Matches in SemOpenAlex for { <https://semopenalex.org/work/W2207336698> ?p ?o ?g. }
Showing items 1 to 100 of
100
with 100 items per page.
- W2207336698 abstract "We discuss the geometric foundation behind the use of stochastic processes in the frame bundle of a smooth manifold to build stochastic models with applications in statistical analysis of non-linear data. The transition densities for the projection to the manifold of Brownian motions developed in the frame bundle lead to a family of probability distributions on the manifold. We explain how data mean and covariance can be interpreted as points in the frame bundle or, more precisely, in the bundle of symmetric positive definite 2-tensors analogously to the parameters describing Euclidean normal distributions. We discuss a factorization of the frame bundle projection map through this bundle, the natural sub-Riemannian structure of the frame bundle, the effect of holonomy, and the existence of subbundles where the Hormander condition is satisfied such that the Brownian motions have smooth transition densities. We identify the most probable paths for the underlying Euclidean Brownian motion and discuss small time asymptotics of the transition densities on the manifold. The geometric setup yields an intrinsic approach to the estimation of mean and covariance in non-linear spaces." @default.
- W2207336698 created "2016-06-24" @default.
- W2207336698 creator A5036585415 @default.
- W2207336698 creator A5077566438 @default.
- W2207336698 date "2015-12-28" @default.
- W2207336698 modified "2023-09-27" @default.
- W2207336698 title "Modelling Anisotropic Covariance using Stochastic Development and Sub-Riemannian Frame Bundle Geometry" @default.
- W2207336698 cites W1503893179 @default.
- W2207336698 cites W1512416545 @default.
- W2207336698 cites W1561367079 @default.
- W2207336698 cites W1941650215 @default.
- W2207336698 cites W1969002377 @default.
- W2207336698 cites W2000679240 @default.
- W2207336698 cites W2099068061 @default.
- W2207336698 cites W2125027820 @default.
- W2207336698 cites W2152887332 @default.
- W2207336698 cites W2168412719 @default.
- W2207336698 cites W238700262 @default.
- W2207336698 cites W2963242253 @default.
- W2207336698 hasPublicationYear "2015" @default.
- W2207336698 type Work @default.
- W2207336698 sameAs 2207336698 @default.
- W2207336698 citedByCount "1" @default.
- W2207336698 countsByYear W22073366982017 @default.
- W2207336698 crossrefType "posted-content" @default.
- W2207336698 hasAuthorship W2207336698A5036585415 @default.
- W2207336698 hasAuthorship W2207336698A5077566438 @default.
- W2207336698 hasConcept C105795698 @default.
- W2207336698 hasConcept C106953101 @default.
- W2207336698 hasConcept C112401455 @default.
- W2207336698 hasConcept C11413529 @default.
- W2207336698 hasConcept C127413603 @default.
- W2207336698 hasConcept C134306372 @default.
- W2207336698 hasConcept C159985019 @default.
- W2207336698 hasConcept C178650346 @default.
- W2207336698 hasConcept C191961195 @default.
- W2207336698 hasConcept C192562407 @default.
- W2207336698 hasConcept C202444582 @default.
- W2207336698 hasConcept C2524010 @default.
- W2207336698 hasConcept C2778134712 @default.
- W2207336698 hasConcept C2779593128 @default.
- W2207336698 hasConcept C32518243 @default.
- W2207336698 hasConcept C33923547 @default.
- W2207336698 hasConcept C44234333 @default.
- W2207336698 hasConcept C529865628 @default.
- W2207336698 hasConcept C56907000 @default.
- W2207336698 hasConcept C57493831 @default.
- W2207336698 hasConcept C66384103 @default.
- W2207336698 hasConcept C78519656 @default.
- W2207336698 hasConcept C95857938 @default.
- W2207336698 hasConceptScore W2207336698C105795698 @default.
- W2207336698 hasConceptScore W2207336698C106953101 @default.
- W2207336698 hasConceptScore W2207336698C112401455 @default.
- W2207336698 hasConceptScore W2207336698C11413529 @default.
- W2207336698 hasConceptScore W2207336698C127413603 @default.
- W2207336698 hasConceptScore W2207336698C134306372 @default.
- W2207336698 hasConceptScore W2207336698C159985019 @default.
- W2207336698 hasConceptScore W2207336698C178650346 @default.
- W2207336698 hasConceptScore W2207336698C191961195 @default.
- W2207336698 hasConceptScore W2207336698C192562407 @default.
- W2207336698 hasConceptScore W2207336698C202444582 @default.
- W2207336698 hasConceptScore W2207336698C2524010 @default.
- W2207336698 hasConceptScore W2207336698C2778134712 @default.
- W2207336698 hasConceptScore W2207336698C2779593128 @default.
- W2207336698 hasConceptScore W2207336698C32518243 @default.
- W2207336698 hasConceptScore W2207336698C33923547 @default.
- W2207336698 hasConceptScore W2207336698C44234333 @default.
- W2207336698 hasConceptScore W2207336698C529865628 @default.
- W2207336698 hasConceptScore W2207336698C56907000 @default.
- W2207336698 hasConceptScore W2207336698C57493831 @default.
- W2207336698 hasConceptScore W2207336698C66384103 @default.
- W2207336698 hasConceptScore W2207336698C78519656 @default.
- W2207336698 hasConceptScore W2207336698C95857938 @default.
- W2207336698 hasLocation W22073366981 @default.
- W2207336698 hasOpenAccess W2207336698 @default.
- W2207336698 hasPrimaryLocation W22073366981 @default.
- W2207336698 hasRelatedWork W1488827591 @default.
- W2207336698 hasRelatedWork W174154882 @default.
- W2207336698 hasRelatedWork W2006430479 @default.
- W2207336698 hasRelatedWork W2013486056 @default.
- W2207336698 hasRelatedWork W2040936135 @default.
- W2207336698 hasRelatedWork W2109038256 @default.
- W2207336698 hasRelatedWork W2163522287 @default.
- W2207336698 hasRelatedWork W2287951136 @default.
- W2207336698 hasRelatedWork W2295863165 @default.
- W2207336698 hasRelatedWork W2511645843 @default.
- W2207336698 hasRelatedWork W2765244194 @default.
- W2207336698 hasRelatedWork W2951912171 @default.
- W2207336698 hasRelatedWork W2963448537 @default.
- W2207336698 hasRelatedWork W2963995312 @default.
- W2207336698 hasRelatedWork W3010061742 @default.
- W2207336698 hasRelatedWork W30336108 @default.
- W2207336698 hasRelatedWork W3087349263 @default.
- W2207336698 hasRelatedWork W3098958569 @default.
- W2207336698 hasRelatedWork W3210503141 @default.
- W2207336698 hasRelatedWork W3213726019 @default.
- W2207336698 isParatext "false" @default.
- W2207336698 isRetracted "false" @default.
- W2207336698 magId "2207336698" @default.
- W2207336698 workType "article" @default.