In this paper, we introduce a novel statistical model for the integrative analysis of Riemannian-valued functional data and high-dimensional data. We apply this model to explore the dependence structure between each subject's dynamic functional connectivity -- represented by a temporally indexed collection of positive definite covariance matrices -- and high-dimensional data representing lifestyle, demographic, and psychometric measures. Specifically, we employ a reformulation of canonical correlation analysis that enables efficient control of the complexity of the functional canonical directions using tangent space sieve approximations. Additionally, we enforce an interpretable group structure on the high-dimensional canonical directions via a sparsity-promoting penalty. The proposed method shows improved empirical performance over alternative approaches and comes with theoretical guarantees. Its application to data from the Human Connectome Project reveals a dominant mode of covariation between dynamic functional connectivity and lifestyle, demographic, and psychometric measures. This mode aligns with results from static connectivity studies but reveals a unique temporal non-stationary pattern that such studies fail to capture.

翻译：本文提出一种新颖的统计模型，用于整合分析黎曼流形函数数据与高维数据。我们将该模型应用于探索每个受试者的动态功能连接（由时间索引的正定协方差矩阵集合表征）与代表生活方式、人口统计学及心理测量指标的高维数据之间的依赖结构。具体而言，我们重构典型相关分析框架，通过切空间筛逼近对功能典型方向复杂度进行有效控制，并利用稀疏惩罚项对高维典型方向施加可解释的分组结构。所提方法在经验性能上优于现有方法，且具备理论保障。将其应用于人类连接组项目数据时，揭示了动态功能连接与生活方式、人口统计学及心理测量指标间的主导共变模式：该模式虽与静态连接研究结果相符，却展现出静态研究无法捕捉的独特时间非平稳特征。