title: Multilayer Perceptrons to Approximate Quaternion Valued Functions.
abstract: 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.
authors.affiliation: University of Catania, Italy
authors.forename: M G.
authors.initials: MG
authors.lastname: Xibilia
authors.forename: G
authors.initials: G
authors.lastname: Muscato
authors.forename: L
authors.initials: L
authors.lastname: Fortuna
authors.forename: P
authors.initials: P
authors.lastname: Arena