Euclidean distance and second derivative based widths optimization of radial basis function neural networks

Abstract

The design of radial basis function widths of Radial Basis Function Neural Network (RBFNN) is thoroughly studied in this paper. Firstly, the influence of the widths on performance ofRBFNN is illustrated with three simple function approximation experiments. Based on the conclusions drawn from the experiments, we find that two key factors including the spatial distribution of the training data set and the nonlinearity of the function should be considered in the width design. We propose to use Euclidean distances between center nodes and the second derivative of function to measure these two factors respectively. Secondly, a two step method is proposed to design the widths based on the information about the aforementioned two key factors obtained from comprehensive analysis of the given training data set. In the first step the data set spatial distribution features are analyzed according to the Euclidean distances between the data points, and the second derivative of each center node is estimated with finite difference approximation method. Based on the analysis an initial design of the widths is given with a heuristic equation. In the second step optimization techniques are used to optimize the widths which can effectively find the optimum with the good initial baseline.Thirdly, one mathematical example is taken to verify the efficiency of the proposed method, and followed by conclusions.

Artificial Neural Model based on radial basis function networks used for prediction of compressive strength of fiber-reinforced concrete mixes

“…Con respecto a la distancia radial, esta es usada para la estimación de las desviaciones, que se calculan de tal manera que cada neurona de la capa oculta se active en una región del espacio de entradas con un solapamiento de las zonas de activación lo más ligero posible para suavizar la interpolación. Se aplica como distancia radial alguna de las distancias estadísticas definidas por [37] y [38], como la distancia euclidiana, de Mahalanobis, de Minkowski, de K. Pearson, de Canberra, de Clark, entre otras.…”

“…Las conexiones entre las neuronas de entrada a la capa oculta se hacen por medio de la función de Gauss definida en (1), de acuerdo con [40]. Las desviaciones a los centros son calculadas usando la distancia radial Euclidiana, definida en [37] y [38].…”

Radial basis function neural networks: a topical state-of-the-art survey

“…Their experimental outcomes have shown that the nonsymmetric partition can lead to the development of more accurate RBF models, with a smaller number of hidden layer nodes. More elaborate methods have been suggested [58][59][60][61] for optimizing the RBF widths in order to improve approximation accuracy. Taking advantage of the linear connection between the hidden and output layer, most training algorithms calculate the synaptic weights of RBF networks by applying linear regression of the output of the hidden units on the target values.…”

Short Term Load Forecasting using genetically optimized Radial Basis Function Neural Network

“…This way, the best recognized RBFNN structure 11-88-1 gives good results. As discussed in previous section, and existing forecasting studies [7], [21]- [22] show that the conventional training procedure to train RBFNN rarely optimizes the training parameters of RBFNN. Hence, it is incapable to result in sufficiently accurate prediction.…”