Common and Individual Structure Explained for Multiple Graphs

Specific dimension reduction methods for replicated graphs
(multiple undirected graphs repeatedly measured on a common set of
nodes). The package contains efficient procedures for estimating
a shared baseline propensity matrix and graph-specific low rank
matrices. The algorithm uses block coordinate descent algorithm to
solve the model, which alternatively performs L2-penalized logistic
regression and multiple partial eigenvalue decompositions, as described
in the paper Wang et al. (2017) .

CISE is an R package that fits the multiple-gragh factorization (M-GRAF) model ( Wang et al., 2017)
for separating common and individual low rank structure for multiple graphs with a common set of nodes.

Installation

install.packages("CISE")
# Or the development version from GitHub:
# install.packages("devtools")
devtools::install_github("wangronglu/CISE")

Usage

The package contains a dataset of binary brain networks of 212 subjects. After loading the data, we can apply 3 variants of M-GRAF model
to decompose the data. Model checking is needed to evaluate which model provides the best fit.

library(CISE)
# load data
# A is an array of adjacency matrices of multiple graphs
data(A)
? MGRAF2
# specify low rank K=5
res = MGRAF2(A = A, K=5, tol=0.01, maxit=5)
# check the common structure - baseline propensities of edges between pairwise nodes
res$Z
# check low rank component for each graph
res$Q
# check joint log-likelihood across iterations
res$LL