Learning Transformations with Complex-Valued Neurocomputing

Top

Neural Network Model

A brief overview of neural networks is given. In the early 1940s, the pioneers of the field, McCulloch and Pitts, proposed a computational model based on a simple neuron-like element (McCulloch & Pitts, 1943). Since then, various types of neurons and neural networks have been developed independently of their direct similarity to biological neural networks. They can now be considered as a powerful branch of present science and technology.

Neurons are the atoms of neural computation. Out of those simple computational neurons all neural networks are build up. An illustration of a (real-valued) neuron is given in Figure 1. The activity of neuron is defined as:

(1)where is the real-valued weight connecting neuron n and m, is the real-valued input signal from neuron , and is the real-valued threshold value of neuron . Then, the output of the neuron is given by . Although several types of activation functions can be used, the most commonly used are the sigmoidal function and the hyperbolic tangent function.