Abstract
This chapter is introductory. A brief observation of neurons and neural networks is given in Section 1.1. We explain what is a neuron, what is a neural network, what are linearly separable and non-linearly separable input/output mappings. How a neuron learns is considered in Section 1.2, where Hebbian learning, the perceptron, and the error-correction learning rule are presented. In Section 1.3, we consider a multilayer feedforward neural network and essentials of backpropagation learning. The Hopfield and cellular neural networks are also presented. Complexvalued neural networks, their naturalness and necessity are observed in Section 1.4. It is shown that a single complex-valued neuron can learn non-linearly separable input/output mappings and is much more functional than a single real-valued neuron. Historical observation of complex-valued neural networks and the state of the art in this area are also presented. Some concluding remarks will be given in Section 1.5.
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© 2011 Springer-Verlag Berlin Heidelberg
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Aizenberg, I. (2011). Why We Need Complex-Valued Neural Networks?. In: Complex-Valued Neural Networks with Multi-Valued Neurons. Studies in Computational Intelligence, vol 353. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-20353-4_1
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DOI: https://doi.org/10.1007/978-3-642-20353-4_1
Publisher Name: Springer, Berlin, Heidelberg
Print ISBN: 978-3-642-20352-7
Online ISBN: 978-3-642-20353-4
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