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

Abstract

The statistical analysis of covariance matrix data is considered and, in particular, methodology is discussed which takes into account the non-Euclidean 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.

Published in at http://dx.doi.org/10.1214/09-AOAS249 the Annals of Applied Statistics (http://www.imstat.org/aoas/) by the Institute of Mathematical Statistics (http://www.imstat.org)

References in corpus (4)

• Regularized estimation of large covariance matrices
• Large sample theory of intrinsic and extrinsic sample means on manifolds--II
• False discovery rate analysis of brain diffusion direction maps
• Statistical analysis on high-dimensional spheres and shape spaces

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