MGRAF2: Second variant of M-GRAF model

In CISE: Common and Individual Structure Explained for Multiple Graphs

Description

MGRAF2 returns the estimated common structure Z and Λ that are shared by all the subjects as well as the subject-specific low rank matrix Q_i for multiple undirected graphs.

Usage

MGRAF2(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.

Details

The subject-specific deviation D_i is decomposed into

D_i = Q_i * Λ * Q_i^{\top},

where each Q_i is a VxK orthonormal matrix and Λ is a KxK diagonal matrix.

Value

A list is returned containing the ingredients below from M-GRAF2 model corresponding to the largest log-likelihood over iterations.

Z	A numeric vector containing the lower triangular entries in the estimated matrix Z.
Lambda	Kx1 vector storing the diagonal entries in Λ.
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 * Λ * Q_i^{\top}; L=V(V-1)/2.
LL_max	Maximum log-likelihood across iterations.
LL	Joint log-likelihood at each iteration.

Examples

data(A)
n = dim(A)[3]
subs = sample.int(n=n,size=30)
A_sub = A[ , , subs]
res = MGRAF2(A=A_sub, K=3, tol=0.01, maxit=5)

CISE documentation built on May 2, 2019, 9:19 a.m.