Non-Euclidean statistics for covariance matrices with applications to diffusion tensor imaging
journal contributionposted on 2015-03-05, 10:21 authored 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.
Supported by a Leverhulme Research Fellowship and a Marie Curie Research Training award.
- Mathematical Sciences