Nonparametric Analysis of Non-Euclidean Data on Shapes and Images

Research output: Contribution to journalArticle

Abstract

The article presents some of the basic theory for nonparametric inference on non-Euclidean spaces using Fréchet means that has been developed during the past two decades. Included are recent results on the asymptotic distribution theory of sample Fréchet means on such spaces, especially differentiable and Riemannian manifolds. Apart from this main theme and its applications, a nonparametric Bayes theory on Riemannian manifolds is outlined for the purpose of density estimation and classification. A final section briefly discusses the problem of machine vision, or robotic recognition of images as Riemannian manifolds.

Original languageEnglish (US)
Pages (from-to)1-36
Number of pages36
JournalSankhya A
DOIs
StateAccepted/In press - Feb 27 2018

Fingerprint

Riemannian Manifold
Nonparametric Bayes
Nonparametric Inference
Differentiable Manifolds
Distribution Theory
Machine Vision
Sample mean
Density Estimation
Asymptotic Theory
Asymptotic distribution
Robotics
Nonparametric analysis
Density estimation
Inference
Machine vision

Keywords

  • density estimation
  • Fréchet means
  • machine vision.
  • nonparametric Bayes on manifolds
  • uniqueness and asymptotic distribution

ASJC Scopus subject areas

  • Statistics, Probability and Uncertainty
  • Statistics and Probability

Cite this

Nonparametric Analysis of Non-Euclidean Data on Shapes and Images. / Bhattacharya, Rabindra N; Oliver, Rachel.

In: Sankhya A, 27.02.2018, p. 1-36.

Research output: Contribution to journalArticle

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