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math.DG2021
The geometry of mixed-Euclidean metrics on symmetric positive definite matrices
Yann Thanwerdas, Xavier Pennec
Several Riemannian metrics and families of Riemannian metrics were defined on the manifold of Symmetric Positive Definite (SPD) matrices. Firstly, we formalize a common general pro…
math.DG2021
O(n)-invariant Riemannian metrics on SPD matrices
Yann Thanwerdas, Xavier Pennec
Symmetric Positive Definite (SPD) matrices are ubiquitous in data analysis under the form of covariance matrices or correlation matrices. Several O(n)-invariant Riemannian metrics…
math.DG2021
Geodesic of the Quotient-Affine Metrics on Full-Rank Correlation Matrices
Yann Thanwerdas, Xavier Pennec
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 Symmetr…