CISE (version 0.1.0)

MGRAF3: Third variant of M-GRAF model

Description

MGRAF3 returns the estimated common structure Z and \(Q\) that are shared by all the subjects as well as the subject-specific low rank matrix \(\Lambda_i\) for multiple undirected graphs.

Usage

MGRAF3(A, K, tol, maxit)

Arguments

A

Binary array with size VxVxn storing the VxV symmetric adjacency matrices of n graphs.

K

An integer that specifies the latent dimension of the graphs

tol

A numeric scalar that specifies the convergence threshold of CISE algorithm. CISE iteration continues until the absolute percent change in joint log-likelihood is smaller than this value. Default is tol = 0.01.

maxit

An integer that specifies the maximum number of iterations. Default is maxit = 5.

Value

A list is returned containing the ingredients below from M-GRAF3 model corresponding to the largest log-likelihood over iterations.

Z

A numeric vector containing the lower triangular entries in the estimated matrix Z.

Lambda

Kxn matrix where each column stores the diagonal entries in \(\Lambda_i\).

Q

VxK orthonormal matrix

LL_max

Maximum log-likelihood across iterations.

LL

Joint log-likelihood at each iteration.

Details

The subject-specific deviation \(D_i\) is decomposed into $$D_i = Q * \Lambda_i * Q^{\top},$$ where \(Q\) is a VxK orthonormal matrix and each \(\Lambda_i\) is a KxK diagonal matrix.

Examples

# NOT RUN {
data(A)
n = dim(A)[3]
subs = sample.int(n=n,size=30)
A_sub = A[ , , subs]
res = MGRAF3(A=A_sub, K=3, tol=0.01, maxit=5)

# }