Non-Euclidean statistical analysis of covariance matrices and diffusion tensors

Details Non-Euclidean statistical analysis of covariance matrices and diffusion tensors Non-Euclidean statistical analysis of covariance matrices and diffusion tensors

2010-10-10

arxiv.org/abs/1010.3955v1

Statistics

Methodology

The paper was presented at the 57th session of the International Statistical Institute, 16-22 August, 2009, Durban, South Afri

Scientific paper

The statistical analysis of covariance matrices occurs in many important applications, e.g. in diffusion tensor imaging and longitudinal data analysis. We consider the situation where it is of interest to estimate an average covariance matrix, describe its anisotropy, to carry out principal geodesic analysis and to interpolate between covariance matrices. There are many choices of metric available, each with its advantages. The particular choice of what is best will depend on the particular application. The use of the Procrustes size-and-shape metric is particularly appropriate when the covariance matrices are close to being deficient in rank. We discuss the use of different metrics for diffusion tensor analysis, and we also introduce certain types of regularization for tensors.

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