Natural gradient works efficiently in learning
Neural Computation
Approximating the exponential from a Lie algebra to a Lie group
Mathematics of Computation
Quasi-Geodesic Neural Learning Algorithms Over the Orthogonal Group: A Tutorial
The Journal of Machine Learning Research
Nonlinear Complex-Valued Extensions of Hebbian Learning: An Essay
Neural Computation
The geometry of prior selection
Neurocomputing
Three-transmit-antenna space-time codes based on SU(3)
IEEE Transactions on Signal Processing - Part I
Equivariant adaptive source separation
IEEE Transactions on Signal Processing
Natural Conjugate Gradient on Complex Flag Manifolds for Complex Independent Subspace Analysis
ICANN '08 Proceedings of the 18th international conference on Artificial Neural Networks, Part I
Lie-group-type neural system learning by manifold retractions
Neural Networks
Learning averages over the lie group of unitary matrices
IJCNN'09 Proceedings of the 2009 international joint conference on Neural Networks
An algorithm to compute averages on matrix Lie groups
IEEE Transactions on Signal Processing
Periodic activation function and a modified learning algorithm for the multivalued neuron
IEEE Transactions on Neural Networks
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Learning on differential manifolds may involve the optimization of a function of many parameters. In this letter, we deal with Riemannian-gradient-based optimization on a Lie group, namely, the group of unitary unimodular matrices SU(3). In this special case, subalgebras of the associated Lie algebra su(3) may be individuated by computing pair-wise Gell-Mann matrices commutators. Subalgebras generate subgroups of a Lie group, as well as manifold foliation. We show that the Riemannian gradient may be projected over tangent structures to foliation, giving rise to foliation gradients. Exponentiations of foliation gradients may be computed in closed forms, which closely resemble Rodriguez forms for the special orthogonal group SO(3). We thus compare optimization by Riemannian gradient and foliation gradients.