Principal Component Analysis for Functional Data on Riemannian Manifolds and Spheres
- Author(s): Dai, Xiongtao
- Müller, Hans-Georg
- et al.
Published Web Locationhttps://arxiv.org/pdf/1705.06226.pdf
Functional data analysis on nonlinear manifolds has drawn recent interest. We propose an intrinsic principal component analysis for smooth Riemannian manifold-valued functional data and study its asymptotic properties. The proposed Riemannian functional principal component analysis (RFPCA) is carried out by first mapping the manifold-valued data through Riemannian logarithm maps to tangent spaces around the time-varying Fr