multiRDPG {multiRDPG}

Fitting Multiple Random Dot Product Graphs

Description

multiRDPG is used to fit Multiple Random Dot Product Graphs from a set of adjacency matrices.

Usage

multiRDPG(A, d, maxiter = 100, tol = 1e-06)

Arguments

A

List of adjacency matrices representing graphs. Each matrix must be symmetric. All matrices of the same size n x n.

d

Dimension of latent space. d<= n.

maxiter

Maximal number of iterations. Default is 100.

tol

Tolerance for update of the objective function. Default is 1e-6.

Value

Returns a list of the following:

U	Matrix of the joint vectors. n x d.
Lambda	List of diagonal matrices. One for each graph. d x d.
Converged	Represent of the algorithm converged. 1 if converged, 0 if not.
iter	Number of iterations
maxiter	Maximal number of iterations.Default is 100.
objfun	Value of the objective function. sum_k ||A^k - U Lambda U^T||_F^2

Author(s)

Agnes Martine Nielsen ([e-mail])

See Also

multiRDPG_test

Examples

#simulate data
U <- matrix(0, nrow=20, ncol=3)
U[,1] <- 1/sqrt(20)
U[,2] <- rep(c(1,-1), 10)/sqrt(20)
U[,3] <- rep(c(1,1,-1,-1), 5)/sqrt(20)

L<-list(diag(c(11,6,2)),diag(c(15,4,1)))
A <- list()
for(i in 1:2){
  P <- U%*%L[[i]]%*%t(U)
  A[[i]] <-apply(P,c(1,2),function(x){rbinom(1,1,x)})
  A[[i]][lower.tri(A[[i]])]<-t(A[[i]])[lower.tri(A[[i]])]
}

#fit model
multiRDPG(A,3)