96 citations · 178 across the 27 of their papers we have counts for
6 papers · 1 filter
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…
Geometry of Sample Spaces
Philipp Harms, Peter W. Michor, Xavier Pennec +1
In statistics, independent, identically distributed random samples do not carry a natural ordering, and their statistics are typically invariant with respect to permutations of the…
Inconsistency of Template Estimation by Minimizing of the Variance/Pre-Variance in the Quotient Space
Loïc Devilliers, Stéphanie Allassonnière, Alain Trouvé +1
We tackle the problem of template estimation when data have been randomly deformed under a group action in the presence of noise. In order to estimate the template, one often minim…
Inconsistency of Template Estimation with the Fr{é}chet mean in Quotient Space
Loïc Devilliers, Xavier Pennec, Stéphanie Allassonnière
We tackle the problem of template estimation when data have been randomly transformed under an isometric group action in the presence of noise. In order to estimate the template, o…
Template estimation in computational anatomy: Fréchet means in top and quotient spaces are not consistent
Loïc Devilliers, Stéphanie Allassonnière, Alain Trouvé +1
In this article, we study the consistency of the template estimation with the Fréchet mean in quotient spaces. The Fréchet mean in quotient spaces is often used when the observatio…
Barycentric Subspace Analysis on Manifolds
Xavier Pennec
This paper investigates the generalization of Principal Component Analysis (PCA) to Riemannian manifolds. We first propose a new and general type of family of subspaces in manifold…