96 citations · 178 across the 27 of their papers we have counts for
14 papers · 1 filter
Effective formulas for the geometry of normal homogeneous spaces. Application to flag manifolds
Dimbihery Rabenoro, Xavier Pennec
Consider a smooth manifold and an action on it of a compact connected Lie group with a bi-invariant metric. Then, any orbit is an embedded submanifold that is isometric to a normal…
Bures-Wasserstein minimizing geodesics between covariance matrices of different ranks
Yann Thanwerdas, Xavier Pennec
The set of covariance matrices equipped with the Bures-Wasserstein distance is the orbit space of the smooth, proper and isometric action of the orthogonal group on the Euclidean s…
Theoretically and computationally convenient geometries on full-rank correlation matrices
Yann Thanwerdas, Xavier Pennec
In contrast to SPD matrices, few tools exist to perform Riemannian statistics on the open elliptope of full-rank correlation matrices. The quotient-affine metric was recently built…
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…
Numerical Accuracy of Ladder Schemes for Parallel Transport on Manifolds
Nicolas Guigui, Xavier Pennec
Parallel transport is a fundamental tool to perform statistics on Rie-mannian manifolds. Since closed formulae don't exist in general, practitioners often have to resort to numeric…
Exploration of Balanced Metrics on Symmetric Positive Definite Matrices
Yann Thanwerdas, Xavier Pennec
Symmetric Positive Definite (SPD) matrices have been used in many fields of medical data analysis. Many Riemannian metrics have been defined on this manifold but the choice of the…
Curvature effects on the empirical mean in Riemannian and affine Manifolds: a non-asymptotic high concentration expansion in the small-sample regime
Xavier Pennec
The asymptotic concentration of the Fr{é}chet mean of IID random variables on a Rieman-nian manifold was established with a central limit theorem by Bhattacharya \& Patrangenaru (B…
Is affine invariance well defined on SPD matrices? A principled continuum of metrics
Yann Thanwerdas, Xavier Pennec
Symmetric Positive Definite (SPD) matrices have been widely used in medical data analysis and a number of different Riemannian met-rics were proposed to compute with them. However,…
Math in the Black Forest: Workshop on New Directions in Shape Analysis
Martin Bauer, Nicolas Charon, Philipp Harms +9
These are the proceedings of the workshop "Math in the Black Forest", which brought together researchers in shape analysis to discuss promising new directions. Shape analysis is an…
Parallel Transport with Pole Ladder: a Third Order Scheme in Affine Connection Spaces which is Exact in Affine Symmetric Spaces
Xavier Pennec
Parallel transport is an important step in many discrete algorithms for statistical computing on manifolds. Numerical methods based on Jacobi fields or geodesics parallelograms are…