  Network-oriented research has been increasingly popular in many scientific
areas. In neuroscience research, imaging-based network connectivity measures
have become the key for understanding brain organizations, potentially serving
as individual neural fingerprints. There are major challenges in analyzing
connectivity matrices including the high dimensionality of brain networks,
unknown latent sources underlying the observed connectivity, and the large
number of brain connections leading to spurious findings. In this paper, we
propose a novel blind source separation method with low-rank structure and
uniform sparsity (LOCUS) as a fully data-driven decomposition method for
network measures. Compared with the existing method that vectorizes
connectivity matrices ignoring brain network topology, LOCUS achieves more
efficient and accurate source separation for connectivity matrices using
low-rank structure. We propose a novel angle-based uniform sparsity
regularization that demonstrates better performance than the existing sparsity
controls for low-rank tensor methods. We propose a highly efficient iterative
Node-Rotation algorithm that exploits the block multi-convexity of the
objective function to solve the non-convex optimization problem for learning
LOCUS. We illustrate the advantage of LOCUS through extensive simulation
studies. Application of LOCUS to Philadelphia Neurodevelopmental Cohort
neuroimaging study reveals biologically insightful connectivity traits which
are not found using the existing method.
