Soft Computing

, Volume 11, Issue 2, pp 169–183

Multilayer Feedforward Neural Network Based on Multi-valued Neurons (MLMVN) and a Backpropagation Learning Algorithm

Original Paper

DOI: 10.1007/s00500-006-0075-5

Cite this article as:
Aizenberg, I. & Moraga, C. Soft Comput (2007) 11: 169. doi:10.1007/s00500-006-0075-5


A multilayer neural network based on multi-valued neurons (MLMVN) is considered in the paper. A multi-valued neuron (MVN) is based on the principles of multiple-valued threshold logic over the field of the complex numbers. The most important properties of MVN are: the complex-valued weights, inputs and output coded by the kth roots of unity and the activation function, which maps the complex plane into the unit circle. MVN learning is reduced to the movement along the unit circle, it is based on a simple linear error correction rule and it does not require a derivative. It is shown that using a traditional architecture of multilayer feedforward neural network (MLF) and the high functionality of the MVN, it is possible to obtain a new powerful neural network. Its training does not require a derivative of the activation function and its functionality is higher than the functionality of MLF containing the same number of layers and neurons. These advantages of MLMVN are confirmed by testing using parity n, two spirals and “sonar” benchmarks and the Mackey–Glass time series prediction.


Feedforward complex-valued neural networkDerivative free backpropagation learning

Copyright information

© Springer-Verlag 2006

Authors and Affiliations

  1. 1.Department of Computer and Information SciencesTexas A&M University–TexarkanaTexarkanaUSA
  2. 2.Department of Computer Science-1University of DortmundDortmundGermany