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Download fileNon-Euclidean statistics for covariance matrices with applications to diffusion tensor imaging
journal contribution
posted on 2015-03-05, 10:21 authored by Ian L. Dryden, Alexey Koloydenko, Diwei ZhouDiwei ZhouThe 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
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Department
- Mathematical Sciences