NDLI: A gradient method for geodesic data fitting on some symmetric Riemannian manifolds

Content Provider	IEEE Xplore Digital Library
Author	Rentmeesters, Q.
Copyright Year	2011
Description	Author affiliation: Department of Mathematical Engineering, Université catholique de Louvain, Avenue Georges Lemaître, 4, B-1348 Louvain-la-Neuve, Belgium (Rentmeesters, Q.)
Abstract	In this paper, a method to compute the best geodesic approximation of a set of points that belong to a Riemannian manifold is proposed. This method is based on a gradient descent technique on the tangent bundle of the manifold. An expression for the gradient is derived using the theory of Jacobi fields and an efficient numerical technique is proposed to compute these Jacobi fields. The presented approach is valid on any locally symmetric space, and the sphere $S^{2},$ the set of symmetric positive definite matrices $Pn^{+},$ the special orthogonal group SO(3) and the Grassmann manifold Grass(n; p) are considered.
Starting Page	7141
Ending Page	7146
File Size	382033
Page Count	6
File Format	PDF
ISBN	9781612848006
ISSN	07431546
e-ISBN	9781612848013
e-ISBN	9781612847993
DOI	10.1109/CDC.2011.6161280
Language	English
Publisher	Institute of Electrical and Electronics Engineers, Inc. (IEEE)
Publisher Date	2011-12-12
Publisher Place	USA
Access Restriction	Subscribed
Rights Holder	Institute of Electrical and Electronics Engineers, Inc. (IEEE)
Subject Keyword	Jacobian matrices Vectors Manifolds Measurement Symmetric matrices Approximation methods Data models curvature Geodesics Riemannian manifolds tangent bundle Jacobi fields
Content Type	Text
Resource Type	Article
Subject	Control and Optimization Control and Systems Engineering Modeling and Simulation

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