96 citations · 109 across the 7 of their papers we have counts for
8 papers
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…
Geomstats: A Python Package for Riemannian Geometry in Machine Learning
Nina Miolane, Alice Le Brigant, Johan Mathe +16
We introduce Geomstats, an open-source Python toolbox for computations and statistics on nonlinear manifolds, such as hyperbolic spaces, spaces of symmetric positive definite matri…