Amplitude Mean of Functional Data on π•Š^2

by   Zhengwu Zhang, et al.

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 π•Š^2, which is invariant to random time warping or re-parameterization. Utilizing the nice geometry of π•Š^2, we develop a set of efficient and accurate tools for temporal alignment of functions, geodesic computing, and sample mean calculation. At the heart of these tools, they rely on gradient descent algorithms with carefully derived gradients. We show the advantages of these newly developed tools over its competitors with extensive simulations and real data and demonstrate the importance of considering the amplitude part of functions instead of mixing it with phase variability in manifold-valued FDA.



There are no comments yet.


page 2

page 8

page 9

page 14

page 15

page 17

page 18

page 25

βˆ™ 06/24/2020

Uniform convergence of local FrΓ©chet regression and time warping for metric-space-valued trajectories

For real-valued functional data, it is well known that failure to separa...
βˆ™ 05/29/2018

Elastic Functional Principal Component Regression

We study regression using functional predictors in situations where thes...
βˆ™ 10/26/2019

Shape-Preserving Prediction for Stationary Functional Time Series

This article presents a novel method for prediction of stationary functi...
βˆ™ 10/19/2020

Variograms for spatial functional data with phase variation

Spatial, amplitude and phase variations in spatial functional data are c...
βˆ™ 05/29/2018

A Geometric Approach for Computing Tolerance Bounds for Elastic Functional Data

In this paper, we develop a method for constructing tolerance bounds for...
βˆ™ 11/30/2021

A Hierarchical Geodesic Model for Longitudinal Analysis on Manifolds

In many applications, geodesic hierarchical models are adequate for the ...
βˆ™ 09/14/2021

A geometric perspective on functional outlier detection

We consider functional outlier detection from a geometric perspective, s...
This week in AI

Get the week's most popular data science and artificial intelligence research sent straight to your inbox every Saturday.