Principal component neural networks: theory and applications
Principal component neural networks: theory and applications
Independent component analysis: theory and applications
Independent component analysis: theory and applications
Learning Lie groups for invariant visual perception
Proceedings of the 1998 conference on Advances in neural information processing systems II
Quasi-Geodesic Neural Learning Algorithms Over the Orthogonal Group: A Tutorial
The Journal of Machine Learning Research
On vector averaging over the unit hypersphere
Digital Signal Processing
Consensus Optimization on Manifolds
SIAM Journal on Control and Optimization
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The present manuscript tackles the problem of merging the connection patterns learnt by a pool of neural networks that share the manifold of special orthogonal matrices as parameter space. The merging technique is implemented as an averaging algorithm over the curved manifold of special orthogonal matrices. In the present manuscript, averaging is computed via the notion of Frechet mean and the associated metric dispersion is interpreted as the variance of the patterns around the Frechet mean. Also, continuous interpolation of two connection patterns is considered as an extension of the Frechet principle.