Robust radial basis function neural networks

Abstract

Abstract-Function approximation has been found in many applications. The radial basis function (RBF) network is one approach which has shown a great promise in this sort of problems because of its faster learning capacity. A traditional RBF network takes Gaussian functions as its basis functions and adopts the least-squares criterion as the objective function. However, it still suffers from two major problems. First, it is difficult to use Gaussian functions to approximate constant values. If a function has nearly constant values in some intervals, the RBF network will be found inefficient in approximating these values. Second, when the training patterns incur a large error, the network will interpolate these training patterns incorrectly. In order to cope with these problems, an RBF network is proposed in this paper which is based on sequences of sigmoidal functions and a robust objective function. The former replaces the Gaussian functions as the basis function of the network so that constantvalued functions can be approximated accurately by an RBF network, while the latter is used to restrain the influence of large errors. Compared with traditional RBF networks, the proposed network demonstrates the following advantages:1) better capability of approximation to underlying functions; 2) faster learning speed; 3) better size of network; 4) high robustness to outliers.

Integrated guidance and control of hypersonic flight vehicle with coordinated mission requirement and input constraint

“…Considering the uncertain aerodynamic parameters, the function $$$ {f}_i(Z) $$$ is approximated by the radial basis function (RBF) NN 31 as follows: $$$$ {f}_i(Z)={\sigma}_{fi}^T{\varphi}_{fi}+{\varepsilon}_{fi}, $$$$ where $$$ {\sigma}_{fi} $$$ is the optimal neural weight, $$$ {\varphi}_{fi}=\frac{1}{\sqrt{2\pi }{\mu}_i}\exp \left(-\frac{{\left\Vert Z-{o}_i\right\Vert}^2}{2{\mu}_i^2}\right) $$$ is the basis function, $$$ {\mu}_i $$$ is the width, $$$ {o}_i $$$ is the center point, $$$ {\varepsilon}_{fi} $$$ is the construction error of NN with $$$ \left|{\varepsilon}_{fi}\right|\le {\overline{\varepsilon}}_{fi} $$$, and $$$ i=v,\gamma, q $$$.…”

A Very High-Speed Validation Scheme Based on Template Matching for Segmented Character Expiration Codes on Beverage Cans

“…A comparison with other popular classifiers was carried out. KNN [30], neural networks MLP with backpropagation [31,32] and RBF [33], and SVM [34,35]. We used three different configurations of the template matching process offered by MONICOD.…”

Feedback Analysis of Interaction between Urban Densities and Travel Mode Split

“…4, the Gaussian function and the least squares (LS) criterion are usually used as the activation function and the objective function, respectively [27,30,31]. The RBF for a neuron in the hidden layer of the neural network has a centre and a radius which is also called a spread.…”

“…In contrast to parametric analyses relying on the assumptions about the shape or form of the underlying population distribution, nonparametric studies make fewer assumptions about the distribution of measurements in the same population [24,25], and therefore, have been more and more extensively applied especially in recent years. Furthermore, as a nonparametric approach, an artificial neural network can be considered as a universal approximator [26] and it possesses the self-learning capability [27]. Therefore, the complexity of seeking the rational functions can be reduced by constructing and learning the nonlinear mappings through the neural network trainings with examples.…”

“…Consequently, radial basis function (RBF) neural networks [27,29] have been put forward to solve such issues. Owing to its faster learning capability compared with other feedforward networks [27] as well as its ability of solving the high-dimensional interpolation problems [29], a RBF neural network is usually regarded as a good candidate for an approximation problem.…”