A clustering algorithm for radial basis function neural network initialization

In this paper, we propose an Output-Constricted Clustering (OCC) algorithm for Radial Basis Function Neural Network (RBFNN) initialization. OCC first roughly partitions the output based on the required precision and then refinedly clusters data based on the input complexity within each output partition. The main contribution of the proposed clustering algorithm is that we introduce the concept of separability, which is a criterion to judge the suitability of the number of sub-clusters in each output partition. As a result, OCC is able to determine the proper number of sub-clusters with appropriate locations within each output partition by considering both input and output information. The resulting clusters from OCC are used to initialize RBFNN, with proper number and initial locations of for hidden neurons. As a result, RBFNN starting it's learning from a good point, is able to achieve better approximation performance than existing clustering methods for RBFNN initialization. This better performance is illustrated by a number of examples.     

Training algorithm for radial basis function neural network based on quantum-behaved particle swarm optimization

Radial basis function (RBF) networks are widely applied in function approximation, system identification, chaotic time series forecasting, etc. To use a RBF network, a training algorithm is absolutely necessary for determining the network parameters. The existing training algorithms, such as orthogonal least squares (OLS) algorithm, clustering and gradient descent algorithm, have their own shortcomings respectively. In this paper, we propose a training algorithm based on a novel population-based evolutionary technique, quantum-behaved particle swarm optimization (QPSO), to train RBF neural network. The proposed QPSO-trained RBF network was tested on non-linear system identification problem and chaotic time series forecasting problem, and the results show that it can identify the system and forecast the chaotic time series more quickly and precisely than that trained by the particle swarm algorithm.     

基于模糊径向基函数神经网络的PID控制算法仿真研究

在传统的PID控制算法基础上,提出了一种基于模糊RBF神经网络的PID控制算法。该算法将RBF神经网络学习能力强与模糊理论的推理能力强的特点结合起来,在线调整比例、积分、微分三个控制参数,仿真结果表明,该算法的控制品质优于常规PID控制,具有较强的自适应能力和鲁棒性。     

Median radial basis function neural network

Radial basis functions (RBFs) consist of a two-layer neural network, where each hidden unit implements a kernel function. Each kernel is associated with an activation region from the input space and its output is fed to an output unit. In order to find the parameters of a neural network which embeds this structure we take into consideration two different statistical approaches. The first approach uses classical estimation in the learning stage and it is based on the learning vector quantization algorithm and its second-order statistics extension. After the presentation of this approach, we introduce the median radial basis function (MRBF) algorithm based on robust estimation of the hidden unit parameters. The proposed algorithm employs the marginal median for kernel location estimation and the median of the absolute deviations for the scale parameter estimation. A histogram-based fast implementation is provided for the MRBF algorithm. The theoretical performance of the two training algorithms is comparatively evaluated when estimating the network weights. The network is applied in pattern classification problems and in optical flow segmentation.     

A novel radial basis function neural network for discriminant analysis

A novel radial basis function neural network for discriminant analysis is presented in this paper. In contrast to many other researches, this work focuses on the exploitation of the weight structure of radial basis function neural networks using the Bayesian method. It is expected that the performance of a radial basis function neural network with a well-explored weight structure can be improved. As the weight structure of a radial basis function neural network is commonly unknown, the Bayesian method is, therefore, used in this paper to study this a priori structure. Two weight structures are investigated in this study, i.e., a single-Gaussian structure and a two-Gaussian structure. An expectation-maximization learning algorithm is used to estimate the weights. The simulation results showed that the proposed radial basis function neural network with a weight structure of two Gaussians outperformed the other algorithms.     

Optimizing radial basis function neural network based on rough sets and affinity propagation clustering algorithm

A novel method based on rough sets (RS) and the affinity propagation (AP) clustering algorithm is developed to optimize a radial basis function neural network (RBFNN). First, attribute reduction (AR) based on RS theory, as a preprocessor of RBFNN, is presented to eliminate noise and redundant attributes of datasets while determining the number of neurons in the input layer of RBFNN. Second, an AP clustering algorithm is proposed to search for the centers and their widths without a priori knowledge about the number of clusters. These parameters are transferred to the RBF units of RBFNN as the centers and widths of the RBF function. Then the weights connecting the hidden layer and output layer are evaluated and adjusted using the least square method (LSM) according to the output of the RBF units and desired output. Experimental results show that the proposed method has a more powerful generalization capability than conventional methods for an RBFNN.     

A fast identification algorithm with outliers under Box-Cox transformation-based annealing robust radial basis function networks

In this article, a Box-Cox transformation-based annealing robust radial basis function networks (ARRBFNs) is proposed for an identification algorithm with outliers. Firstly, a fixed Box-Cox transformation-based ARRBFN model with support vector regression (SVR) is derived to determine the initial structure. Secondly, the results of the SVR are used as the initial structure in the fixed Box-Cox transformation-based ARRBFNs for the identification algorithm with outliers. At the same time, an annealing robust learning algorithm (ARLA) is used as the learning algorithm for the fixed Box-Cox transformation-based ARRBFNs, and applied to adjust the parameters and weights. Hence, the fixed Box-Cox transformation-based ARRBFNs with an ARLA have a fast convergence speed for an identification algorithm with outliers. Finally, the proposed algorithm and its efficacy are demonstrated with an illustrative example in comparison with Box-Cox transformation-based radial basis function networks.     

A gradient-based sequential radial basis function neural network modeling method

Radial basis function neural network (RBFNN) is widely used in nonlinear function approximation. One of the key issues in RBFNN modeling is to improve the approximation ability with samples as few as possible, so as to limit the network’s complexity. To solve this problem, a gradient-based sequential RBFNN modeling method is proposed. This method can utilize the gradient information of the present model to expand the sample set and refine the model sequentially, so as to improve the approximation accuracy effectively. Two mathematical examples and one practical problem are tested to verify the efficiency of this method. This article was originally presented in the fifth International Symposium on Neural Networks.     

A local linear radial basis function neural network for financial time-series forecasting

In this paper a Local Linear Radial Basis Function Neural Network (LLRBFN) is presented. The difference between the proposed neural network and the conventional Radial Basis Function Neural Network (RBFN) is connection weights between the hidden layer and the output layer which are replaced by a local linear model in the LLRBFN. A modified Particle Swarm Optimization (PSO) with hunter particles is introduced for training the LLRBFN. The proposed methods have been applied for prediction of financial time-series and the result shows the feasibility and effectiveness.     

A fuzzy hybrid learning algorithm for radial basis function neural network with application in human face recognition

This paper presents a fuzzy hybrid learning algorithm (FHLA) for the radial basis function neural network (RBFNN). The method determines the number of hidden neurons in the RBFNN structure by using cluster validity indices with majority rule while the characteristics of the hidden neurons are initialized based on advanced fuzzy clustering. The FHLA combines the gradient method and the linear least-squared method for adjusting the RBF parameters and the neural network connection weights. The RBFNN with the proposed FHLA is used as a classifier in a face recognition system. The inputs to the RBFNN are the feature vectors obtained by combining shape information and principal component analysis. The designed RBFNN with the proposed FHLA, while providing a faster convergence in the training phase, requires a hidden layer with fewer neurons and less sensitivity to the training and testing patterns. The efficiency of the proposed method is demonstrated on the ORL and Yale face databases, and comparison with other algorithms indicates that the FHLA yields excellent recognition rate in human face recognition.     

A novel self-adaptive extreme learning machine based on affinity propagation for radial basis function neural network

In this paper, a novel self-adaptive extreme learning machine (ELM) based on affinity propagation (AP) is proposed to optimize the radial basis function neural network (RBFNN). As is well known, the parameters of original ELM which developed by G.-B. Huang are randomly determined. However, that cannot objectively obtain a set of optimal parameters of RBFNN trained by ELM algorithm for different realistic datasets. The AP algorithm can automatically produce a set of clustering centers for the different datasets. According to the results of AP, we can, respectively, get the cluster number and the radius value of each cluster. In that case, the above cluster number and radius value can be used to initialize the number and widths of hidden layer neurons in RBFNN and that is also the parameters of coefficient matrix H of ELM. This may successfully avoid the subjectivity prior knowledge and randomness of training RBFNN. Experimental results show that the method proposed in this thesis has a more powerful generalization capability than conventional ELM for an RBFNN.     

A hybrid radial basis function and data envelopment analysis neural network for classification

We propose a hybrid radial basis function network-data envelopment analysis (RBFN-DEA) neural network for classification problems. The procedure uses the radial basis function to map low dimensional input data from input space ℜ to a high dimensional ℜ⁺ feature space where DEA can be used to learn the classification function. Using simulated datasets for a non-linearly separable binary classification problem, we illustrate how the RBFN-DEA neural network can be used to solve it. We also show how asymmetric misclassification costs can be incorporated in the hybrid RBFN-DEA model. Our preliminary experiments comparing the RBFN-DEA with feed forward and probabilistic neural networks show that the RBFN-DEA fares very well.     

A forecasting system for car fuel consumption using a radial basis function neural network

A predictive system for car fuel consumption using a radial basis function (RBF) neural network is proposed in this paper. The proposed work consists of three parts: information acquisition, fuel consumption forecasting algorithm and performance evaluation. Although there are many factors affecting the fuel consumption of a car in a practical drive procedure, in the present system the relevant factors for fuel consumption are simply decided as make of car, engine style, weight of car, vehicle type and transmission system type which are used as input information for the neural network training and fuel consumption forecasting procedure. In fuel consumption forecasting, to verify the effect of the proposed RBF neural network predictive system, an artificial neural network with a back-propagation (BP) neural network is compared with an RBF neural network for car fuel consumption prediction. The prediction results demonstrated the proposed system using the neural network is effective and the performance is satisfactory in terms of fuel consumption prediction.     

基于GA-RBF神经网络及边界不变特征的车辆识别

修正的边界不变矩在目标旋转、缩放和平移过程中能保持不变性．将其作为车辆目标的识别特征,并且利用遗传算法（GA）优化径向基函数（RBF）神经网络参数,能很好地实现对车辆目标的识别．实验表明,该方法在复杂背景下对目标的识别具有很强的鲁棒性,能快速准确地识别车辆类型;并且边界不变特征的引入,减少了数据运算量,提高了识别效率．     

基于RBF神经网络曲线重构的算法研究

提出一种基于径向基(RBF)函数神经网络的曲线重构学习方法,即由描述物体轮廓特征的样本点作为RBF神经网络的学习样本,利用RBF神经网络强大的函教逼近能力对样本点进行学习和训练,从而仿真出包含这些样本点的原始曲线,同时对于曲线一些样本点缺少的情况下,仍然能构通过调整参数训练得到这些样本点的原始拟和曲线.实验表明,基于径向基(RBF)函数的神经网络具有很强的物体边界描述能力和缺损修复能力.     

基于径向基函数神经网络的网络流量识别模型

提出了一种基于径向基函数神经网络的网络流量识别方法。根据实际网络中的流量数据,建立了一个基于RBF神经网络的流量识别模型。先介绍了RBF神经网络的结构设计及学习算法,针对RBF神经网络在隐节点过多的情况下算法过于复杂的缺点,采用了优化的算法计算隐含层节点。仿真实验证明,该模型具有较好的准确率、低复杂度、高识别效果和良好的自适应性。     

Blind equalization using a predictive radial basis function neural network

In this paper, we propose a novel blind equalization approach based on radial basis function (RBF) neural networks. By exploiting the short-term predictability of the system input, a RBF neural net is used to predict the inverse filter output. It is shown here that when the prediction error of the RBF neural net is minimized, the coefficients of the inverse system are identical to those of the unknown system. To enhance the identification performance in noisy environments, the improved least square (ILS) method based on the concept of orthogonal distance to reduce the estimation bias caused by additive measurement noise is proposed here to perform the training. The convergence rate of the ILS learning is analyzed, and the asymptotic mean square error (MSE) of the proposed predictive RBF identification method is derived theoretically. Monte Carlo simulations show that the proposed method is effective for blind system identification. The new blind technique is then applied to two practical applications: equalization of real-life radar sea clutter collected at the east coast of Canada and deconvolution of real speech signals. In both cases, the proposed blind equalization technique is found to perform satisfactory even when the channel effects and measurement noise are strong.     

新型广义径向基函数神经网络结构研究

提出了一种新型的广义径向基函数(RBF)神经网络,并研究了该网络的学习方法.不同于传统三层结构的RBF网络,广义RBF网络增加了基函数输出加权层,并在输出层采用超曲面去逼近任意的非线性曲面.实例仿真结果表明,与传统的RBF网络相比,该网络具有良好的逼近性能,收敛速度快,可逼近任意多变量非线性函数.     

A fast learning algorithm of neural network with tunable activation function

This paper presents a modified structure of a neural network with tunable activation function and provides a new learning algorithm for the neural network training. Simulation results of XOR problem, Feigenbaum function, and Henon map show that the new algorithm has better performance than BP (back propagation) algorithm in terms of shorter convergence time and higher convergence accuracy. Further modifications of the structure of the neural network with the faster learning algorithm demonstrate simpler structure with even faster convergence speed and better convergence accuracy.     

The improved radial basis function neural network and its application

Compared with other feed-forward neural networks, radial basis function neural networks (RBFNN) have many advantages which make them more suitable for nonlinear system modeling, and they have recently received considerable attention. In this paper, a RBFNN is employed to model strongly nonlinear systems. First, the problems of nonlinear system modeling are analyzed, and then the structure of the RBFNN as well as the training algorithm are improved to solve these problems. Finally, an industrial high-purity distillation column, which is a strongly nonlinear system, is successfully modeled with the improved RBFNN. Owing to the complexities of a nonlinear system, it is necessary to use a real-time model correction method to modify the parameters of the RBFNN model in real time. One efficient method is proposed in this paper. The idea is to employ the Givens transformation to modify the parameters of the RBFNN-based model. This work was presented, in part, at the International Symposium on Artificial Life and Robotics, Oita, Japan, February 18–20, 1996