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.     

Online identification using radial basis function neural network coupled with KPCA

In this paper, we are going to propose an online radial basis function (RBF) neural network algorithm without any preprocessing step. Then a kernel principal component analysis (KPCA) is coupled with the proposed online RBF neural network algorithm. Indeed, the KPCA method is used as a preprocessing step to reduce the feature dimension which fed to the RBF neural network. Reducing memory requirements of the models makes RBF neural network training efficient and fast. These two proposed algorithms are applied, with success, for identification of a mobile robot position. The simulation results present that the used sigmoid function as a kernel, compared to other kernel functions, which gives an excellent model and a minimum mean square error.     

基于径向基函数的多帧图像超分辨重建算法

神经网络具有强大的非线性学习能力,基于神经网络的多帧超分辨重建方法获得了初步研究,但这些方法一般只能应用于帧间具有标准位移的控制成像情形,难以推广应用到其他实际情况。为了将神经网络强大的学习能力应用到非控制成像多帧超分辨重建中,以获得更好的超分辨效果,提出了一种利用径向基函数(RBF)神经网络进行解模糊的算法,并将其与多帧非均匀插值结合起来,形成了一种新的两步超分辨算法。仿真实验结果表明,该算法的结构相似度为0.55～0.7。该算法不但扩展了RBF神经网络的应用范围,还获得了更好的超分辨性能。     

基于遗传优化径向基概率神经网络的岩性识别应用

岩性识别是测井数据解释中最关键的一环,但传统的岩性识别方法解释效率慢,精度低,受人为因素影响大。为此,提出一种遗传优化径向基概率神经网络(RBPNN)的岩性识别方法。该方法融合概率神经网络(PNN)和径向基函数神经网络(RBFNN)的优势来构造RBPNN,采用遗传算法搜索使得RBPNN训练法误差最小的最优隐中心矢量和相匹配的核函数控制参数,优化网络结构,提高收敛速度与精度,形成全结构遗传优化的RBPNN模型。实例应用表明,基于遗传优化RBPNN的岩性识别能够达到工程实际应用的规范标准,且是可行有效的,能够为油田地质勘探领域的岩性识别提供科学的理论支持与依靠。     

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.     

Multi-layer radial basis function neural network based on multi-scale kernel learning

The conversion functions in the hidden layer of radial basis function neural networks (RBFNN) are Gaussian functions. The Gaussian functions are local to the kernel centers. In most of the existing research, the spatial local response of the sample is inaccurately calculated because the kernels have the same shape as a hypersphere, and the kernel parameters in the network are determined by experience. The influence of the fine structure in the local space is not considered during feature extraction. In addition, it is difficult to obtain a better feature extraction ability with less computational complexity. Therefore, this paper develops a multi-scale RBF kernel learning algorithm and proposes a new multi-layer RBF neural network model. For the samples of each class, the expectation maximization (EM) algorithm is used to obtain multi-layer nested sub-distribution models with different local response ranges, which are called multi-scale kernels in the network. The prior information of each sub-distribution is used as the connection weight between the multi-scale kernels. Finally, feature extraction is implemented using multi-layer kernel subspace embedding. The multi-scale kernel learning model can efficiently and accurately describe the fine structure of the samples and is fault tolerant to setting the number of kernels to a certain extent. Considering the prior probability of each kernel as the weight makes the feature extraction process satisfy the Bayes rule, which can enhance the interpretability of feature extraction in the network. This paper also theoretically proves that the proposed neural network is a generalized version of the original RBFNN. The experimental results show that the proposed method has better performance compared with some state-of-the-art algorithms.     

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.     

基于QPSO算法的RBF神经网络参数优化仿真研究

针对粒子群优化(PSO)算法搜索空间有限,容易陷入局部最优点的缺陷,提出一种以量子粒子群优化(QPSO)算法为基础的RBF神经网络训练算法,将RBF神经网络的参数组成一个多维向量,作为算法中的粒子进行进化,由此在可行解空间范围内搜索最优解。实例仿真表明,该学习算法相比于传统的学习算法计算简单,收敛速度快,并由于其算法模型的自身特性比基于PSO的学习算法具有更好的全局收敛性能。     

基于径向基函数神经网络的多级离心压缩机混合模型

大型离心压缩机作为多影响因素和强非线性的复杂系统,其性能的准确预测难以实现.针对这一问题,结合径向基函数(RBF)神经网络,本文建立了多级离心压缩机性能预测的混合模型.首先基于热力学第一定律和压缩机能量损失机理建立了多级离心压缩机性能预测的机理模型.该模型无需任何实验确定的性能曲线,完全由压缩机的几何结构参数预测出压缩机在设计工况和非设计工况下的性能.然后利用RBF神经网络修正机理模型的误差,并通过对RBF神经网络的不断更新,进一步提高了模型的预测精度和适用性.将所建立的混合模型应用于实际的离心压缩机,结果表明该方法具有良好的预测性能.     

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.     

基于径向基函数神经网络的泥石流危险性评价*

泥石流危险性的主要评价指标与危险程度之间有着某种复杂的非线性的关系,通常采用统计分析、模糊评价、BP神经网络等评价方法,但这些方法均存在不足之处,难以进行准确评价。为了克服以上方法的不足,结合泥石流危险性评价指标,建立了基于径向基函数神经网络的泥石流危险性评价模型,并将该模型结果与BP神经网络的评价结果进行了对比。实验结果表明,径向基函数神经网络的模拟结果比BP神经网络更接近测量数据,精度更高,训练所需时间更少。因此,径向基函数神经网络经过充分训练后,能够较为准确地对泥石流的危险性进行评价,具有较好的应用     

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.     

基于径向基神经网络的称重设备传感器故障检测方法

在对称重设备数字化改造的过程中,有些研究人员提出了对某一特定传感器的故障诊断方法,但对于非指定传感器或者两个传感器同时发生故障的情况却没有检测方法.为此,本文提出了一种基于径向基神经网络预测的任意一个或两个称重传感器的故障检测方法.本文首先建立单个传感器的预测模型和任意两个传感器的预测模型,然后通过这两个预测模型计算出任意一个称重传感器的预测值和任意两个传感器的预测值,根据预测值与实际值之间的差值判断称重传感器故障个数、位置、类型等信息.实验表明,当称重传感器的输出误差大于0.3 t时使用此方法可以准确检测出称重传感器的故障信息.     

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.