Non-Euclidian statistics for covariance matrices, with applications to diffusion tensor imaging

Ian Dryden, Alexey Koloydenko, Diwei Zhou

Research output: Contribution to journalArticle

Abstract

The statistical analysis of covariance matrix data is consideredand, in particular, methodology is discussed which takes into accountthe non-Euclidean nature of the space of positive semi-definite sym-metric matrices. The main motivation for the work is the analysis ofdiffusion tensors in medical image analysis. The primary focus is onestimation of a mean covariance matrix and, in particular, on the useof Procrustes size-and-shape space. Comparisons are made with otherestimation techniques, including using the matrix logarithm, matrixsquare root and Cholesky decomposition. Applications to diffusiontensor imaging are considered and, in particular, a new measure offractional anisotropy called Procrustes Anisotropy is discussed
Original languageEnglish
Pages (from-to)1102-1123
Number of pages22
JournalAnnals of Applied Statistics
Volume3
Issue number3
DOIs
Publication statusPublished - 30 Sep 2009

Keywords

  • Anisotropy
  • Cholesky
  • geodesic
  • matrix logarithm
  • principal components
  • Procrustes
  • Riemannian
  • shape
  • size
  • Wishart

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