# Learning algorithms utilizing quasi-geodesic flows on the Stiefel manifold

@article{Nishimori2005LearningAU,
title={Learning algorithms utilizing quasi-geodesic flows on the Stiefel manifold},
author={Yasunori Nishimori and Shotaro Akaho},
journal={Neurocomputing},
year={2005},
volume={67},
pages={106-135}
}
In this paper we extend the natural gradient method for neural networks to the case where the weight vectors are constrained to the Stiefel manifold. The proposed methods involve numerical integration techniques of the gradient flow without violating the manifold constraints. The extensions are based on geodesics. We rigorously formulate the previously proposed natural gradient and geodesics on the manifold exploiting the fact that the Stiefel manifold is a homogeneous space having a transitive… CONTINUE READING
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