  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.
