RBF神经网络在遥感影像分类中的应用研究

用RBF神经网络进行遥感影像分类，在网络结构设计上使RBF层与输出层的节点数都等于所要分类的类别数。用Kohonen聚类算法确定RBF中心的时候，用训练样本的均值作为初始中心，并在RBF宽度进行求取的时候进行了改进，以避免内存溢出。所设计的RBF神经网络分类模型具有结构简单、算法简洁的优点。实验结果表明，该方法用于遥感影像分类取得了较高的分类精度，具有实际应用价值。     

Kernelized LARS–LASSO for constructing radial basis function neural networks

Model structure selection is of crucial importance in radial basis function (RBF) neural networks. Existing model structure selection algorithms are essentially forward selection or backward elimination methods that may lead to sub-optimal models. This paper proposes an alternative selection procedure based on the kernelized least angle regression (LARS)–least absolute shrinkage and selection operator (LASSO) method. By formulating the RBF neural network as a linear-in-the-parameters model, we derive a l ₁-constrained objective function for training the network. The proposed algorithm makes it possible to dynamically drop a previously selected regressor term that is insignificant. Furthermore, inspired by the idea of LARS, the computing of output weights in our algorithm is greatly simplified. Since our proposed algorithm can simultaneously conduct model structure selection and parameter optimization, a network with better generalization performance is built. Computational experiments with artificial and real world data confirm the efficacy of the proposed algorithm.     

一种新型的广义RBF神经网络及其训练方法

提出一种新型的广义RBF神经网络模型,将径向基输出权值改为权函数,采用高次函数取代线性加权.给出网络学习方法,并通过仿真分析研究隐单元宽度、权函数幂次等参数的选取对网络逼近精度以及训练时间的影响.结果表明,和传统的RBF神经网络相比,该网络具有良好的逼近能力和较快的计算速度,在系统辨识和控制中具有广阔的应用前景.     

Selecting radial basis function network centers with recursiveorthogonal least squares training

Recursive orthogonal least squares (ROLS) is a numerically robust method for solving for the output layer weights of a radial basis function (RBF) network, and requires less computer memory than the batch alternative. In the paper, the use of ROLS is extended to selecting the centers of an RBF network. It is shown that the information available in an ROLS algorithm after network training can be used to sequentially select centers to minimize the network output error. This provides efficient methods for network reduction to achieve smaller architectures with acceptable accuracy and without retraining. Two selection methods are developed, forward and backward. The methods are illustrated in applications of RBF networks to modeling a nonlinear time series and a real multiinput-multioutput chemical process. The final network models obtained achieve acceptable accuracy with significant reductions in the number of required centers.     

基于信息强度的RBF神经网络结构设计研究

在系统研究前馈神经网络的基础上,针对径向基函数(Radial basis function, RBF) 网络的结构设计问题,提出一种弹性RBF神经网络结构优化设计方法. 利用隐含层神经元的输出信息(Output-information, OI)以及隐含层神经元与输出层神经元间的交互信息(Multi-information, MI)分析网络的连接强度, 以此判断增加或删除RBF神经网络隐含层神经元, 同时调整神经网络的拓扑结构,有效地解决了RBF神经网络结构设计问题; 利用梯度下降的参数修正算法保证了最终RBF网络的精度, 实现了神经网络的结构和参数自校正. 通过对典型非线性函数的逼近与污水处理过程关键水质参数建模, 结果证明了该弹性RBF具有良好的动态特征响应能力和逼近能力, 尤其是在训练速度、泛化能力、最终网络结构等方面较之最小资源神经网络(Minimal resource allocation net works, MRAN)、增长修剪RBF 神经网络(Generalized growing and pruning RBF, GGAP-RBF)和自组织RBF神经网络(Self-organizing RBF, SORBF)有较大的提高.     

一种优化的RBF神经网络在调制识别中的应用

提出了一种基于径向基函数 (RBF) 神经网络的通信信号调制识别方法, 该方法采用模糊 C-均值 (FCM) 聚类算法对数据进行聚类, 并获取基函数的参数, 采用梯度下降法训练网络权值. 利用最优停止法对网络进行了优化, 避免了过学习现象, 提高了 RBF 网络的训练速度和泛化能力, 以实际信号数据对该网络进行性能检验, 实验结果表明了该 RBF 网络具有较高的识别精度.     

Design of a radial basis function neural network with a radius-modification algorithm using response surface methodology

A radial basis function (RBF) neural network was designed for time series forecasting using both an adaptive learning algorithm and response surface methodology (RSM). To improve the traditional RBF networks forecasting capability, the generalized delta rule learning method was employed to modify the radius of the kernel function. Then RSM was utilized to explore the mean square error response surface so that the appropriate combination of network parameters, such as the number of hidden nodes and the initial learning rates, could be found. Extensive studies were performed on the effect of the initial values of connection weights on the accuracy of the backpropagation learning method that was employed in the training of the RBF artificial neural network. The effectiveness of the neural network with the proposed radius-modification technique and the RSM method was demonstrated with an example of forecasting intensity pulsations of a laser. It was found that, by utilizing the proposed techniques, the neural network provided a more accurate prediction of the response.     

Cooperative learning for radial basis function networks using particle swarm optimization

This paper presents a new evolutionary cooperative learning scheme, able to solve function approximation and classification problems with improved accuracy and generalization capabilities. The proposed method optimizes the construction of radial basis function (RBF) networks, based on a cooperative particle swarm optimization (CPSO) framework. It allows for using variable-width basis functions, which increase the flexibility of the produced models, while performing full network optimization by concurrently determining the rest of the RBF parameters, namely center locations, synaptic weights and network size. To avoid the excessive number of design variables, which hinders the optimization task, a compact representation scheme is introduced, using two distinct swarms. The first swarm applies the non-symmetric fuzzy means algorithm to calculate the network structure and RBF kernel center coordinates, while the second encodes the basis function widths by introducing a modified neighbor coverage heuristic. The two swarms work together in a cooperative way, by exchanging information towards discovering improved RBF network configurations, whereas a suitably tailored reset operation is incorporated to help avoid stagnation. The superiority of the proposed scheme is illustrated through implementation in a wide range of benchmark problems, and comparison with alternative approaches.     

权值与结构双确定法的RBF神经网络分类器

为了解决径向基函数(RBF)神经网络权值与结构难以确定的问题,基于权值直接确定法,及隐层神经元中心、方差、数目与神经网络性能的关系,提出一种边增边删型的网络权值与结构双确定法。在此方法基础之上,构建一种RBF神经网络分类器并探讨其分类性能和抗噪能力。计算机数值实验结果验证所提出的边增边删型的权值与结构双确定法能够快速、有效地确定网络的中心、方差和网络最优的权值与结构,所构造的模式分类器具有优越的分类性能和抗噪能力。     

Efficient training of RBF neural networks for pattern recognition.

The problem of training a radial basis function (RBF) neural network for distinguishing two disjoint sets in R(n) is considered. The network parameters can be determined by minimizing an error function that measures the degree of success in the recognition of a given number of training patterns. In this paper, taking into account the specific feature of classification problems, where the goal is to obtain that the network outputs take values above or below a fixed threshold, we propose an approach alternative to the classical one that makes use of the least-squares error function. In particular, the problem is formulated in terms of a system of nonlinear inequalities, and a suitable error function, which depends only on the violated inequalities, is defined. Then, a training algorithm based on this formulation is presented. Finally, the results obtained by applying the algorithm to two test problems are compared with those derived by adopting the commonly used least-squares error function. The results show the effectiveness of the proposed approach in RBF network training for pattern recognition, mainly in terms of computational time saving.     

基于QPSO—RBF NN的混沌时间序列预测*

提出一种基于量子粒子群优化算法训练径向基函数神经网络进行混沌时间序列预测的新方法.在确定径向基函数网络的隐层节点数后,将相应网络的参数,包括隐层基函数中心、扩展常数,以及输出权值和偏移编码成学习算法中的粒子个体,在全局空间中搜索具有最优适应值的参数向量.实例仿真证实了该方法的有效性.     

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K均值与WPA-RBF神经网络模拟电路故障诊断

针对模拟电路故障诊断进行了研究,提出了一种新的方法。该方法包括haar的小波分解,对数据的归一化处理,以及用K均值优化RBF的中心向量和宽度,用狼群算法优化RBF的权值。首先用haar小波对所得的电路原始故障数据集进行变换,然后对变换后的数据进行归一化处理,最终得出RBF神经网络训练所需的输入数据。针对RBF神经网络中隐层节点中心、基函数宽度及权值选取困难问题,这里用K均值优化RBF的中心向量和宽度,用狼群算法优化RBF的权值,以提高网络训练稳定性与诊断成功率。最终通过两个电路的诊断实例,来论述该方法的具体实现过程,验证用该方法进行模拟电路故障诊断的可行性。     

Prediction of noisy chaotic time series using an optimal radialbasis function neural network

This paper considers the problem of optimum prediction of noisy chaotic time series using a basis function neural network, in particular, the radial basis function (RBF) network. In the noiseless environment, predicting a chaotic time series is equivalent to approximating a nonlinear function. The optimal generalization is achieved when the number of hidden units of a RBF predictor approaches infinity. When noise exists, it is shown that an optimal RBF predictor should use a finite number of hidden units. To determine the structure of an optimal RBF predictor, we propose a new technique called the cross-validated subspace method to estimate the optimum number of hidden units. While the subspace technique is used to identify a suitable number of hidden units by detecting the dimension of the subspace spanned by the signal eigenvectors, the cross validation method is applied to prevent the problem of overfitting. The effectiveness of this new method is evaluated using simulated noisy chaotic time series as well as real-life oceanic radar signals. Results show that the proposed method can find the correct number of hidden units of an RBF network for an optimal prediction.     

Adaptive fuzzy c-means clustering algorithm for a radial basis function network

This paper presents a new recursive hybrid algorithm for training a radial basis function (RBF) network. The algorithm consists of a proposed clustering algorithm to position the RBF centres and the Givens least-squares algorithm to estimate the weights. This paper begins with a discussion about the problems of clustering in positioning RBF centres. Then a new clustering algorithm called adaptive fuzzy c-means clustering algorithm is proposed to reduce the problems. The capability of the proposed algorithm was tested to model three data sets: one simulated and two real data sets. It was found that the algorithm provided good performance. The performance of the algorithm was then compared with adaptive k-means, non-adaptive k-means and non-adaptive fuzzy cmeans clustering algorithms. Overall performance of the RBF network that used the proposed clustering algorithm was found to be much better than those that used other clustering algorithms. Simulation results also revealed that the algorithm was not sensitive to initial centres.     

Nonlinear blind source separation using a radial basis functionnetwork

This paper proposes a novel neural-network approach to blind source separation in nonlinear mixture. The approach utilizes a radial basis function (RBF) neural-network to approximate the inverse of the nonlinear mixing mapping which is assumed to exist and able to be approximated using an RBF network. A contrast function which consists of the mutual information and partial moments of the outputs of the separation system, is defined to separate the nonlinear mixture. The minimization of the contrast function results in the independence of the outputs with desirable moments such that the original sources are separated properly. Two learning algorithms for the parametric RBF network are developed by using the stochastic gradient descent method and an unsupervised clustering method. By virtue of the RBF neural network, this proposed approach takes advantage of high learning convergence rate of weights in the hidden layer and output layer, natural unsupervised learning characteristics, modular structure, and universal approximation capability. Simulation results are presented to demonstrate the feasibility, robustness, and computability of the proposed method.     

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.     

A classification technique based on radial basis function neural networks

In this paper, a new classification method is proposed based on the radial basis function (RBF) neural network architecture. The method is particularly useful for manufacturing processes, in cases where on-line sensors for classifying the product quality are not available. More specifically, the fuzzy means algorithm is employed on a set of training data, where the input data refer to variables that are measured on-line and the output data correspond to quality variables that are classified by human experts. The produced neural network model acts as an artificial sensor that is able to classify the product quality in real time. The proposed method is illustrated through an application to real data collected from a paper machine. The method produces successful results and outperforms a number of classifiers, which are based on the feedforward neural network (FNN) architecture.     

基于神经网络生成图像语义的算法研究

提出一种利用神经网络获取图像语义的算法。通过构建一个RBF神经网络,在图像的颜色、纹理、形状等低层视觉特征和高层语义特征之间建立映射关系。利用遗传算法训练RBF网络,获得RBF网络的隐节点个数、中心、宽度和连接权值等参数值,训练成功后的神经网络能够自动获取图像的语义。实验结果表明,该算法具有较好的基于语义的检索效果,体现了人对图像内容的理解,符合人的思维习惯。     

基于Bagging算法和遗传神经网络的交通事件检测

提出一种集成遗传神经网络的交通事件检测方法,以上下游的流量和占有率作为特征,RBF神经网络作为分类器进行交通事件的自动分类与检测。在RBF神经网络的训练过程中,采用遗传算法GA（Genetic Algorithm）对RBF神经网络的隐层中心值和宽度进行优化,用递推最小二乘法训练隐层和输出层之间的权值。为了提高神经网络的分类能力,采用Bagging算法,进行网络集成。通过Matlab仿真实验,证明该方法相对于传统的事件检测算法能更准确、快速地实现分类。