Statistical regression analysis of functional and shape data

Mengmeng Guo, Jingyong Su, Li Sun, Guofeng Cao

Research output: Contribution to journalArticlepeer-review

Abstract

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.

Original languageEnglish
Pages (from-to)28-44
Number of pages17
JournalJournal of Applied Statistics
Volume47
Issue number1
DOIs
StatePublished - Jan 2 2020

Keywords

  • PCA
  • Riemannian manifolds
  • Shape analysis
  • functional regression
  • square-root velocity function

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