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Abstract: The statistical analysis of covariance matrix data is considered and, inparticular, methodology is discussed which takes into account the non-Euclideannature of the space of positive semi-definite symmetric matrices. The mainmotivation for the work is the analysis of diffusion tensors in medical imageanalysis. The primary focus is on estimation of a mean covariance matrix and,in particular, on the use of Procrustes size-and-shape space. Comparisons aremade with other estimation techniques, including using the matrix logarithm,matrix square root and Cholesky decomposition. Applications to diffusion tensorimaging are considered and, in particular, a new measure of fractionalanisotropy called Procrustes Anisotropy is discussed.



Autor: Ian L. Dryden, Alexey Koloydenko, Diwei Zhou

Fuente: https://arxiv.org/







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