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.
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© 2007 Springer-Verlag Berlin Heidelberg
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Fiori, S. (2007). Neural Learning Algorithms Based on Mappings: The Case of the Unitary Group of Matrices. In: de Sá, J.M., Alexandre, L.A., Duch, W., Mandic, D. (eds) Artificial Neural Networks – ICANN 2007. ICANN 2007. Lecture Notes in Computer Science, vol 4668. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-540-74690-4_87
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DOI: https://doi.org/10.1007/978-3-540-74690-4_87
Publisher Name: Springer, Berlin, Heidelberg
Print ISBN: 978-3-540-74689-8
Online ISBN: 978-3-540-74690-4
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