biostudies-literatureCho MHNCI NIH HHSNational Institutes of HealthNational Science FoundationEngineering and Physical Sciences Research Council104870https://www.ebi.ac.uk/biostudies/studies/S-EPMC9122284biostudies-literatureUnknown189It is quite common for functional data arising from imaging data to assume values in infinite-dimensional manifolds. Uncovering associations between two or more such nonlinear functional data extracted from the same object across medical imaging modalities can assist development of personalized treatment strategies. We propose a method for canonical correlation analysis between paired probability densities or shapes of closed planar curves, routinely used in biomedical studies, which combines a convenient linearization and dimension reduction of the data using tangent space coordinates. Leveraging the fact that the corresponding manifolds are submanifolds of unit Hilbert spheres, we describe how finite-dimensional representations of the functional data objects can be easily computed, whichJournal of multivariate analysisTangent functional canonical correlation analysis for densities and shapes, with applications to multimodal imaging data.PMC9122284R37 CA214955EP/V048104/1CCF-1839252CCF-1740761DMS-2015226DMS-1613054DMS-2015374R37-CA214955Cho MHBharath KKurtek SfalseTangent functional canonical correlation analysis for densities and shapes, with applications to multimodal imaging data.It is quite common for functional data arising from imaging data to assume values in infinite-dimensional manifolds. Uncovering associations between two or more such nonlinear functional data extracted from the same object across medical imaging modalities can assist development of personalized treatment strategies. We propose a method for canonical correlation analysis between paired probability densities or shapes of closed planar curves, routinely used in biomedical studies, which combines a convenient linearization and dimension reduction of the data using tangent space coordinates. Leveraging the fact that the corresponding manifolds are submanifolds of unit Hilbert spheres, we describe how finite-dimensional representations of the functional data objects can be easily computed, which2022-01-01T00:00:00Z2022 May2025-04-19T13:31:41.731Z2025-04-19T13:31:41.731ZS-EPMC91222843560147310.1016/j.jmva.2021.104870