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Title: Non-Euclidean statistics for covariance matrices with applications to diffusion tensor imaging
Authors: Dryden, Ian L.
Koloydenko, Alexey
Zhou, Diwei
Keywords: Anisotropy
Matrix logarithm
Principal components
Issue Date: 2009
Publisher: © Institute of Mathematical Statistics
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.
Abstract: 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.
Description: This article is also available at: http://dx.doi.org/10.1214/09-AOAS249
Sponsor: Supported by a Leverhulme Research Fellowship and a Marie Curie Research Training award.
Version: Published
DOI: 10.1214/09-AOAS249
URI: https://dspace.lboro.ac.uk/2134/16886
Publisher Link: http://dx.doi.org/10.1214/09-AOAS249
ISSN: 1932-6157
Appears in Collections:Published Articles (Maths)

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