Geodesic of the Quotient-Affine Metrics on Full-Rank Correlation Matrices
Differential Geometry
2021-03-09 v1
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.
Keywords
Cite
@article{arxiv.2103.04621,
title = {Geodesic of the Quotient-Affine Metrics on Full-Rank Correlation Matrices},
author = {Yann Thanwerdas and Xavier Pennec},
journal= {arXiv preprint arXiv:2103.04621},
year = {2021}
}