  There have been many attempts to identify high-dimensional network features
via multivariate approaches. Specifically, when the number of voxels or nodes,
denoted as p, are substantially larger than the number of images, denoted as n,
it produces an under-determined model with infinitely many possible solutions.
The small-n large-p problem is often remedied by regularizing the
under-determined system with additional sparse penalties. Popular sparse
network models include sparse correlations, LASSO, sparse canonical
correlations and graphical-LASSO. These popular sparse models require
optimizing L1-norm penalties, which has been the major computational bottleneck
for solving large-scale problems. Thus, many existing sparse brain network
models in brain imaging have been restricted to a few hundreds nodes or less.
2527 MRI features used in a LASSO model for Alzheimer's disease is probably the
largest number of features used in any sparse model in the brain imaging
literature.
