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Hebbian and error-correction learning for complex-valued neurons

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Abstract

In this paper, we observe some important aspects of Hebbian and error-correction learning rules for complex-valued neurons. These learning rules, which were previously considered for the multi-valued neuron (MVN) whose inputs and output are located on the unit circle, are generalized for a complex-valued neuron whose inputs and output are arbitrary complex numbers. The Hebbian learning rule is also considered for the MVN with a periodic activation function. It is experimentally shown that Hebbian weights, even if they still cannot implement an input/output mapping to be learned, are better starting weights for the error-correction learning, which converges faster starting from the Hebbian weights rather than from the random ones.

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Notes

  1. The data are available at http://www.commsp.ee.ic.ac.uk/~mandic/wind-dataset.zip and the same data were used in Goh et al. (2006).

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Acknowledgments

This work is supported by the National Science Foundation under Grant 0925080.

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  1. Texas A&M University-Texarkana, 7101 University Ave, Texarkana, TX, 75503, USA

    Igor Aizenberg

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  1. Igor Aizenberg
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Correspondence to Igor Aizenberg.

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Aizenberg, I. Hebbian and error-correction learning for complex-valued neurons. Soft Comput 17, 265–273 (2013). https://doi.org/10.1007/s00500-012-0891-8

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