Riemannian Gaussian Distributions on the Space of Positive-Definite Quaternion Matrices View Full Text


Ontology type: schema:Chapter      Open Access: True


Chapter Info

DATE

2017-10-24

AUTHORS

Salem Said , Nicolas Le Bihan , Jonathan H. Manton

ABSTRACT

Recently, Riemannian Gaussian distributions were defined on spaces of positive-definite real and complex matrices. The present paper extends this definition to the space of positive-definite quaternion matrices. In order to do so, it develops the Riemannian geometry of the space of positive-definite quaternion matrices, which is shown to be a Riemannian symmetric space of non-positive curvature. The paper gives original formulae for the Riemannian metric of this space, its geodesics, and distance function. Then, it develops the theory of Riemannian Gaussian distributions, including the exact expression of their probability density, their sampling algorithm and statistical inference. More... »

PAGES

709-716

References to SciGraph publications

Book

TITLE

Geometric Science of Information

ISBN

978-3-319-68444-4
978-3-319-68445-1

Identifiers

URI

http://scigraph.springernature.com/pub.10.1007/978-3-319-68445-1_82

DOI

http://dx.doi.org/10.1007/978-3-319-68445-1_82

DIMENSIONS

https://app.dimensions.ai/details/publication/pub.1092381068


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