Name
Title | ||
|---|---|---|
Riemannian Gaussian Distributions On The Space Of Positive-Definite Quaternion Matrices |
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. |
Year | DOI | Venue |
|---|---|---|
2017 | 10.1007/978-3-319-68445-1_82 | GEOMETRIC SCIENCE OF INFORMATION, GSI 2017 |
Keywords | Field | DocType |
Riemannian gaussian distribution, Quaternion, Positive-definite matrix, Symplectic group, Riemannian barycentre | Curvature,Mathematical analysis,Matrix (mathematics),Quaternion,Metric (mathematics),Gaussian,Riemannian geometry,Symmetric space,Geodesic,Mathematics | Conference |
Volume | ISSN | Citations |
10589 | 0302-9743 | 0 |
PageRank | References | Authors |
0.34 | 3 | 3 |
Name | Order | Citations | PageRank |
|---|---|---|---|
| Salem Said | 1 | 59 | 12.54 |
| Nicolas Le Bihan | 2 | 254 | 23.35 |
| Jonathan H. Manton | 3 | 843 | 71.93 |