1254773280.pdf (1.97 MB)
Download file

Non-Euclidean statistics for covariance matrices with applications to diffusion tensor imaging

Download (1.97 MB)
journal contribution
posted on 05.03.2015, 10:21 by Ian L. Dryden, Alexey Koloydenko, Diwei ZhouDiwei Zhou
The statistical analysis of covariance matrix data is considered and, in particular, methodology is discussed which takes into account the nonEuclidean nature of the space of positive semi-definite symmetric matrices. The main motivation for the work is the analysis of diffusion tensors in medical image analysis. The primary focus is on estimation of a mean covariance matrix and, in particular, on the use of Procrustes size-and-shape space. Comparisons are made with other estimation techniques, including using the matrix logarithm, matrix square root and Cholesky decomposition. Applications to diffusion tensor imaging are considered and, in particular, a new measure of fractional anisotropy called Procrustes Anisotropy is discussed.

Funding

Supported by a Leverhulme Research Fellowship and a Marie Curie Research Training award.

History

School

  • Science

Department

  • Mathematical Sciences

Published in

Annals of Applied Statistics

Volume

3

Pages

1102 - 1123

Citation

DRYDEN, I.L., KOLOYDENKO, A. and ZHOU, D., 2009. Non-Euclidean statistics for covariance matrices with applications to diffusion tensor imaging. Annals of Applied Statistics, 3 (3), pp. 1102 - 1123.

Publisher

© Institute of Mathematical Statistics

Version

VoR (Version of Record)

Publisher statement

This work is made available according to the conditions of the Creative Commons Attribution-NonCommercial-NoDerivatives 4.0 International (CC BY-NC-ND 4.0) licence. Full details of this licence are available at: https://creativecommons.org/licenses/by-nc-nd/4.0/

Publication date

2009

Notes

This article is also available at: http://dx.doi.org/10.1214/09-AOAS249

ISSN

1932-6157

Language

en