Asymmetric canonical correlation analysis of Riemannian and high-dimensional data

James Buenfil, Eardi Lila

Abstract:

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 con-
nectivity – represented by a temporally indexed collection of positive definite co-
variance 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 en-
force 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.