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#' Generates data from a stochastic block model for multiple network data views
#'
#' Generates data from a stochastic block model for multiple network data views
#' with n observations and two views.
#'
#' @param n number of observations
#' @param Pi K1 x K2 matrix where the (k, k')th entry contains the probability of an observation
#' belonging to community k in View 1 and community k' in View 2
#' @param theta1 K1 x K1 matrix containing the between-community edge probabilities for View 1
#' @param theta2 K2 x K2 matrix containing the between-community edge probabilities for View 2
#' @param sparse If true, return data views in sparseMatrix format
#'
#' @importFrom Matrix sparseMatrix
#' @importFrom stats runif
#' @export
#' @return
#' A list containing the following components:
#' \item{data}{A list with two items: the n x n view 1 adjacency matrix and
#' the n x n view 2 adjacency matrix}
#' \item{communities}{A list with two items: the view 1 community memberships and
#' the view 2 community memberships}
#'
#' @examples
#' # 50 draws from a stochastic block model for two network data views
#' # where the communities are dependent
#' n <- 50
#' Pi <- diag(c(0.5, 0.5))
#' theta1 <- rbind(c(0.5, 0.1), c(0.1, 0.5))
#' theta2 <- cbind(c(0.1, 0.5), c(0.5, 0.1))
#'
#' mv_sbm_gen(n, Pi, theta1, theta2)
#'
#' @references
#' Gao, L.L., Witten, D., Bien, J. Testing for Association in Multi-View Network Data, preprint.
mv_sbm_gen <- function(n, Pi, theta1, theta2, sparse=FALSE) {
input_check <- function(n, Pi, theta1, theta2) {
if(!is.matrix(Pi) | !is.numeric(Pi)) {
stop("Pi must be a numeric matrix")
}
if(any(Pi < 0) | (abs(sum(Pi) - 1) > 1e-15)) {
stop("Pi must be non-negative and sum to 1")
}
if(!is.numeric(n)) {
stop("n must be a positive integer")
}
if((n %% 1 != 0) | n <= 0) {
stop("n must be a positive integer")
}
if(!is.matrix(theta1) | !is.numeric(theta1) | !is.matrix(theta2) | !is.numeric(theta2)) {
stop("theta1 and theta2 must be numeric matrices")
}
if((ncol(theta1) != nrow(Pi)) | nrow(theta1) != nrow(Pi) |
nrow(theta2) != ncol(Pi) | (ncol(theta2) != ncol(Pi))) {
stop("theta1 must be K1 x K1 and theta2 must be K2 x K2, where Pi is K1 x K2")
}
if(any(theta1 < 0) | any(theta1 > 1) | any(theta2 < 0) | any(theta2 > 1)) {
stop("theta1 and theta2 must have non-negative elements that are < 1")
}
if(!isSymmetric(theta1) | !isSymmetric(theta2)) {
stop("theta1 and theta2 must be symmetric matrices")
}
}
# outputs random adjacency matrix X with E[X] = pmat
generate_random_graph <- function(pmat) {
n <- nrow(pmat)
upper.ind <- which(upper.tri(pmat), arr.ind=T)
upper.unif <- runif(n = nrow(upper.ind))
edge.ind <- upper.ind[which(upper.unif < pmat[upper.ind]), ]
Matrix::sparseMatrix(edge.ind[, 1], edge.ind[, 2], dims=c(n, n), symmetric=T)
}
generate_sv_sbm <- function(theta, com) {
n <- length(com)
K <- nrow(theta)
# expected value of adjacency matrix:
# n x n matrix with ijth entry = theta[com[i], com[j]]
outer <- matrix(0, n, K)
outer[cbind(1:n, com)] <- 1
outer <- outer
pmat <- outer%*%tcrossprod(theta, outer)
generate_random_graph(pmat)
}
input_check(n, Pi, theta1, theta2)
com <- mv_memberships_gen(n, Pi)
X1 <- generate_sv_sbm(theta1, com[, 1])
X2 <- generate_sv_sbm(theta2, com[, 2])
if(!sparse) {
X1 <- as.matrix(X1)*1 # convert to regular matrix object
X2 <- as.matrix(X2)*1
}
return(list(data=list(view1=X1, view2=X2), communities=list(view1=com[, 1], view2=com[, 2])))
}
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