© 2011

Complex-Valued Neural Networks with Multi-Valued Neurons

  • Cutting-edge research on Complex-Valued Networks with Multi-Valued Neurons

  • Written by leading experts in this field

  • State-of-the-Art book


Part of the Studies in Computational Intelligence book series (SCI, volume 353)

Table of contents

  1. Front Matter
  2. Igor Aizenberg
    Pages 55-94
  3. Igor Aizenberg
    Pages 95-132
  4. Igor Aizenberg
    Pages 207-248
  5. Back Matter

About this book


Complex-Valued Neural Networks have higher functionality, learn faster and generalize better than their real-valued counterparts.

This book is devoted to the Multi-Valued Neuron (MVN) and MVN-based neural networks. It contains a comprehensive observation of MVN theory, its learning, and applications. MVN is a complex-valued neuron whose inputs and output are located on the unit circle. Its activation function is a function only of argument (phase) of the weighted sum. MVN derivative-free learning is based on the error-correction rule. A single MVN can learn those input/output mappings that are non-linearly separable in the real domain. Such classical non-linearly separable problems as XOR and Parity n are the simplest that can be learned by a single MVN. Another important advantage of MVN is a proper treatment of the phase information.

These properties of MVN become even more remarkable when this neuron is used as a basic one in neural networks. The Multilayer Neural Network based on Multi-Valued Neurons (MLMVN) is an MVN-based feedforward neural network. Its backpropagation learning algorithm is derivative-free and based on the error-correction rule. It does not suffer from the local minima phenomenon. MLMVN outperforms many other machine learning techniques in terms of learning speed, network complexity and generalization capability when solving both benchmark and real-world classification and prediction problems. Another interesting application of MVN is its use as a basic neuron in multi-state associative memories.


The book is addressed to those readers who develop theoretical fundamentals of neural networks and use neural networks for solving various real-world problems. It should also be very suitable for Ph.D. and graduate students pursuing their degrees in computational intelligence.

Authors and affiliations

  1. 1.Texas A&m University-TexarkanaTexarkanaUSA

Bibliographic information

  • Book Title Complex-Valued Neural Networks with Multi-Valued Neurons
  • Authors Igor Aizenberg
  • Series Title Studies in Computational Intelligence
  • DOI
  • Copyright Information Springer Berlin Heidelberg 2011
  • Publisher Name Springer, Berlin, Heidelberg
  • eBook Packages Engineering Engineering (R0)
  • Hardcover ISBN 978-3-642-20352-7
  • Softcover ISBN 978-3-662-50631-8
  • eBook ISBN 978-3-642-20353-4
  • Series ISSN 1860-949X
  • Series E-ISSN 1860-9503
  • Edition Number 1
  • Number of Pages XV, 262
  • Number of Illustrations 0 b/w illustrations, 0 illustrations in colour
  • Topics Computational Intelligence
    Artificial Intelligence
  • Buy this book on publisher's site
Industry Sectors
Chemical Manufacturing
IT & Software
Consumer Packaged Goods
Materials & Steel
Finance, Business & Banking
Energy, Utilities & Environment
Oil, Gas & Geosciences