Neural Networks in Non-Euclidean Spaces

Authors:
Włodzisław Duch;Rafał Adamczak;Geerd H. F. Diercksen
Affiliations:
Department of Computer Methods, Nicholas Copernicus University, Grudziądzka 5, 87–100 Toruń, Poland, e-mail: duch@phys.uni.torun.pl;Department of Computer Methods, Nicholas Copernicus University, Grudziądzka 5, 87–100 Toruń, Poland, e-mail: duch@phys.uni.torun.pl;Max-Planck Institute of Astrophysics, 85740-Garching, Germany, e-mail: gdiercksen@mpa-garching.mpg.de
Venue:
Neural Processing Letters
Year:
1999

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Abstract

Multilayer Perceptrons (MLPs) use scalar products to compute weighted activation of neurons providing decision borders using combinations of soft hyperplanes. The weighted fun-in activation function may be replaced by a distance function between the inputs and the weights, offering a natural generalization of the standard MLP model. Non-Euclidean distance functions may also be introduced by normalization of the input vectors into an extended feature space. Both approaches influence the shapes of decision borders dramatically. An illustrative example showing these changes is provided.