Learning by Natural Gradient on Noncompact Matrix-Type Pseudo-Riemannian Manifolds

This paper deals with learning by natural-gradient optimization on noncompact manifolds. In a Riemannian manifold, the calculation of entities such as the closed form of geodesic curves over noncompact manifolds might be infeasible. For this reason, it is interesting to study the problem of learning by optimization over noncompact manifolds endowed with pseudo-Riemannian metrics, which may give rise to tractable calculations. A general theory for natural-gradient-based learning on noncompact manifolds as well as specific cases of interest of learning are discussed.