96 citations · 178 across the 27 of their papers we have counts for
34 papers
Principal subbundles for dimension reduction
Morten Akhøj, James Benn, Erlend Grong +2
In this paper we demonstrate how sub-Riemannian geometry can be used for manifold learning and surface reconstruction by combining local linear approximations of a point cloud to o…
Flagfolds: an approach to multi-dimensional varifolds
Blanche Buet, Xavier Pennec
By interpreting the product of the Principal Component Analysis, that is the covariance matrix, as a sequence of nested subspaces naturally coming with weights according to the lev…
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…
A geometric framework for asymptotic inference of principal subspaces in PCA
Dimbihery Rabenoro, Xavier Pennec
In this article, we develop an asymptotic method for constructing confidence regions for the set of all linear subspaces arising from PCA, from which we derive hypothesis tests on…
Tangent phylogenetic PCA
Morten Akhøj, Xavier Pennec, Stefan Sommer
Phylogenetic PCA (p-PCA) is a version of PCA for observations that are leaf nodes of a phylogenetic tree. P-PCA accounts for the fact that such observations are not independent, du…
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…