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Network-oriented research has been increasingly popular in many scientificareas. In neuroscience research, imaging-based network connectivity measureshave become the key for understanding brain organizations, potentially servingas individual neural fingerprints. There are major challenges in analyzingconnectivity matrices including the high dimensionality of brain networks,unknown latent sources underlying the observed connectivity, and the largenumber of brain connections leading to spurious findings. In this paper, wepropose a novel blind source separation method with low-rank structure anduniform sparsity (LOCUS) as a fully data-driven decomposition method fornetwork measures. Compared with the existing method that vectorizesconnectivity matrices ignoring brain network topology, LOCUS achieves moreefficient and accurate source separation for connectivity matrices usinglow-rank structure. We propose a novel angle-based uniform sparsityregularization that demonstrates better performance than the existing sparsitycontrols for low-rank tensor methods. We propose a highly efficient iterativeNode-Rotation algorithm that exploits the block multi-convexity of theobjective function to solve the non-convex optimization problem for learningLOCUS. We illustrate the advantage of LOCUS through extensive simulationstudies. Application of LOCUS to Philadelphia Neurodevelopmental Cohortneuroimaging study reveals biologically insightful connectivity traits whichare not found using the existing method.

LOCUS: A Novel Decomposition Method for Brain Network Connectivity Matrices using Low-rank Structure with Uniform Sparsity