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arXiv · 2103.04621

Geodesic of the Quotient-Affine Metrics on Full-Rank Correlation Matrices

Yann Thanwerdas·Xavier Pennec
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Abstract

Correlation matrices are used in many domains of neurosciences such as fMRI, EEG, MEG. However, statistical analyses often rely on embeddings into a Euclidean space or into Symmetric Positive Definite matrices which do not provide intrinsic tools. The quotient-affine metric was recently introduced as the quotient of the affine-invariant metric on SPD matrices by the action of diagonal matrices. In this work, we provide most of the fundamental Riemannian operations of the quotient-affine metric: the expression of the metric itself, the geodesics with initial tangent vector, the Levi-Civita connection and the curvature.

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BibTeXRIS

Yann Thanwerdas, Xavier Pennec. 2021-03-08. Geodesic of the Quotient-Affine Metrics on Full-Rank Correlation Matrices. https://arxiv.org/abs/2103.04621

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