تقرير
Non-Euclidean statistics for covariance matrices, with applications to diffusion tensor imaging
| العنوان: | Non-Euclidean statistics for covariance matrices, with applications to diffusion tensor imaging |
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| المؤلفون: | Dryden, Ian L., Koloydenko, Alexey, Zhou, Diwei |
| المصدر: | Annals of Applied Statistics 2009, Vol. 3, No. 3, 1102-1123 |
| سنة النشر: | 2009 |
| المجموعة: | Statistics |
| مصطلحات موضوعية: | Statistics - Applications |
| الوصف: | 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. Comment: 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) |
| نوع الوثيقة: | Working Paper |
| DOI: | 10.1214/09-AOAS249 |
| URL الوصول: | http://arxiv.org/abs/0910.1656 |
| رقم الأكسشن: | edsarx.0910.1656 |
| قاعدة البيانات: | arXiv |
| DOI: | 10.1214/09-AOAS249 |
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