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Riemannian Means on Special Euclidean Group and Unipotent Matrices Group
Joint Authors
Sun, Huafei
Duan, Xiaomin
Peng, Linyu
Source
Issue
Vol. 2013, Issue 2013 (31 Dec. 2013), pp.1-9, 9 p.
Publisher
Hindawi Publishing Corporation
Publication Date
2013-10-24
Country of Publication
Egypt
No. of Pages
9
Main Subjects
Medicine
Information Technology and Computer Science
Abstract EN
Among the noncompact matrix Lie groups, the special Euclidean group and the unipotent matrix group play important roles in both theoretic and applied studies.
The Riemannian means of a finite set of the given points on the two matrix groups are investigated, respectively.
Based on the left invariant metric on the matrix Lie groups, the geodesic between any two points is gotten.
And the sum of the geodesic distances is taken as the cost function, whose minimizer is the Riemannian mean.
Moreover, a Riemannian gradient algorithm for computing the Riemannian mean on the special Euclidean group and an iterative formula for that on the unipotent matrix group are proposed, respectively.
Finally, several numerical simulations in the 3-dimensional case are given to illustrate our results.
American Psychological Association (APA)
Duan, Xiaomin& Sun, Huafei& Peng, Linyu. 2013. Riemannian Means on Special Euclidean Group and Unipotent Matrices Group. The Scientific World Journal،Vol. 2013, no. 2013, pp.1-9.
https://search.emarefa.net/detail/BIM-1011887
Modern Language Association (MLA)
Duan, Xiaomin…[et al.]. Riemannian Means on Special Euclidean Group and Unipotent Matrices Group. The Scientific World Journal No. 2013 (2013), pp.1-9.
https://search.emarefa.net/detail/BIM-1011887
American Medical Association (AMA)
Duan, Xiaomin& Sun, Huafei& Peng, Linyu. Riemannian Means on Special Euclidean Group and Unipotent Matrices Group. The Scientific World Journal. 2013. Vol. 2013, no. 2013, pp.1-9.
https://search.emarefa.net/detail/BIM-1011887
Data Type
Journal Articles
Language
English
Notes
Includes bibliographical references
Record ID
BIM-1011887