Abstract

In this talk, I will introduce a novel statistical model for the integrative analysis of Riemannian-valued functional data and high-dimensional data. This model is applied 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, including lifestyle, demographic, and psychometric measures. Specifically, a reformulation of canonical correlation analysis is employed, enabling efficient control of the complexity of the functional canonical directions through tangent space sieve approximations. Additionally, an interpretable group structure on the high-dimensional canonical directions is enforced via a sparsity-promoting penalty. The proposed method demonstrates improved empirical performance over alternative approaches and is supported by 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 uncovers a unique temporal non-stationary pattern that static studies fail to capture.