Multivariate general linear models (MGLM) on Riemannian manifolds with applications to statistical analysis of diffusion weighted images

Hyunwoo J. Kim, Barbara B. Bendlin, Nagesh Adluru, Maxwell D. Collins, Moo K. Chung, Sterling C. Johnson, Richard J. Davidson, Vikas Singh

Research output: Chapter in Book/Report/Conference proceedingConference contribution

27 Citations (Scopus)

Abstract

Linear regression is a parametric model which is ubiquitous in scientific analysis. The classical setup where the observations and responses, i.e., (xi, yi) pairs, are Euclidean is well studied. The setting where yi is manifold valued is a topic of much interest, motivated by applications in shape analysis, topic modeling, and medical imaging. Recent work gives strategies for max-margin classifiers, principal components analysis, and dictionary learning on certain types of manifolds. For parametric regression specifically, results within the last year provide mechanisms to regress one real-valued parameter, xi ∈ R, against a manifold-valued variable, yi ε M. We seek to substantially extend the operating range of such methods by deriving schemes for multivariate multiple linear regression - a manifold-valued dependent variable against multiple independent variables, i.e., f: Rn→ M. Our variational algorithm efficiently solves for multiple geodesic bases on the manifold concurrently via gradient updates. This allows us to answer questions such as: what is the relationship of the measurement at voxel y to disease when conditioned on age and gender. We show applications to statistical analysis of diffusion weighted images, which give rise to regression tasks on the manifold GL(n)/O(n) for diffusion tensor images (DTI) and the Hilbert unit sphere for orientation distribution functions (ODF) from high angular resolution acquisition. The companion open-source code is available on nitrc.org/projects/riem-mglm.

Original languageEnglish
Title of host publicationProceedings of the IEEE Computer Society Conference on Computer Vision and Pattern Recognition
PublisherIEEE Computer Society
Pages2705-2712
Number of pages8
ISBN (Electronic)9781479951178, 9781479951178
DOIs
Publication statusPublished - 2014 Sep 24
Event27th IEEE Conference on Computer Vision and Pattern Recognition, CVPR 2014 - Columbus, United States
Duration: 2014 Jun 232014 Jun 28

Publication series

NameProceedings of the IEEE Computer Society Conference on Computer Vision and Pattern Recognition
ISSN (Print)1063-6919

Other

Other27th IEEE Conference on Computer Vision and Pattern Recognition, CVPR 2014
CountryUnited States
CityColumbus
Period14/6/2314/6/28

Keywords

  • Multivariate general linear models
  • diffusion weighted images
  • geodesic regression
  • manifold statistics

ASJC Scopus subject areas

  • Software
  • Computer Vision and Pattern Recognition

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  • Cite this

    Kim, H. J., Bendlin, B. B., Adluru, N., Collins, M. D., Chung, M. K., Johnson, S. C., Davidson, R. J., & Singh, V. (2014). Multivariate general linear models (MGLM) on Riemannian manifolds with applications to statistical analysis of diffusion weighted images. In Proceedings of the IEEE Computer Society Conference on Computer Vision and Pattern Recognition (pp. 2705-2712). [6909742] (Proceedings of the IEEE Computer Society Conference on Computer Vision and Pattern Recognition). IEEE Computer Society. https://doi.org/10.1109/CVPR.2014.352