TY - JOUR
T1 - Statistical regression analysis of functional and shape data
AU - Guo, Mengmeng
AU - Su, Jingyong
AU - Sun, Li
AU - Cao, Guofeng
N1 - Publisher Copyright:
© 2019, © 2019 Informa UK Limited, trading as Taylor & Francis Group.
Copyright:
Copyright 2019 Elsevier B.V., All rights reserved.
PY - 2020/1/2
Y1 - 2020/1/2
N2 - We develop a multivariate regression model when responses or predictors are on nonlinear manifolds, rather than on Euclidean spaces. The nonlinear constraint makes the problem challenging and needs to be studied carefully. By performing principal component analysis (PCA) on tangent space of manifold, we use principal directions instead in the model. Then, the ordinary regression tools can be utilized. We apply the framework to both shape data (ozone hole contours) and functional data (spectrums of absorbance of meat in Tecator dataset). Specifically, we adopt the square-root velocity function representation and parametrization-invariant metric. Experimental results have shown that we can not only perform powerful regression analysis on the non-Euclidean data but also achieve high prediction accuracy by the constructed model.
AB - We develop a multivariate regression model when responses or predictors are on nonlinear manifolds, rather than on Euclidean spaces. The nonlinear constraint makes the problem challenging and needs to be studied carefully. By performing principal component analysis (PCA) on tangent space of manifold, we use principal directions instead in the model. Then, the ordinary regression tools can be utilized. We apply the framework to both shape data (ozone hole contours) and functional data (spectrums of absorbance of meat in Tecator dataset). Specifically, we adopt the square-root velocity function representation and parametrization-invariant metric. Experimental results have shown that we can not only perform powerful regression analysis on the non-Euclidean data but also achieve high prediction accuracy by the constructed model.
KW - PCA
KW - Riemannian manifolds
KW - Shape analysis
KW - functional regression
KW - square-root velocity function
UR - http://www.scopus.com/inward/record.url?scp=85073967841&partnerID=8YFLogxK
U2 - 10.1080/02664763.2019.1669541
DO - 10.1080/02664763.2019.1669541
M3 - Article
AN - SCOPUS:85073967841
VL - 47
SP - 28
EP - 44
JO - Journal of Applied Statistics
JF - Journal of Applied Statistics
SN - 0266-4763
IS - 1
ER -