An efficient multilayer RBF neural network and its application to regression problems

By combining multilayer perceptrons (MLPs) and radial basis function neural networks (RBF-NNs), an efficient multilayer RBF network is proposed in this work for regression problems. As an extension to the existing multilayer RBF network (RBF-MLP-I), the new multilayer RBF network (RBF-MLP-II) first nonlinearly transforms the multi-dimensional input data by adopting a set of multivariate basis functions. Then, linear weighted sums of these basis functions, i.e., the RBF approximations, are computed in the first hidden layer and used as the features of this layer. Subsequently, in the following hidden layers, each feature of the preceding hidden layer is fed into a univariate RBF characterized by the trainable scalar center and width, and then, RBF approximations are also applied to these basis functions. Finally, the features of the last hidden layer are linearly transformed to approximate the target output data. RBF-MLP-II reduces the number of parameters in basis functions and thus the network complexity of RBF-MLP-I. Verified by four regression problems, it is demonstrated that the proposed RBF-MLP-II exhibits the best approximation accuracy and fastest training convergence compared to conventional MLPs, RBF-NNs, and RBF-MLP-I.