A Divide-and-Conquer Learning Approach to Radial Basis Function Networks

Abstract

This paper presents a new divide-and-conquer based learning approach to radial basis function (RBF) networks, in which a conventional RBF network is divided into several RBF sub-networks. Each of them individually takes an input sub-space as its input. The original network's output then becomes a linear combination of the sub-networks' outputs with the coefficients adaptively learned together with the system parameters of each sub-network. Since this approach reduces the structural complexity of a RBF network by describing a high-dimensional modelling problem via several low-dimensional ones, the network's learning speed is considerably improved as a whole with the comparable generalization capability. The empirical studies have shown its outstanding performance on forecasting two real time series as well as synthetic data. Besides, we have found that the performance of this approach generally varies with the different decompositions of the network's input and the hidden layer. We therefore further explore the decomposition rule with the results verified by the experiments.

Enhanced hybrid method of divide-and-conquer and RBF neural networks for function approximation of complex problems

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A new fast reduction technique based on binary nearest neighbor tree

“…Although a large number of strategies have been proposed to improve these two traditional approaches, the embedded approach has been developed rapidly. For instance, merged with Neural Network, Cheung and Huang [25] adopted divide-and-conquer strategy to divide the conventional RBF network into several sub-networks and it can deal with a highdimensional modeling problem via several low-dimensional ones. Furthermore, Cheung and Law [26] proposed a novel rival-model penalized self-organizing map learning algorithm that can adaptively chooses several rivals of the best-matching unit and penalizes their associated models.…”

A Locally Gaussian Mixture Based RBF Network for Classification of Chinese Herbal Infrared Spectrum Fingerprint

“…This is similar to model each class with a Gaussian mixture, thus we call the proposed network as Locally Gaussian Mixture Based RBF (LGM-RBF) network. In this new network, the weights between the mix layer and the output layer are nonlinear functions of the input vectors, which can therefore provide more flexibility to reduce the error of outputs as shown in [1]. Moreover, we have noticed that the goodness of training set has great impact on the complexity and performance of a classification system.…”