13.1 Concept of Neural Networks

Neural networks are a relatively new means of data processing. Interpreted in this way, it can be said that a neural network realises a mapping from an input vector space into the output vector space,

{x} ? {y},

(Figure 13.1); the dimensions of both spaces are generally different. The physical separation of inputs and outputs, as indicated in the Figure, need not be kept with some types of neural networks; the same nodes may carry input or output values in different time instants according to a convention and mode of experimenting. Understood so generally, neural networks can be applied in very different ways. We shall concentrate our attention primarily on neural-network applications as signal processors, when the input and output vectors represent the relevant signals. Another, perhaps more frequent use is their application as classifiers then the input vector represents a section of a signal or image and the output indicates to which class the section belongs. Further, it is possible to utilise the ability of some networks to solve optimisation problems; they can be used for signal restoration with respect to chosen criteria. An important application of certain networks is their use as associative memory able to retrieve information on the basis of incomplete assignment. It is also possible to design neural nets in such a way that the transferred information is passed through a 'bottleneck' a part of the network capable of transferring only a limited rate of information.