Multilayer perceptrons to approximate quaternion valued functions
Multilayer perceptrons to approximate quaternion valued functions
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DOI：
10.1016/s0893-6080(96)00048-2
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发表时间：
1997-03-01
期刊：
影响因子：
7.8
通讯作者：
Xibilia, MG
中科院分区：
文献类型：
--
作者：
Arena, P;Fortuna, L;Xibilia, MG
本文介绍了一种新型的多层前向神经网络。这种结构称为超复数多层感知器（HMLP），它是在四元数代数中发展起来的，它允许处理四元数的输入和输出信号，所需的神经元数比真实的MLP少，从而降低了计算复杂度。所介绍的结构是文献中报道的复空间多层感知器（CMLP）的推广。本文的基本结果是一个新的密度定理，它使四元数值连续函数的HMLPs插值成为普遍的插值。此外，密度定理的证明可以被限制，以便在复空间中形成密度定理。由于四元数和四维真实的空间之间的同一性，这样的结构对于用较低数量的真实的参数来近似多维真实的值函数也是有用的，从而降低了在学习阶段期间被困在局部最小值中的概率。一个数值例子也报告，以显示所提出的结构的效率。(C)1997爱思唯尔科技有限公司版权所有。
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. (C) 1997 Elsevier Science Ltd. All Rights Reserved.