Extrinsic local regression on manifold-valued data.

Published

Journal Article

We propose an extrinsic regression framework for modeling data with manifold valued responses and Euclidean predictors. Regression with manifold responses has wide applications in shape analysis, neuroscience, medical imaging and many other areas. Our approach embeds the manifold where the responses lie onto a higher dimensional Euclidean space, obtains a local regression estimate in that space, and then projects this estimate back onto the image of the manifold. Outside the regression setting both intrinsic and extrinsic approaches have been proposed for modeling i.i.d manifold-valued data. However, to our knowledge our work is the first to take an extrinsic approach to the regression problem. The proposed extrinsic regression framework is general, computationally efficient and theoretically appealing. Asymptotic distributions and convergence rates of the extrinsic regression estimates are derived and a large class of examples are considered indicating the wide applicability of our approach.

Full Text

Duke Authors

Cited Authors

  • Lin, L; St Thomas, B; Zhu, H; Dunson, DB

Published Date

  • January 2017

Published In

Volume / Issue

  • 112 / 519

Start / End Page

  • 1261 - 1273

PubMed ID

  • 29225385

Pubmed Central ID

  • 29225385

Electronic International Standard Serial Number (EISSN)

  • 1537-274X

International Standard Serial Number (ISSN)

  • 0162-1459

Digital Object Identifier (DOI)

  • 10.1080/01621459.2016.1208615

Language

  • eng