Empirical Means on Pseudo-Orthogonal Groups

Jing Wang, Huafei Sun and Simone Fiori
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Jing Wang: School of Information, Beijing Wuzi University, Beijing 101149, China
Huafei Sun: School of Mathematics and Statistics, Beijing Institute of Technology, Beijing 100081, China
Simone Fiori: Dipartimento di Ingegneria dell’Informazione, Università Politecnica delle Marche, 60026 Ancona, Italy

Mathematics, 2019, vol. 7, issue 10, 1-20

Abstract: The present article studies the problem of computing empirical means on pseudo-orthogonal groups. To design numerical algorithms to compute empirical means, the pseudo-orthogonal group is endowed with a pseudo-Riemannian metric that affords the computation of the exponential map in closed forms. The distance between two pseudo-orthogonal matrices, which is an essential ingredient, is computed by both the Frobenius norm and the geodesic distance. The empirical-mean computation problem is solved via a pseudo-Riemannian-gradient-stepping algorithm. Several numerical tests are conducted to illustrate the numerical behavior of the devised algorithm.

Keywords: pseudo-orthogonal group; pseudo-Riemannian geometry; gradient-based function minimization on manifolds; geodesic stepping (search for similar items in EconPapers)
JEL-codes: C (search for similar items in EconPapers)
Date: 2019
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