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.

翻译：网络导向研究在众多科学领域中日益流行。在神经科学研究中，基于影像的网络连接度量已成为理解大脑组织的关键，并可能作为个体神经指纹。分析连接矩阵面临主要挑战，包括大脑网络的高维性、观测连接下未知的潜在来源，以及大量大脑连接导致的假阳性发现。本文提出一种新型盲源分离方法——具有低秩结构与均匀稀疏性的LOCUS，作为网络度量的完全数据驱动分解方法。与忽视大脑网络拓扑结构而将连接矩阵向量化的现有方法相比，LOCUS利用低秩结构实现了更高效、更准确的连接矩阵源分离。我们提出一种新颖的基于角度的均匀稀疏正则化方法，其性能优于现有低秩张量方法的稀疏控制策略。我们设计了一种高效的迭代节点旋转算法，利用目标函数的块多凸性来求解学习LOCUS的非凸优化问题。通过大量仿真研究展示了LOCUS的优势。将LOCUS应用于费城神经发育队列神经影像研究，揭示了现有方法未能发现的具有生物学洞察力的连接特征。