  In many human brain network studies, we do not have sufficient number (n) of
images relative to the number (p) of voxels due to the prohibitively expensive
cost of scanning enough subjects. Thus, brain network models usually suffer the
small-n large-p problem. Such a problem is often remedied by sparse network
models, which are usually solved numerically by optimizing L1-penalties.
Unfortunately, due to the computational bottleneck associated with optimizing
L1-penalties, it is not practical to apply such methods to construct
large-scale brain networks at the voxel-level. In this paper, we propose a new
scalable sparse network model using cross-correlations that bypass the
computational bottleneck. Our model can build sparse brain networks at the
voxel level with p > 25000. Instead of using a single sparse parameter that may
not be optimal in other studies and datasets, the computational speed gain
enables us to analyze the collection of networks at every possible sparse
parameter in a coherent mathematical framework via persistent homology. The
method is subsequently applied in determining the extent of heritability on a
functional brain network at the voxel-level for the first time using twin fMRI.
