Neural learning algorithms based on mappings: The case of the unitary group of matrices

Neural learning algorithms based on optimization on manifolds differ by the way the single learning steps are effected on the neural system's parameter space. In this paper, we present a class counting four neural learning algorithms based on the differential geometric concept of mappings from the tangent space of a manifold to the manifold itself. A learning stepsize adaptation theory is proposed as well under the hypothesis of additiveness of the learning criterion. The numerical performances of the discussed algorithms are illustrated on a learning task and are compared to a reference algorithm known from literature. © Springer-Verlag Berlin Heidelberg 2007.