Zobrazeno 1 - 10
of 566
pro vyhledávání: '"Pennec , Xavier"'
Autor:
Sanborn, Sophia, Mathe, Johan, Papillon, Mathilde, Buracas, Domas, Lillemark, Hansen J, Shewmake, Christian, Bertics, Abby, Pennec, Xavier, Miolane, Nina
The enduring legacy of Euclidean geometry underpins classical machine learning, which, for decades, has been primarily developed for data lying in Euclidean space. Yet, modern machine learning increasingly encounters richly structured data that is in
Externí odkaz:
http://arxiv.org/abs/2407.09468
Autor:
Szwagier, Tom, Pennec, Xavier
This paper raises an important issue about the interpretation of principal component analysis. The curse of isotropy states that a covariance matrix with repeated eigenvalues yields rotation-invariant eigenvectors. In other words, principal component
Externí odkaz:
http://arxiv.org/abs/2307.15348
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 obtain lower dimensional bundles. Local approximations obtained by loca
Externí odkaz:
http://arxiv.org/abs/2307.03128
Autor:
Buet, Blanche, Pennec, Xavier
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 level of approximation they provide, we are able to embed all $d$--dimens
Externí odkaz:
http://arxiv.org/abs/2305.10583
Autor:
Rabenoro, Dimbihery, Pennec, Xavier
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 homogeneous space for the group. In this paper, we establish new expl
Externí odkaz:
http://arxiv.org/abs/2302.14810
Autor:
Rabenoro, Dimbihery, Pennec, Xavier
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 this set. Our method is based on the geometry of Riemannian manifolds
Externí odkaz:
http://arxiv.org/abs/2209.02025
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, due to shared evolutionary history. The method works on Euclidean data,
Externí odkaz:
http://arxiv.org/abs/2208.12730
Autor:
Thanwerdas, Yann, Pennec, Xavier
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 space of square matrices. This construction induces a natural orbit str
Externí odkaz:
http://arxiv.org/abs/2204.09928
Autor:
Thanwerdas, Yann, Pennec, Xavier
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 as the quotient of the affine-invariant metric by the congruence acti
Externí odkaz:
http://arxiv.org/abs/2201.06282