CISE (version 0.1.0)

MGRAF1: First variant of M-GRAF model

Description

MGRAF1 returns the estimated common structure Z and subject-specific low rank components \(Q_i\) and \(\Lambda_i\) for multiple undirected graphs.

Usage

MGRAF1(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-GRAF1 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

VxKxn array containing the estimated VxK orthonormal matrix \(Q_i\), i=1,...,n.

D_LT

Lxn matrix where each column stores the lower triangular entries in \(D_i = Q_i * \Lambda_i * Q_i^{\top}\); L=V(V-1)/2.

LL_max

Maximum log-likelihood across iterations.

LL

Joint log-likelihood at each iteration.

Details

The subject-specific deviation \(D_i\) is decomposed into $$D_i = Q_i * \Lambda_i * Q_i^{\top},$$ where each \(Q_i\) 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 = MGRAF1(A=A_sub, K=3, tol=0.01, maxit=5)

# }