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Amplitude Mean of Functional Data on $\mathbb{S}^2$. (arXiv:2107.13721v4 [stat.ML] UPDATED)
May 27, 2022, 1:11 a.m. | Zhengwu Zhang, Bayan Saparbayeva
stat.ML updates on arXiv.org arxiv.org
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 …
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