标题： 脑连接的时间功能因子分析 显示英文标题

标题： Temporal Functional Factor Analysis of Brain Connectivity

摘要： 许多功能磁共振成像（fMRI）的分析研究功能连接（FC），即远距离脑区之间的统计依赖性。 这些分析通常是探索性的，指导未来的确认性研究。 在本工作中，我们提出了一种基于因子分析（FA）的方法，该方法非常适合研究FC。 在这一背景下，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有指导的研究，这与连接分析的探索性角色一致。 然而，将FA应用于fMRI数据会带来三个问题：（1）其目标子空间捕捉了应被视为噪声的短程空间依赖性，（2）它需要对大规模的空间协方差进行分解，（3）它忽略了数据中的时间依赖性。 为了解决这些限制，我们在功能数据分析的框架内开发了一个因子模型——该领域将某些数据视为来自平滑的潜在曲线。 所提出的方法（1）使用矩阵补全技术从其目标子空间中过滤掉短程空间依赖性，（2）采用分布式算法对大规模协方差矩阵进行分解，（3）利用功能回归来利用时间动态。 这些创新共同产生了一种全面且可扩展的方法来研究FC。 显示英文摘要

摘要： 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.