Statistical analysis of the main parameters in the definition of Radial Basis Function networks

Abstract

As there are many possibilities to select the set of basic functions, parameters and operators used in the design of a Radial Basis Function network (RBF) and in general in Artificial Neural Networks, the search for operators and parameters that are most suitable for the design of an RBF, its characterization and evaluation, is an important topic in the field of Neural Network design. A better insight into the performance of the alternative parameters in the design of an RBF (the distance used, the number of neurons and their nonlinear function in the hidden layer, the number of bits used for weight storage, etc) would make it easier to develop a practical application that uses this type of neural network. In the present contribution, the relevance and relative importance of the parameters involved in the design of an RBF are investigated by using a statistical tool, the ANalysis Of the VAriance (ANOVA)[9]. In order to analyzed the behaviour of the RBF, three different examples were used: the recognition of 26 different letters represented as a 5 by 7 grid of integer values, chaos time-series prediction using the Mackey-Glass differential equation and finally function estimation from samples. This methodology can also be applied to others Neural Networks. The results obtained show that the type of function in the hidden layer and the distance used are the most relevant factors in the behaviour of an RBF. Moreover, this statistical analysis is able to establish a classification of latter factors according to their intrinsic characteristics.