Many analyses of functional magnetic resonance imaging (fMRI) examine functional connectivity (FC), or the statistical dependencies among distant brain regions. These analyses are typically exploratory, guiding future confirmatory research. In this work, we present an approach based on factor analysis (FA) that is well-suited to studying FC. FA is appealing in this context because its flexible model assumptions permit a guided investigation of its target subspace consistent with the exploratory role of connectivity analyses. However, applying FA to fMRI data poses three problems: (1) its target subspace captures short-range spatial dependencies that should be treated as noise, (2) it requires factorization of a massive spatial covariance, and (3) it overlooks temporal dependencies in the data. To address these limitations, we develop a factor model within the framework of functional data analysis--a field which views certain data as arising from smooth underlying curves. The proposed approach (1) uses matrix completion techniques to filter short-range spatial dependencies out of its target subspace, (2) employs a distributed algorithm for factorizing large-scale covariance matrices, and (3) leverages functional regression to exploit temporal dynamics. Together, these innovations yield a comprehensive and scalable method for studying FC.

翻译：许多功能磁共振成像（fMRI）分析研究功能连接性（FC），即远距离脑区之间的统计依赖性。这类分析通常具有探索性，为未来的验证性研究提供指导。本研究提出一种基于因子分析（FA）的方法，该方法非常适合研究FC。在此背景下，FA具有吸引力，因为其灵活的模型假设允许对其目标子空间进行引导性探究，这与连接性分析的探索性角色相一致。然而，将FA应用于fMRI数据存在三个问题：（1）其目标子空间捕获了应被视为噪声的短程空间依赖性；（2）需要对大规模空间协方差矩阵进行分解；（3）忽略了数据中的时间依赖性。为应对这些局限，我们在函数数据分析框架内开发了一个因子模型——该领域将某些数据视为源自平滑的潜在曲线。所提出的方法（1）使用矩阵补全技术从其目标子空间中滤除短程空间依赖性；（2）采用分布式算法分解大规模协方差矩阵；（3）利用函数回归来挖掘时间动态特性。这些创新共同构成了一种全面且可扩展的研究FC的方法。