Human brain functional connectivity (FC) is often measured as the similarity of functional MRI responses across brain regions when a brain is either resting or performing a task. This paper aims to statistically analyze the dynamic nature of FC by representing the collective time-series data, over a set of brain regions, as a trajectory on the space of covariance matrices, or symmetric-positive definite matrices (SPDMs). We use a newly developed metric on the space of SPDMs to quantify differences across FC observations and for clustering and classification of FC trajectories. To facilitate large scale and high-dimensional data analysis, we propose a novel, metric-based dimensionality reduction technique to reduce data from large SPDMs to small SPDMs. We illustrate this comprehensive framework using data from the Human Connectome Project (HCP) database for multiple subjects and tasks, with classification rates that match or outperform state-of-the-art techniques.
翻译:人类大脑功能连接(FC)通常被测量为在大脑正在休息或执行任务时,大脑区域功能性磁共振反应的相似性。本文件旨在从统计上分析FC的动态性质,代表一组脑区域的集体时间序列数据,作为共变矩阵空间的轨迹,或对称确定矩阵(SPDMs)的轨迹。我们使用新开发的关于SPDMs空间的测量尺度来量化FC观测之间的差异,并对FC轨迹进行分组和分类。为了便利大规模和高维度数据分析,我们提出了一种新型的、基于多维度的减少技术,以将大型SPDMs的数据从大型SPDMs到小型SPDMs的数据减少。我们用人类连接项目(HCP)数据库的数据来说明这一全面的框架,用于多个主题和任务,其分类率符合或超过最新技术的分类率。