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2017 | OriginalPaper | Buchkapitel

10. Multiple-Valued Logic and Complex-Valued Neural Networks

verfasst von : Igor Aizenberg

Erschienen in: Claudio Moraga: A Passion for Multi-Valued Logic and Soft Computing

Verlag: Springer International Publishing

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Abstract

In classical multiple-valued logic its values are encoded by integers. This complicates the use of multiple-valued logic as a basic model, which can be utilized in an artificial neuron, because the values of k-valued logic encoded by integers 0, 1, 2, ..., k are not normalized. To overcome this obstacle, it was suggested to encode the values of k-valued logic by complex numbers located on the unit circle, namely by the kth roots of unity. It is described in the paper how this model of multiple-valued logic over the field of complex numbers was suggested and how it was used to develop a multi-valued neuron (MVN). Then it is considered how a feedforward neural network based on MVN—a multilayer neural network with multi-valued neurons (MLMVN) was designed and its derivative-free learning algorithm based on the error-correction learning rule was presented. Different applications of MLMVN, which outperforms many other machine learning tools in terms of learning speed and generalization capability are also observed.

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Vorheriges Kapitel The Reed-Muller-Fourier Transform—Computing Methods and Factorizations

Nächstes Kapitel Sequential Bayesian Estimation of Recurrent Neural Networks

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13.

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14.

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15.

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16.

I. Aizenberg: A Periodic Activation Function and a Modified Learning Algorithm for a Multi-Valued Neuron, IEEE Transactions on Neural Networks, vol. 21, No 12, December 2010, pp. 1939–1949.CrossRef

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18.

I. Aizenberg, M. Caudill, J. Jackson, and S. Alexander: Learning Nonlinearly Separable mod k Addition Problem Using a Single Multi-Valued Neuron With a Periodic Activation Function, Proceedings of the 2010 IEEE World Congress on Computational Intelligence—2010 IEEE International Joint Conference on Neural Networks, Barcelona, Spain, July 18-23, 2010, pp. 2577–2584.

19.

I. Aizenberg and C. Moraga: Multi-Layered Neural Network based on Multi-Valued Neurons (MLMVN) and a Backpropagation Learning Algorithm, Technical Report No CI 171/04 (ISSN 1433-3325) of the Collaborative Research Center for Computational Intelligence of the University of Dortmund (SFB 531), available online at http://sfbci.cs.uni-dortmund.de/Publications/Reference/Downloads/17104.pdf, 2004.

20.

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21.

I. Aizenberg and C. Moraga: The Genetic Code as a Function of Multiple-Valued Logic Over the Field of Complex Numbers and its Learning using Multilayer Neural Network Based on Multi-Valued Neurons, Journal of Multiple-Valued Logic and Soft Computing, No 4-6, November 2007, pp. 605–618.MATH

22.

I. Aizenberg, D. Paliy, J. Zurada, and J. Astola: Blur Identification by Multilayer Neural Network based on Multi-Valued Neurons, IEEE Transactions on Neural Networks, vol. 19, No 5, May 2008, pp. 883–898.CrossRef

23.

Aizenberg I., Alexander S., and Jackson J.: Recognition of Blurred Images Using Multilayer Neural Network Based on Multi-Valued Neurons, Proceedings of the 41st IEEE International Symposium on Multiple-Valued Logic (ISMVL-2011), to appear in the Proceedings, May 23-35, 2011, IEEE Computer Society Press, pp. 282–287.

24.

Manyakov N.V., Aizenberg I., Chumerin N., and Van Hulle M.: Phase-Coded Brain-Computer Interface Based on MLMVN, in: A. Hirose (ed): Complex-Valued Neural Networks: Advances and Applications, Wiley, 2013, pp. 185–208.

25.

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26.

Aizenberg I., Sheremetov L., Villa-Vargas L., and Martinez-Muñoz J.: Multilayer Neural Network with Multi-Valued Neurons in Time Series Forecasting of Oil Production, Neurcomputing, published “Online first” , December 2015, published in a hard copy Vol. 175, Part B, 29 January 2016, pp. 980–989.

27.

I. Aizenberg: MLMVN with Soft Margins Learning, IEEE Transactions on Neural Networks and Learning Systems, vol. 25, No 9, September 2014, pp. 1632–1644.CrossRef

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I. Aizenberg. A. Luchetta, and S. Manetti: A modified Learning Algorithms for the Multilayer Neural Network with Multi-Valued Neurons based on the Complex QR Decomposition, Soft Computing, vol. 16, April 2012, pp. 563–575.

29.

I. Aizenberg and E. Aizenberg: Batch LLS-based Learning Algorithm for MLMVN with Soft Margins, Proceedings of the 2014 IEEE Symposium Series of Computational Intelligence (SSCI-2014), December, 2014, pp. 48–55.

Titel: Multiple-Valued Logic and Complex-Valued Neural Networks
verfasst von: Igor Aizenberg
Verlag: Springer International Publishing
Buch: Claudio Moraga: A Passion for Multi-Valued Logic and Soft Computing
Print ISBN: 978-3-319-48316-0

Electronic ISBN: 978-3-319-48317-7

Copyright-Jahr: 2017
DOI: https://doi.org/10.1007/978-3-319-48317-7_10

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