# A MULTI-VALUED NEURON WITH A PERIODIC ACTIVATION FUNCTION

### Igor Aizenberg

#### Abstract

In this paper, a new activation function for the multi-valued neuron (MVN) is presented. The MVN is a neuron with complex-valued weights and inputs/output, which are located on the unit circle. Although the MVN has a greater functionality than a sigmoidal or radial basis function neurons, it has a limited capability of learning highly nonlinear functions. A periodic activation function, which is introduced in this paper, makes it possible to learn nonlinearly separable problems and non-threshold multiple-valued functions using a single multi-valued neuron. The MVN’s functionality becomes higher and the MVN becomes more efficient in solving various classification problems. A learning algorithm based on the error-correction rule for an MVN with the introduced activation function is also presented.

#### References

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#### Paper Citation

#### in Harvard Style

Aizenberg I. (2009). **A MULTI-VALUED NEURON WITH A PERIODIC ACTIVATION FUNCTION** . In *Proceedings of the International Joint Conference on Computational Intelligence - Volume 1: ICNC, (IJCCI 2009)* ISBN 978-989-674-014-6, pages 347-354. DOI: 10.5220/0002286203470354

#### in Bibtex Style

@conference{icnc09,

author={Igor Aizenberg},

title={A MULTI-VALUED NEURON WITH A PERIODIC ACTIVATION FUNCTION},

booktitle={Proceedings of the International Joint Conference on Computational Intelligence - Volume 1: ICNC, (IJCCI 2009)},

year={2009},

pages={347-354},

publisher={SciTePress},

organization={INSTICC},

doi={10.5220/0002286203470354},

isbn={978-989-674-014-6},

}

#### in EndNote Style

TY - CONF

JO - Proceedings of the International Joint Conference on Computational Intelligence - Volume 1: ICNC, (IJCCI 2009)

TI - A MULTI-VALUED NEURON WITH A PERIODIC ACTIVATION FUNCTION

SN - 978-989-674-014-6

AU - Aizenberg I.

PY - 2009

SP - 347

EP - 354

DO - 10.5220/0002286203470354