96 citations · 178 across the 27 of their papers we have counts for
5 papers · 2 filters
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…
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…
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…
Parallel Transport on Kendall Shape Spaces
Nicolas Guigui, Elodie Maignant, Alain Trouvé +1
Kendall shape spaces are a widely used framework for the statistical analysis of shape data arising from many domains, often requiring the parallel transport as a tool to normalise…
A reduced parallel transport equation on Lie Groups with a left-invariant metric
Nicolas Guigui, Xavier Pennec
This paper presents a derivation of the parallel transport equation expressed in the Lie algebra of a Lie group endowed with a left-invariant metric.The use of this equation is exe…