Averaging over the Lie group SO(p) of special orthogonal matrices has several applications in the neural network field. The problem of averaging over the group SO(3) has been studied in details and, in some specific cases, it admits a closed form solution. Averaging over a generic-dimensional group SO(p) has also been studied recently, although the common formulation in terms of Riemannian mean leads to a matrix-type non-linear problem to solve, which, in general, may be tackled via iterative algorithms only. In the present paper, we propose a novel formulation of the problem that gives rise to a closed form solution for the average SO(p)-matrix. © 2010 Springer-Verlag.

A closed-form solution to the problem of averaging over the lie group of special orthogonal matrices

FIORI, Simone
2010-01-01

Abstract

Averaging over the Lie group SO(p) of special orthogonal matrices has several applications in the neural network field. The problem of averaging over the group SO(3) has been studied in details and, in some specific cases, it admits a closed form solution. Averaging over a generic-dimensional group SO(p) has also been studied recently, although the common formulation in terms of Riemannian mean leads to a matrix-type non-linear problem to solve, which, in general, may be tackled via iterative algorithms only. In the present paper, we propose a novel formulation of the problem that gives rise to a closed form solution for the average SO(p)-matrix. © 2010 Springer-Verlag.
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Utilizza questo identificativo per citare o creare un link a questo documento: https://hdl.handle.net/11566/73859
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