Amplitude Mean of Functional Data on $\mathbb{S}^2$. (arXiv:2107.13721v4 [stat.ML] UPDATED)

Manifold-valued functional data analysis (FDA) recently becomes an active
area of research motivated by the raising availability of trajectories or
longitudinal data observed on non-linear manifolds. The challenges of analyzing
such data come from many aspects, including infinite dimensionality and
nonlinearity, as well as time-domain or phase variability. In this paper, we
study the amplitude part of manifold-valued functions on $\mathbb{S}^2$, which
is invariant to random time warping or re-parameterization. Utilizing the nice
geometry of $\mathbb{S}^2$, we develop a set …

amplitude arxiv data mean ml