title: Riemannian-gradient-based learning on the complex matrix-hypersphere.
abstract: This brief tackles the problem of learning over the complex-valued matrix-hypersphere S(α)(n,p)(C). The developed learning theory is formulated in terms of Riemannian-gradient-based optimization of a regular criterion function and is implemented by a geodesic-stepping method. The stepping method is equipped with a geodesic-search sub-algorithm to compute the optimal learning stepsize at any step. Numerical results show the effectiveness of the developed learning method and of its implementation.
authors: Dipartimento di Ingegneria dell’Informazione, Facoltà di Ingegneria, Università Politecnica delle Marche, Via Brecce Bianche, Ancona I-60131, Italy. s.fiori@univpm.it
authors: Simone
authors: S
authors: Fiori
mesh_terms: D000465:Algorithms; D001185:Artificial Intelligence; D003198:Computer Simulation; D008962:Models, Theoretical