Multilayer perceptrons to approximate quaternion valued functions

In this paper a new type of multilayer feedforward neural network is introduced. Such a structure, called hypercomplex multilayer perceptron (HMLP), is developed in quaternion algebra and allows quaternionic input and output signals to be dealt with, requiring a lower number of neurons than the real...

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Bibliographic Details
Published in:Neural networks 1997-03, Vol.10 (2), p.335-342
Main Authors: ARENA, P, FORTUNA, L, MUSCATO, G, XIBILIA, M. G
Format: Article
Language:English
Subjects:
Applied sciences
Artificial intelligence
Computer science
control theory
systems
Connectionism. Neural networks
Exact sciences and technology
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Summary:In this paper a new type of multilayer feedforward neural network is introduced. Such a structure, called hypercomplex multilayer perceptron (HMLP), is developed in quaternion algebra and allows quaternionic input and output signals to be dealt with, requiring a lower number of neurons than the real MLP, thus providing a reduced computational complexity. The structure introduced represents a generalization of the multilayer perceptron in the complex space (CMLP) reported in the literature. The fundamental result reported in the paper is a new density theorem which makes HMLPs universal interpolators of quaternion valued continuous functions. Moreover the proof of the density theorem can be restricted in order to formulate a density theorem in the complex space. Due to the identity between the quaternion and the four-dimensional real space, such a structure is also useful to approximate multidimensional real valued functions with a lower number of real parameters, decreasing the probability of being trapped in local minima during the learning phase. A numerical example is also reported in order to show the efficiency of the proposed structure. Copyright 1997 Elsevier Science Ltd. All Rights Reserved.
ISSN:0893-6080
1879-2782
DOI:10.1016/s0893-6080(96)00048-2