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：本文提出了一种新颖的统计模型，用于整合分析黎曼流形值函数数据与高维数据。我们将该模型应用于探索个体动态功能连接性（以时间索引的正定协方差矩阵集合表示）与表征生活方式、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，我们采用典型相关分析的重构框架，通过切空间筛近似实现对函数型典型方向复杂性的高效控制。此外，我们通过稀疏促进惩罚在高维典型方向上施加可解释的群组结构。所提方法在实证性能上优于现有替代方案，并具备理论保证。将其应用于人类连接组计划数据，揭示了动态功能连接性与生活方式、人口统计学及心理测量指标之间存在主导的协变模式。该模式与静态连接性研究结果一致，但揭示出此类研究未能捕捉的独特时间非平稳性模式。