Abstract
In this paper, we observe some important aspects of Hebbian and errorcorrection learning rules for the multi-valued neuron with complex-valued weights. It is shown that Hebbian weights are the best starting weights for the errorcorrection learning. Both learning rules are also generalized for a complex-valued neuron whose inputs and output are arbitrary complex numbers.
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Aizenberg, N.N., Aizenberg, I.N.: CNN Based on Multi-Valued Neuron as a Model of Associative Memory for Gray-Scale Images. In: The Second IEEE Int. Workshop on Cellular Neural Networks and their Applications, October 1992, pp. 36–41. Technical University Munich, Germany (1992)
Aizenberg, N.N., Ivaskiv, Y.L., Pospelov, D.A.: About one generalization of the threshold function. Doklady Akademii Nauk SSSR (The Reports of the Academy of Sciences of the USSR) 196(6), 1287–1290 (1971) (in Russian)
Aizenberg, N.N., Ivaskiv, Y.L.: Multiple-Valued Threshold Logic. Naukova Dumka Publisher House, Kiev (1977) (in Russian)
Aizenberg, I., Aizenberg, N., Vandewalle, J.: Multi-valued and universal binary neurons: theory, learning, applications. Kluwer Academic Publishers, Boston (2000)
Aizenberg, I., Moraga, C.: Multilayer Feedforward Neural Network Based on Multi-Valued Neurons (MLMVN) and a Backpropagation Learning Algorithm. Soft Computing 11(2), 169–183 (2007)
Aizenberg, I.: A Periodic Activation Function and a Modified Learning Algorithm for a Multi-Valued Neuron. IEEE Transactions on Neural Networks 21(12), 1939–1949 (2010)
Aizenberg, I., Paliy, D., Zurada, J.M., Astola, J.: Blur Identification by Multilayer Neural Network based on Multi-Valued Neurons. IEEE Transactions on Neural Networks 19(5), 883–898 (2008)
Jankowski, S., Lozowski, A., Zurada, J.M.: Complex-Valued Multistate Neural Associative Memory. IEEE Trans. Neural Networks 7(6), 1491–1496 (1996)
Muezzinoglu, M.K., Guzelis, C., Zurada, J.M.: A New Design Method for the Complex-Valued Multistate Hopfield Associative Memory. IEEE Trans. Neural Networks 14(4), 891–899 (2003)
Hebb, D.O.: The Organization of Behavior. John Wiley & Sons, New York (1949)
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Aizenberg, I. (2011). Multi-Valued Neurons: Hebbian and Error-Correction Learning. In: Cabestany, J., Rojas, I., Joya, G. (eds) Advances in Computational Intelligence. IWANN 2011. Lecture Notes in Computer Science, vol 6691. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-21501-8_5
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DOI: https://doi.org/10.1007/978-3-642-21501-8_5
Publisher Name: Springer, Berlin, Heidelberg
Print ISBN: 978-3-642-21500-1
Online ISBN: 978-3-642-21501-8
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