On the Development and Performance Evaluation of Improved Radial Basis Function Neural Networks

This article deals with the development of four modified radial basis function neural network (RBFNN) models. The corresponding learning algorithms associated with the updating of internal parameters of the models are derived. The conventional inputs are used in the first and second modified RBFNN models (models 3 and 4) whereas exponential nonlinear inputs are used in the fifth and sixth RBFNN models to provide additional nonlinearity for achieving a better solution of nonlinear classification, and direct and inverse modeling problems. To assess and compare the performance potentiality of the proposed four new RBFNN models, one classification problem, one direct modeling problem, and one inverse modeling problem are solved through computer simulation-based experiments. For comparison and to assign the performance rank of each of the four modified RBFNN models, two conventional and commonly used RBFNN models (models 1 and 2) are also simulated. To access the performance of different models during the training phase of Examples 1 and 2, the root mean-square error (RMSE) value, mean absolute deviation (MAD), and the number of iterations required to achieve convergence are obtained. For the third example, only the first two performance measures are found. During the testing or validation phase, the output responses of the different models of Example 2 are compared with the desired response analysis. For Example 3, the bit-error rate (BER) plots are compared. The observation of all the results demonstrates consistent ranks of all models in the case of all three examples. It is, in general, found that the ranks of the models 1–6 are 6, 4, 3, 2, 5, and 1, respectively. In essence, in terms of all performance measures, model M-6 with an exponential version of inputs with weights on both layers occupies the first position whereas model M-4 with conventional inputs as the second position.

I. Introduction

The radial basis function neural network (RBFNN) essentially comprises input and output layers and a single hidden layer and an output stage. The hidden layer contains a set of radial basis functions at each node, and the hidden to output layer contains adjustable weights to produce the desired output. The RBFNN finds applications in areas of function approximation [1], clustering [2], classification [3], [4], forecasting [5], [6], estimation [7], direct system modeling [8], inverse system modeling [9], and adaptive control [10]. The two domains of research works in RBFNN are theoretical development in architectures and learning algorithms, as well as potential applications in different areas of science, engineering, and economics. A review of reported work in these two domains is presented in the sequel.