Learning Lie groups for invariant visual perception
Proceedings of the 1998 conference on Advances in neural information processing systems II
Means and Averaging in the Group of Rotations
SIAM Journal on Matrix Analysis and Applications
Quasi-Geodesic Neural Learning Algorithms Over the Orthogonal Group: A Tutorial
The Journal of Machine Learning Research
A Theory for Learning by Weight Flow on Stiefel-Grassman Manifold
Neural Computation
An algorithm to compute averages on matrix Lie groups
IEEE Transactions on Signal Processing
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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.