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

Authors:
Simone Fiori
Affiliations:
Dipartimento di Elettronica, Intelligenza Artificiale e Telecomunicazioni, Università Politecnica delle Marche, Ancona, Italy
Venue:
ICANN'07 Proceedings of the 17th international conference on Artificial neural networks
Year:
2007

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Abstract

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.