VII - Foundations of neural networks

Abstract

This chapter presents the artificial neural networks to emulate the processing capabilities of biological neural systems. The basic idea is to realize systems capable of performing complex processing tasks by interconnecting a high number of very simple processing elements that might even work in parallel. They solve cumbersome and intractable problems by learning directly from data. The main features of artificial neural networks are their massive parallel processing architectures and the capabilities of learning from the presented inputs. The chapter describes the mathematical background that is necessary to understand radial basis neural networks. It reviews the concept of interpolation and shows how the interpolation problem is implemented by a radial basis neural network. Since there are an infinite number of solutions for a given approximation problem, some restrictions on the solutions need to be imposed to choose one particular solution. This leads to a regularization approach to the approximation problem and can be easily implemented by the radial basis neural network. The chapter also presents a different method by looking into the design of a neural network as an approximation problem in a high-dimensional space because data processing in a radial basis function neural network is quite different from standard supervised or unsupervised learning techniques.