions = NULL )
Mat |
: a matrix representing the network |
dimLabels |
: a vector of length 1 or 2 specifying the types of nodes in row and col (functional group) (Default is |
clustering |
: a list of length 2 specifying a clustering on row and col |
plotOptions |
: a list providing options. See details below. |
The list of parameters plotOptions for the matrix plot is
"legend": Boolean. Set TRUE if you want to see the legend. Default value is FALSE
"legend.title": Boolean. Set TRUE if you want to print the title of the legend. Default value is FALSE
"legend.position": Position of the legend. Possible values are 'bottom', 'top','left,'right'. Default value is 'bottom'
"rowNames": Set true if the rownames must be plotted. Default value is FALSE
"colNames": Set true if the colNames must be plotted. Default value is FALSE
"line.color": Chain of character. The color of the lines to separate groups if a clustering is provided. Default value is red
"line.width": Numeric. Width of the lines to separate groups. Default value is NULL, automatically chosen
"title": Chain of character. Title of the plot. Default value is NULL
a ggplot object corresponding to the plot
M <- matrix(sample(c(0,1),900,replace=TRUE),30,30) plotMyMatrix(M, dimLabels = c('individulals'), plotOptions= list(legend = FALSE)) M2 <- matrix( rpois(800,10),40,20) plotMyMatrix(M2, dimLabels = c(row = 'reader',col = 'book'), plotOptions = list(legend = TRUE))M <- matrix(sample(c(0,1),900,replace=TRUE),30,30) plotMyMatrix(M, dimLabels = c('individulals'), plotOptions= list(legend = FALSE)) M2 <- matrix( rpois(800,10),40,20) plotMyMatrix(M2, dimLabels = c(row = 'reader',col = 'book'), plotOptions = list(legend = TRUE))
Plot the matrices corresponding to a Multipartite Network
plotMyMultipartiteMatrix(listSBM, memberships = NULL, plotOptions = list())plotMyMultipartiteMatrix(listSBM, memberships = NULL, plotOptions = list())
listSBM |
: a list of objects representing the multipartite network (see) |
memberships |
: a list of length equal to the number of Functional Groups providing the clusterings inside each group. |
plotOptions |
: a list containing the options. See details. |
plotOptions is a list containing the following items
"normalized": Boolean. TRUE if the various matrices are presented in the same scale (between O and 1). FALSE otherwise. Default value FALSE
"compact": Boolean. Default value is TRUE if you ask for the matrices to be transposed to have a more compact view
"legend": Boolean. Set TRUE if you want to see the legend. Default value is FALSE
"legend.title": Boolean. Set TRUE if you want to print the title of the legend. Default value is FALSE
"legend.position": Position of the legend. Possible values are 'bottom', 'top','left,'right'. Default value is 'bottom'
"nodeNames": Set true if the node Names must be plotted. Default value is FALSE
"line.color": The color of the lines to separate groups. Default value is red
"line.width": Width of the lines to separate groups. Default value is NULL, automatically chosen
"title": Title of the plot. Default value is NULL
a ggplot object corresponding to the plot
data("multipartiteEcologicalNetwork") Net <- multipartiteEcologicalNetwork type='bipartite' model = 'bernoulli' directed = FALSE listNet <- list() listNet[[1]] = defineSBM(Net$Inc_plant_ant, model,type,directed, dimLabels = c(row = "Plants", col = "Ants")) listNet[[2]] = defineSBM(Net$Inc_plant_bird,model,type,directed, dimLabels =c(row = "Plants",col = "Birds")) plotMyMultipartiteMatrix(listNet,plotOptions=list(legend = TRUE,title='Ecology')) listNet <- list() listNet[[1]] <- defineSBM(matrix(rbinom(1000,1,0.5),20,50), model = 'bernoulli', type ='bipartite', directed = NA, dimLabels = c(row="Questions",col="Students")) listNet[[2]] <- defineSBM(matrix(rpois(20*30,8),30,20), model = 'poisson', type ='bipartite',directed = NA, dimLabels = c(row="Competences",col="Questions")) plotMyMultipartiteMatrix(listNet,plotOptions=list(legend = TRUE,compact = FALSE)) plotMyMultipartiteMatrix(listNet,plotOptions=list(legend = TRUE,normalized = TRUE))data("multipartiteEcologicalNetwork") Net <- multipartiteEcologicalNetwork type='bipartite' model = 'bernoulli' directed = FALSE listNet <- list() listNet[[1]] = defineSBM(Net$Inc_plant_ant, model,type,directed, dimLabels = c(row = "Plants", col = "Ants")) listNet[[2]] = defineSBM(Net$Inc_plant_bird,model,type,directed, dimLabels =c(row = "Plants",col = "Birds")) plotMyMultipartiteMatrix(listNet,plotOptions=list(legend = TRUE,title='Ecology')) listNet <- list() listNet[[1]] <- defineSBM(matrix(rbinom(1000,1,0.5),20,50), model = 'bernoulli', type ='bipartite', directed = NA, dimLabels = c(row="Questions",col="Students")) listNet[[2]] <- defineSBM(matrix(rpois(20*30,8),30,20), model = 'poisson', type ='bipartite',directed = NA, dimLabels = c(row="Competences",col="Questions")) plotMyMultipartiteMatrix(listNet,plotOptions=list(legend = TRUE,compact = FALSE)) plotMyMultipartiteMatrix(listNet,plotOptions=list(legend = TRUE,normalized = TRUE))
Plot the matrices corresponding to a Multiplex Network
plotMyMultiplexMatrix(listSBM, memberships = NULL, plotOptions = list())plotMyMultiplexMatrix(listSBM, memberships = NULL, plotOptions = list())
listSBM |
: a list of objects representing the multiplex network (see) |
memberships |
: a list of length equal to the number of Functional Groups providing the clusterings inside each group. |
plotOptions |
: a list containing the options. See details. |
plotOptions is a list containing the following items
"normalized": Boolean. TRUE if the various matrices are presented in the same scale (between O and 1). FALSE otherwise. Default value FALSE
"compact": Boolean. Default value is TRUE if you ask for the matrices to be transposed to have a more compact view
"legend": Boolean. Set TRUE if you want to see the legend. Default value is FALSE
"legend.title": Boolean. Set TRUE if you want to print the title of the legend. Default value is FALSE
"legend.position": Position of the legend. Possible values are 'bottom', 'top','left,'right'. Default value is 'bottom'
"nodeNames": Set true if the node Names must be plotted. Default value is FALSE
"line.color": The color of the lines to separate groups. Default value is red
"line.width": Width of the lines to separate groups. Default value is NULL, automatically chosen
"title": Title of the plot. Default value is NULL
a ggplot object corresponding to the plot
Nnodes <- c(40,30) blockProp <- list(c(.4,.6),c(0.5,0.5)) nbLayers <- 2 connectParam <- list(list(mean=matrix(rbeta(4,.5,.5),2,2)),list(mean=matrix(rexp(4,.5),2,2))) names(connectParam) <- c('Read','Score') model <- c("bernoulli","poisson") type <- "bipartite" mySampleMultiplexSBM <- sampleMultiplexSBM( nbNodes = Nnodes, blockProp = blockProp, nbLayers = nbLayers, connectParam = connectParam, model=model, dimLabels = c('readers','books'), type=type) listNet <- mySampleMultiplexSBM$listSBM names(listNet) <- c("Read","Affinity") plotMyMultiplexMatrix(listNet,plotOptions=list(legend = TRUE))Nnodes <- c(40,30) blockProp <- list(c(.4,.6),c(0.5,0.5)) nbLayers <- 2 connectParam <- list(list(mean=matrix(rbeta(4,.5,.5),2,2)),list(mean=matrix(rexp(4,.5),2,2))) names(connectParam) <- c('Read','Score') model <- c("bernoulli","poisson") type <- "bipartite" mySampleMultiplexSBM <- sampleMultiplexSBM( nbNodes = Nnodes, blockProp = blockProp, nbLayers = nbLayers, connectParam = connectParam, model=model, dimLabels = c('readers','books'), type=type) listNet <- mySampleMultiplexSBM$listSBM names(listNet) <- c("Read","Affinity") plotMyMultiplexMatrix(listNet,plotOptions=list(legend = TRUE))
Make predictions from an SBM.
## S3 method for class 'SBM' predict(object, covarList = object$covarList, theta_p0 = 0, ...)## S3 method for class 'SBM' predict(object, covarList = object$covarList, theta_p0 = 0, ...)
object |
an R6 object inheriting from class SBM_fit (like SimpleSBM_fit or BipartiteSBM_fit) |
covarList |
a list of covariates. By default, we use the covariates associated with the model. |
theta_p0 |
a threshold... |
... |
additional parameters for S3 compatibility. Not used |
a matrix of expected values for each dyad
This function samples a simple Stochastic Block Models, with various model for the distribution of the edges: Bernoulli, Poisson, or Gaussian models, and possibly with covariates
sampleBipartiteSBM( nbNodes, blockProp, connectParam, model = "bernoulli", dimLabels = c(row = "row", col = "col"), covariates = list(), covariatesParam = numeric(0) )sampleBipartiteSBM( nbNodes, blockProp, connectParam, model = "bernoulli", dimLabels = c(row = "row", col = "col"), covariates = list(), covariatesParam = numeric(0) )
nbNodes |
number of nodes in the network |
blockProp |
parameters for block proportions: list of size two with row and column block proportions |
connectParam |
list of parameters for connectivity with a matrix of means 'mean' and an optional matrix of variances 'var', the sizes of which must match |
model |
character describing the model for the relation between nodes ( |
dimLabels |
an optional list of labels for each dimension (in row, in column) |
covariates |
a list of matrices with same dimension as mat describing covariates at the edge level. No covariate per Default. |
covariatesParam |
optional vector of covariates effect. A zero length numeric vector by default. |
an object with class BipartiteSBM
### ======================================= ### BIPARTITE BERNOULLI SBM ## Graph parameters nbNodes <- c(100, 120) blockProp <- list(c(.5, .5), c(1/3, 1/3, 1/3)) # group proportions means <- matrix(runif(6), 2, 3) # connectivity matrix # In Bernoulli SBM, parameters is a list with # a matrix of means 'mean' which are probabilities of connection connectParam <- list(mean = means) ## Graph Sampling dimLabels = c(row='Reader',col='Book') mySampler <- sampleBipartiteSBM(nbNodes, blockProp, connectParam, model = 'bernoulli',dimLabels) plot(mySampler) plot(mySampler,type='meso',plotOptions = list(vertex.label.name=list(row='Reader',col='Book'))) plot(mySampler,type='meso',plotOptions = list(vertex.label.name=c('A','B'),vertex.size = 1.4)) mySampler$rMemberships() # sample new memberships mySampler$rEdges() # sample new edges mySampler$rNetwork() # sample a new networrk (blocks and edges) ### ======================================= ### BIPARTITE POISSON SBM ## Graph parameters nbNodes <- c(100, 120) blockProp <- list(c(.5, .5), c(1/3, 1/3, 1/3)) # group proportions means <- matrix(rbinom(6, 30, 0.25), 2, 3) # connectivity matrix # In Poisson SBM, parameters is a list with a matrix of # means 'mean' which are a mean integer value taken by edges connectParam <- list(mean = means) ## Graph Sampling dimLabels = c(row = 'Ind', col = 'Service') mySampler <- sampleBipartiteSBM(nbNodes, blockProp, connectParam, model = 'poisson', dimLabels) plot(mySampler,type='expected') plotOptions = list(vertex.label.name=c('U','V'),vertex.size = c(1.4,1.3)) plot(mySampler, type='meso', plotOptions = plotOptions) hist(mySampler$networkData) ### ======================================= ### BIPARTITE GAUSSIAN SBM ## Graph parameters nbNodes <- c(100, 120) blockProp <- list(c(.5, .5), c(1/3, 1/3, 1/3)) # group proportions means <- 20 * matrix(runif(6), 2, 3) # connectivity matrix # In Gaussian SBM, parameters is a list with a matrix # of means 'mean' and a matrix of variances 'var' connectParam <- list(mean = means, var = 1) ## Graph Sampling mySampler <- sampleBipartiteSBM(nbNodes, blockProp, connectParam, model = 'gaussian') plot(mySampler) hist(mySampler$networkData)### ======================================= ### BIPARTITE BERNOULLI SBM ## Graph parameters nbNodes <- c(100, 120) blockProp <- list(c(.5, .5), c(1/3, 1/3, 1/3)) # group proportions means <- matrix(runif(6), 2, 3) # connectivity matrix # In Bernoulli SBM, parameters is a list with # a matrix of means 'mean' which are probabilities of connection connectParam <- list(mean = means) ## Graph Sampling dimLabels = c(row='Reader',col='Book') mySampler <- sampleBipartiteSBM(nbNodes, blockProp, connectParam, model = 'bernoulli',dimLabels) plot(mySampler) plot(mySampler,type='meso',plotOptions = list(vertex.label.name=list(row='Reader',col='Book'))) plot(mySampler,type='meso',plotOptions = list(vertex.label.name=c('A','B'),vertex.size = 1.4)) mySampler$rMemberships() # sample new memberships mySampler$rEdges() # sample new edges mySampler$rNetwork() # sample a new networrk (blocks and edges) ### ======================================= ### BIPARTITE POISSON SBM ## Graph parameters nbNodes <- c(100, 120) blockProp <- list(c(.5, .5), c(1/3, 1/3, 1/3)) # group proportions means <- matrix(rbinom(6, 30, 0.25), 2, 3) # connectivity matrix # In Poisson SBM, parameters is a list with a matrix of # means 'mean' which are a mean integer value taken by edges connectParam <- list(mean = means) ## Graph Sampling dimLabels = c(row = 'Ind', col = 'Service') mySampler <- sampleBipartiteSBM(nbNodes, blockProp, connectParam, model = 'poisson', dimLabels) plot(mySampler,type='expected') plotOptions = list(vertex.label.name=c('U','V'),vertex.size = c(1.4,1.3)) plot(mySampler, type='meso', plotOptions = plotOptions) hist(mySampler$networkData) ### ======================================= ### BIPARTITE GAUSSIAN SBM ## Graph parameters nbNodes <- c(100, 120) blockProp <- list(c(.5, .5), c(1/3, 1/3, 1/3)) # group proportions means <- 20 * matrix(runif(6), 2, 3) # connectivity matrix # In Gaussian SBM, parameters is a list with a matrix # of means 'mean' and a matrix of variances 'var' connectParam <- list(mean = means, var = 1) ## Graph Sampling mySampler <- sampleBipartiteSBM(nbNodes, blockProp, connectParam, model = 'gaussian') plot(mySampler) hist(mySampler$networkData)
This function samples a Multipartite Stochastic Block Models, with various model for the distribution of the edges: Bernoulli, Poisson, or Gaussian models
sampleMultipartiteSBM( nbNodes, blockProp, archiMultipartite, connectParam, model, directed, dimLabels = NULL, seed = NULL )sampleMultipartiteSBM( nbNodes, blockProp, archiMultipartite, connectParam, model, directed, dimLabels = NULL, seed = NULL )
nbNodes |
number of nodes in each functional group involved in the multipartite network |
blockProp |
a list of parameters for block proportions in each functional group |
archiMultipartite |
a matrix with two columns and nbNetworks lines, each line specifying the index of the functional groups in interaction. |
connectParam |
list of parameters for connectivity (of length nbNetworks). Each element is a list of one or two elements: a matrix of means 'mean' and an optional matrix of variances 'var', the sizes of which must match |
model |
a vector of characters describing the model for each network of the Multipartite relation between nodes ( |
directed |
a vector of logical, directed network or not for each network. Default is |
dimLabels |
an optional list of labels for functional group involved in the network |
seed |
numeric to set the seed. |
a list of two elements : simulatedMemberships are the clustering of each node in each Functional Group,
multipartiteNetwork is the list of the simulated networks (each one being a simple or bipartite network)
### ======================================= ### MULTIPARTITE SBM : 4 networks between 3 Functional Groups ## Graph parameters # About the Functional Groups (FG) nbNodes <- c(100,50,40) blockProp <- vector("list", 3) # parameters of clustering in each functional group blockProp[[1]] <- c(0.4,0.3,0.3) # in Functional Group 1 blockProp[[2]] <- c(0.6,0.4) # in Functional Group 2 blockProp[[3]] <- c(0.6,0.4) # in Functional Group 3 # About the interactions between the FG archiMultipartite <- rbind(c(1,2),c(2,3),c(2,2),c(1,3)) # model <- c('bernoulli','poisson','gaussian','gaussian') # type of distribution in each network # for each network : directed or not (not required for an interaction between two different FG) directed <- c( NA, NA , FALSE , NA) connectParam <- list() connectParam[[1]] <- list(mean = matrix(c(0.3, 0.3, 0.5, 0.2, 0.6, 0.6),3,2)) connectParam[[2]] <- list(mean = matrix(c(1000 , 500, 400 , 950),2,2)) connectParam[[3]] <- list(mean = matrix(c(10, 0, -10, 20), 2,2), var = matrix(1,2,2)) connectParam[[4]] <- list(mean = matrix(c(3, 23 ,11 ,16 , 2 ,25), 3,2)) connectParam[[4]]$var <- matrix(c(10,20,1,5,0.1,10), 3,2) dimLabels <- c('A','B','C') ## Graph Sampling mySampleMBM <- sampleMultipartiteSBM(nbNodes, blockProp, archiMultipartite, connectParam, model, directed, dimLabels,seed = 3) listSBM <- mySampleMBM$listSBM memberships <- mySampleMBM$memberships plotMyMultipartiteMatrix(listSBM) plotMyMultipartiteMatrix(listSBM,plotOptions = list(normalized = TRUE)) plotMyMultipartiteMatrix(listSBM,memberships = memberships,plotOptions = list(normalized = TRUE))### ======================================= ### MULTIPARTITE SBM : 4 networks between 3 Functional Groups ## Graph parameters # About the Functional Groups (FG) nbNodes <- c(100,50,40) blockProp <- vector("list", 3) # parameters of clustering in each functional group blockProp[[1]] <- c(0.4,0.3,0.3) # in Functional Group 1 blockProp[[2]] <- c(0.6,0.4) # in Functional Group 2 blockProp[[3]] <- c(0.6,0.4) # in Functional Group 3 # About the interactions between the FG archiMultipartite <- rbind(c(1,2),c(2,3),c(2,2),c(1,3)) # model <- c('bernoulli','poisson','gaussian','gaussian') # type of distribution in each network # for each network : directed or not (not required for an interaction between two different FG) directed <- c( NA, NA , FALSE , NA) connectParam <- list() connectParam[[1]] <- list(mean = matrix(c(0.3, 0.3, 0.5, 0.2, 0.6, 0.6),3,2)) connectParam[[2]] <- list(mean = matrix(c(1000 , 500, 400 , 950),2,2)) connectParam[[3]] <- list(mean = matrix(c(10, 0, -10, 20), 2,2), var = matrix(1,2,2)) connectParam[[4]] <- list(mean = matrix(c(3, 23 ,11 ,16 , 2 ,25), 3,2)) connectParam[[4]]$var <- matrix(c(10,20,1,5,0.1,10), 3,2) dimLabels <- c('A','B','C') ## Graph Sampling mySampleMBM <- sampleMultipartiteSBM(nbNodes, blockProp, archiMultipartite, connectParam, model, directed, dimLabels,seed = 3) listSBM <- mySampleMBM$listSBM memberships <- mySampleMBM$memberships plotMyMultipartiteMatrix(listSBM) plotMyMultipartiteMatrix(listSBM,plotOptions = list(normalized = TRUE)) plotMyMultipartiteMatrix(listSBM,memberships = memberships,plotOptions = list(normalized = TRUE))
This function samples a Multiplex Stochastic Block Models, with various model for the distribution of the edges: Bernoulli, Poisson, or Gaussian models
sampleMultiplexSBM( nbNodes, blockProp, nbLayers, connectParam, model, type = c("directed", "undirected", "bipartite"), dependent = FALSE, dimLabels = NULL, seed = NULL )sampleMultiplexSBM( nbNodes, blockProp, nbLayers, connectParam, model, type = c("directed", "undirected", "bipartite"), dependent = FALSE, dimLabels = NULL, seed = NULL )
nbNodes |
number of nodes in each functional group involved in the Multiplex network |
blockProp |
a vector for block proportion if the networks are simple, a list of parameters for block proportions for both functional groups if the networks are bipartite |
nbLayers |
a matrix with two columns and nbNetworks lines, each line specifying the index of the functional groups in interaction. |
connectParam |
list of parameters for connectivity (of length nbNetworks). Each element is a list of one or two elements: a matrix of means 'mean' and an optional matrix of variances 'var', the sizes of which must match |
model |
a vector of characters describing the model for each network of the Multiplex relation between nodes ( |
type |
a string of character indicating whether the networks are directed, undirected or bipartite |
dependent |
connection parameters in each network |
dimLabels |
an optional list of labels for functional group involved in the network |
seed |
numeric to set the seed. |
a list of two elements : simulatedMemberships are the clustering of each node in each Functional Group, MultiplexNetwork is the list of the simulated networks (each one being a simple or bipartite network)
nbLayers <- 2 ## MultiplexSBM without dependence between layers Nnodes <- 40 blockProp <- c(.4,.6) connectParam <- list(list(mean=matrix(rbeta(4,.5,.5),2,2)),list(mean=matrix(rexp(4,.5),2,2))) model <- c("bernoulli","poisson") type <- "directed" mySampleMultiplexSBM <- sampleMultiplexSBM( nbNodes = Nnodes, blockProp = blockProp, nbLayers = nbLayers, connectParam = connectParam, model=model, type=type) listSBM <- mySampleMultiplexSBM$listSBM ## MultiplexSBM Gaussian with dependence Q <- 3 nbLayers <- 2 connectParam <- list() connectParam$mu <- vector("list",nbLayers) connectParam$mu[[1]] <- matrix(.1,Q,Q) + diag(1:Q) connectParam$mu[[2]] <- matrix(-2,Q,Q) + diag(rev(Q:1)) connectParam$Sigma <- matrix(c(2,1,1,4),nbLayers,nbLayers) model <- rep("gaussian",2) type <- "directed" Nnodes <- 80 blockProp <- c(.3,.3,.4) mySampleMultiplexSBM <- sampleMultiplexSBM( nbNodes = Nnodes, blockProp = blockProp, nbLayers = nbLayers, connectParam = connectParam, model=model, type="undirected", dependent=TRUE) listSBM <- mySampleMultiplexSBM$listSBM ## MultiplexSBM Bernoulli with dependence Q <- 2 P00<-matrix(runif(Q*Q),Q,Q) P10<-matrix(runif(Q*Q),Q,Q) P01<-matrix(runif(Q*Q),Q,Q) P11<-matrix(runif(Q*Q),Q,Q) SumP<-P00+P10+P01+P11 P00<-P00/SumP P01<-P01/SumP P10<-P10/SumP P11<-P11/SumP connectParam <- list() connectParam$prob00 <- P00 connectParam$prob01 <- P01 connectParam$prob10 <- P10 connectParam$prob11 <- P11 model <- rep("bernoulli",2) type <- "directed" nbLayers <- 2 Nnodes <- 40 blockProp <- c(.6,.4) mySampleMultiplexSBM <- sampleMultiplexSBM( nbNodes = Nnodes, blockProp = blockProp, nbLayers = nbLayers, connectParam = connectParam, model=model, type=type, dependent=TRUE) listSBM_BB <- mySampleMultiplexSBM$listSBMnbLayers <- 2 ## MultiplexSBM without dependence between layers Nnodes <- 40 blockProp <- c(.4,.6) connectParam <- list(list(mean=matrix(rbeta(4,.5,.5),2,2)),list(mean=matrix(rexp(4,.5),2,2))) model <- c("bernoulli","poisson") type <- "directed" mySampleMultiplexSBM <- sampleMultiplexSBM( nbNodes = Nnodes, blockProp = blockProp, nbLayers = nbLayers, connectParam = connectParam, model=model, type=type) listSBM <- mySampleMultiplexSBM$listSBM ## MultiplexSBM Gaussian with dependence Q <- 3 nbLayers <- 2 connectParam <- list() connectParam$mu <- vector("list",nbLayers) connectParam$mu[[1]] <- matrix(.1,Q,Q) + diag(1:Q) connectParam$mu[[2]] <- matrix(-2,Q,Q) + diag(rev(Q:1)) connectParam$Sigma <- matrix(c(2,1,1,4),nbLayers,nbLayers) model <- rep("gaussian",2) type <- "directed" Nnodes <- 80 blockProp <- c(.3,.3,.4) mySampleMultiplexSBM <- sampleMultiplexSBM( nbNodes = Nnodes, blockProp = blockProp, nbLayers = nbLayers, connectParam = connectParam, model=model, type="undirected", dependent=TRUE) listSBM <- mySampleMultiplexSBM$listSBM ## MultiplexSBM Bernoulli with dependence Q <- 2 P00<-matrix(runif(Q*Q),Q,Q) P10<-matrix(runif(Q*Q),Q,Q) P01<-matrix(runif(Q*Q),Q,Q) P11<-matrix(runif(Q*Q),Q,Q) SumP<-P00+P10+P01+P11 P00<-P00/SumP P01<-P01/SumP P10<-P10/SumP P11<-P11/SumP connectParam <- list() connectParam$prob00 <- P00 connectParam$prob01 <- P01 connectParam$prob10 <- P10 connectParam$prob11 <- P11 model <- rep("bernoulli",2) type <- "directed" nbLayers <- 2 Nnodes <- 40 blockProp <- c(.6,.4) mySampleMultiplexSBM <- sampleMultiplexSBM( nbNodes = Nnodes, blockProp = blockProp, nbLayers = nbLayers, connectParam = connectParam, model=model, type=type, dependent=TRUE) listSBM_BB <- mySampleMultiplexSBM$listSBM
This function samples a simple Stochastic Block Models, with various model for the distribution of the edges: Bernoulli, Poisson, or Gaussian models, and possibly with covariates
sampleSimpleSBM( nbNodes, blockProp, connectParam, model = "bernoulli", directed = FALSE, dimLabels = c("node"), covariates = list(), covariatesParam = numeric(0) )sampleSimpleSBM( nbNodes, blockProp, connectParam, model = "bernoulli", directed = FALSE, dimLabels = c("node"), covariates = list(), covariatesParam = numeric(0) )
nbNodes |
number of nodes in the network |
blockProp |
parameters for block proportions |
connectParam |
list of parameters for connectivity with a matrix of means 'mean' and an optional matrix of variances 'var', the sizes of which must match |
model |
character describing the model for the relation between nodes ( |
directed |
logical, directed network or not. Default is |
dimLabels |
an optional list of labels for each dimension (in row, in column) |
covariates |
a list of matrices with same dimension as mat describing covariates at the edge level. No covariate per Default. |
covariatesParam |
optional vector of covariates effect. A zero length numeric vector by default. |
an object with class SimpleSBM
### ======================================= ### SIMPLE BINARY SBM (Bernoulli model) ## Graph parameters nbNodes <- 90 blockProp <- c(.5, .25, .25) # group proportions means <- diag(.4, 3) + 0.05 # connectivity matrix: affiliation network # In Bernoulli SBM, parameters is a list with a # matrix of means 'mean' which are probabilities of connection connectParam <- list(mean = means) ## Graph Sampling mySampler <- sampleSimpleSBM(nbNodes, blockProp, connectParam, model = 'bernoulli') plot(mySampler) plot(mySampler) plot(mySampler,type='meso') hist(mySampler$networkData) ### ======================================= ### SIMPLE POISSON SBM ## Graph parameters nbNodes <- 90 blockProp <- c(.5, .25, .25) # group proportions means <- diag(15., 3) + 5 # connectivity matrix: affiliation network # In Poisson SBM, parameters is a list with # a matrix of means 'mean' which are a mean integer value taken by edges connectParam <- list(mean = means) ## Graph Sampling mySampler <- sampleSimpleSBM(nbNodes, blockProp, list(mean = means), model = "poisson") plot(mySampler) plot(mySampler,type='meso') hist(mySampler$networkData) ### ======================================= ### SIMPLE GAUSSIAN SBM ## Graph parameters nbNodes <- 90 blockProp <- c(.5, .25, .25) # group proportions means <- diag(15., 3) + 5 # connectivity matrix: affiliation network # In Gaussian SBM, parameters is a list with # a matrix of means 'mean' and a matrix of variances 'var' connectParam <- list(mean = means, var = 2) ## Graph Sampling mySampler <- sampleSimpleSBM(nbNodes, blockProp, connectParam, model = "gaussian",dimLabels='Tree') plot(mySampler) plot(mySampler,type='meso') hist(mySampler$networkData)### ======================================= ### SIMPLE BINARY SBM (Bernoulli model) ## Graph parameters nbNodes <- 90 blockProp <- c(.5, .25, .25) # group proportions means <- diag(.4, 3) + 0.05 # connectivity matrix: affiliation network # In Bernoulli SBM, parameters is a list with a # matrix of means 'mean' which are probabilities of connection connectParam <- list(mean = means) ## Graph Sampling mySampler <- sampleSimpleSBM(nbNodes, blockProp, connectParam, model = 'bernoulli') plot(mySampler) plot(mySampler) plot(mySampler,type='meso') hist(mySampler$networkData) ### ======================================= ### SIMPLE POISSON SBM ## Graph parameters nbNodes <- 90 blockProp <- c(.5, .25, .25) # group proportions means <- diag(15., 3) + 5 # connectivity matrix: affiliation network # In Poisson SBM, parameters is a list with # a matrix of means 'mean' which are a mean integer value taken by edges connectParam <- list(mean = means) ## Graph Sampling mySampler <- sampleSimpleSBM(nbNodes, blockProp, list(mean = means), model = "poisson") plot(mySampler) plot(mySampler,type='meso') hist(mySampler$networkData) ### ======================================= ### SIMPLE GAUSSIAN SBM ## Graph parameters nbNodes <- 90 blockProp <- c(.5, .25, .25) # group proportions means <- diag(15., 3) + 5 # connectivity matrix: affiliation network # In Gaussian SBM, parameters is a list with # a matrix of means 'mean' and a matrix of variances 'var' connectParam <- list(mean = means, var = 2) ## Graph Sampling mySampler <- sampleSimpleSBM(nbNodes, blockProp, connectParam, model = "gaussian",dimLabels='Tree') plot(mySampler) plot(mySampler,type='meso') hist(mySampler$networkData)
R6 virtual class for SBM representation (mother class of SimpleSBM, BipartiteSBM, MultipartiteSBM)
R6 virtual class for SBM representation (mother class of SimpleSBM, BipartiteSBM, MultipartiteSBM)
modelNamecharacter, the family of model for the distribution of the edges
directedmode of the network data (directed or not or not applicable)
dimLabelsvector or list of characters, the label of each dimension
nbNodesvector describing the number of the successive elements connecting the network
nbCovariatesinteger, the number of covariates
blockPropblock proportions (aka prior probabilities of each block)
connectParamparameters associated to the connectivity of the SBM, e.g. matrix of inter/inter block probabilities when model is Bernoulli
covarParamvector of regression parameters associated with the covariates.
covarListlist of matrices of covariates
covarArraythe array of covariates
covarEffecteffect of covariates
networkDatathe network data (adjacency or incidence matrix or list of such object)
expectationexpected values of connection under the current model
new()
constructor for SBM
SBM$new(
model = vector("character", 0),
directed = vector("logical", 0),
dimension = vector("numeric", 0),
dimLabels = vector("character", 0),
blockProp = vector("numeric", 0),
connectParam = vector("list", 0),
covarParam = numeric(length(covarList)),
covarList = list()
)modelcharacter describing the type of model
directedlogical describing if the network data is directed or not
dimensiondimension of the network data
dimLabelslabels of each dimension
blockPropparameters for block proportions (vector or list of vectors)
connectParamlist of parameters for connectivity
covarParamoptional vector of covariates effect
covarListoptional list of covariates data
rNetwork()
a method to sample a network data for the current SBM (blocks and edges)
SBM$rNetwork(store = FALSE)
storeshould the sampled network be stored (and overwrite the existing data)? Default to FALSE
a list with the sampled block and network
show()
print method
SBM$show(type = "Stochastic Block Model")
typecharacter to tune the displayed name
print()
print method
SBM$print()
clone()
The objects of this class are cloneable with this method.
SBM$clone(deep = FALSE)
deepWhether to make a deep clone.
R6 class for Simple SBM
R6 class for Simple SBM
sbm::SBM -> SimpleSBM
dimLabelsa single character giving the label of the nodes
blockPropvector of block proportions (aka prior probabilities of each block)
connectParamparameters associated to the connectivity of the SBM, e.g. matrix of inter/inter block probabilities when model is Bernoulli
probMembershipsmatrix of estimated probabilities for block memberships for all nodes
nbBlocksnumber of blocks
nbDyadsnumber of dyads (potential edges in the network)
nbConnectParamnumber of parameter used for the connectivity
membershipsvector of clustering
indMembershipsmatrix for clustering memberships
new()
constructor for SBM
SimpleSBM$new(
model,
nbNodes,
directed,
blockProp,
connectParam,
dimLabels = c("node"),
covarParam = numeric(length(covarList)),
covarList = list()
)modelcharacter describing the type of model
nbNodesnumber of nodes in the network
directedlogical, directed network or not.
blockPropparameters for block proportions (vector of list of vectors)
connectParamlist of parameters for connectivity with a matrix of means 'mean' and an optional scalar for the variance 'var'. The size of mu must match blockProp length
dimLabelsoptional label for the node (default is "nodeName")
covarParamoptional vector of covariates effect
covarListoptional list of covariates data
rMemberships()
a method to sample new block memberships for the current SBM
SimpleSBM$rMemberships(store = FALSE)
storeshould the sampled blocks be stored (and overwrite the existing data)? Default to FALSE
the sampled blocks
rEdges()
a method to sample a network data (edges) for the current SBM
SimpleSBM$rEdges(store = FALSE)
storeshould the sampled edges be stored (and overwrite the existing data)? Default to FALSE
the sampled network
predict()
prediction under the currently parameters
SimpleSBM$predict(covarList = self$covarList, theta_p0 = 0)
covarLista list of covariates. By default, we use the covariates with which the model was estimated
theta_p0a threshold...
a matrix of expected values for each dyad
show()
show method
SimpleSBM$show(type = "Simple Stochastic Block Model")
typecharacter used to specify the type of SBM
plot()
basic matrix plot method for SimpleSBM object or mesoscopic plot
SimpleSBM$plot(
type = c("data", "expected", "meso"),
ordered = TRUE,
plotOptions = list()
)typecharacter for the type of plot: either 'data' (true connection), 'expected' (fitted connection) or 'meso' (mesoscopic view). Default to 'data'.
orderedlogical: should the rows and columns be reordered according to the clustering? Default to TRUE.
plotOptionslist with the parameters for the plot. See help of the corresponding S3 method for details.
a ggplot2 object for the 'data' and 'expected', a list with the igraph object g, the layout and the plotOptions for the 'meso'
clone()
The objects of this class are cloneable with this method.
SimpleSBM$clone(deep = FALSE)
deepWhether to make a deep clone.
R6 Class definition of a Simple SBM fit
R6 Class definition of a Simple SBM fit
This class is designed to give a representation and adjust an SBM fitted with blockmodels.
sbm::SBM -> sbm::SimpleSBM -> SimpleSBM_fit
loglikdouble: approximation of the log-likelihood (variational lower bound) reached
ICLdouble: value of the integrated classification log-likelihood
penaltydouble, value of the penalty term in ICL
entropydouble, value of the entropy due to the clustering distribution
storedModelsdata.frame of all models fitted (and stored) during the optimization
new()
constructor for a Simple SBM fit
SimpleSBM_fit$new( adjacencyMatrix, model, directed, dimLabels = c(node = "nodeName"), covarList = list() )
adjacencyMatrixsquare (weighted) matrix
modelcharacter ('bernoulli', 'poisson', 'gaussian')
directedlogical, directed network or not. In not, adjacencyMatrix must be symmetric.
dimLabelslist of labels of each dimension (in row, in columns)
covarListand optional list of covariates, each of whom must have the same dimension as adjacencyMatrix
optimize()
function to perform optimization
SimpleSBM_fit$optimize(estimOptions = list())
estimOptionsa list of parameters controlling the inference algorithm and model selection. See details.
setModel()
method to select a specific model among the ones fitted during the optimization. Fields of the current SBM_fit will be updated accordingly.
SimpleSBM_fit$setModel(index)
indexinteger, the index of the model to be selected (row number in storedModels)
reorder()
permute group labels by order of decreasing probability
SimpleSBM_fit$reorder()
show()
show method
SimpleSBM_fit$show(type = "Fit of a Simple Stochastic Block Model")
typecharacter used to specify the type of SBM
clone()
The objects of this class are cloneable with this method.
SimpleSBM_fit$clone(deep = FALSE)
deepWhether to make a deep clone.
This dataset contains two networks where the nodes are countries and an
edge in network "belligerent" means that the two countries have been at
least once at war between years 1816 to 2007 while an edge in network "alliance"
means that the two countries have had a formal alliance between years 1816 to 2012.
The network belligerent have less nodes since countries which have not been at
war are not considered.
warwar
A list with 2 two igraph objects, alliance and belligerent.
Each graph have three attributes: 'name' (the country name), 'power' (a score related to military power: the higher, the better) and
'trade' (a score related to the trade effort between pairs of countries).
networks were extracted from https://correlatesofwar.org/
Sarkees, Meredith Reid and Frank Wayman (2010). Resort to War: 1816 - 2007. Washington DC: CQ Press.
Gibler, Douglas M. 2009. International military alliances, 1648-2008. CQ Press
data(war) class(war$belligerent) igraph::gorder(war$alliance) igraph::gorder(war$belligerent) igraph::edges(war$alliance) igraph::get.graph.attribute(war$alliance)data(war) class(war$belligerent) igraph::gorder(war$alliance) igraph::gorder(war$belligerent) igraph::edges(war$alliance) igraph::get.graph.attribute(war$alliance)