RBF neural network based on q-Gaussian function in function approximation

To enhance the generalization performance of radial basis function (RBF) neural networks, an RBF neural network based on a q-Gaussian function is proposed. A q-Gaussian function is chosen as the radial basis function of the RBF neural network, and a particle swarm optimization algorithm is employed to select the parameters of the network. The non-extensive entropic index q is encoded in the particle and adjusted adaptively in the evolutionary process of population. Simulation results of the function approximation indicate that an RBF neural network based on q-Gaussian function achieves the best generalization performance.     

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.     

Efficient clustering of radial basis perceptron neural network for pattern recognition

This paper studies how to train a new feed-forward neural network, radial basis perceptron (RBP) neural network, for distinguishing different sets in R^L. RBP neural network is based on radial basis function (RBF) neural network and perceptron neural network. It has two hidden layers where the nodes are not fully connected but use selective connection. A training algorithm corresponding to the structure of RBP network is presented. It adopts the input-output clustering (IOC) method to provide an efficient and powerful procedure for constructing a RBP network that generalizes very well. First, during the learning procedure, RBP neural network adopts IOC method to define the number of units of hidden layers and select centers. Second, the width parameter σ of centers is self-adjustable according to the information included in the learning samples. The effectiveness of this network is illustrated using an example taken from applications for component analysis of civil building materials. Simulation shows that RBP neural network can be used to predict the components of civil building materials successfully and gets good generalization ability.     

A fast identification algorithm for box-cox transformation based radial basis function neural network

In this letter, a Box-Cox transformation-based radial basis function (RBF) neural network is introduced using the RBF neural network to represent the transformed system output. Initially a fixed and moderate sized RBF model base is derived based on a rank revealing orthogonal matrix triangularization (QR decomposition). Then a new fast identification algorithm is introduced using Gauss-Newton algorithm to derive the required Box-Cox transformation, based on a maximum likelihood estimator. The main contribution of this letter is to explore the special structure of the proposed RBF neural network for computational efficiency by utilizing the inverse of matrix block decomposition lemma. Finally, the Box-Cox transformation-based RBF neural network, with good generalization and sparsity, is identified based on the derived optimal Box-Cox transformation and a D-optimality-based orthogonal forward regression algorithm. The proposed algorithm and its efficacy are demonstrated with an illustrative example in comparison with support vector machine regression.     

Prediction of reservoir sensitivity using RBF neural network with trainable radial basis function

Reservoir sensitivity prediction is an important basis for designing reservoir protection program scientifically and exploiting oil and gas resources efficiently. Researchers have long endeavored to establish a method to predict reservoir sensitivity, but all of the methods have some limitations. Radial basis function (RBF) neural network, which provided a powerful technique to model non-linear mapping and the learning algorithm for RBF neural networks, corresponds to the solution of a linear problem, therefore it is unnecessary to establish an accurate model or organize rules in large number, and it enjoys the advantages such as simple network structure, fast convergence rate, and strong approximation ability, etc. However, different radial basis function has different non-linear mapping ability, and different data require different radial basis functions. Nowadays, the choice of radial basis function in the network is based on experience or test result only, which exerts a great adverse impact on the network performance. In this study, a new RBF neural network with trainable radial basis function was proposed by the linear combination of common radial basis functions. The input parameters of the network were the influence factors of reservoir sensitivity such as porosity and permeability, etc. The output parameter was the corresponding sensitivity index. The network was trained and tested with the data collected from our own experiments. The results showed that the new RBF neural network is effective and improved, of which the accuracy is obviously higher than the network with single radial basis function for the prediction of reservoir sensitivity.     

Parameter estimation of q-Gaussian Radial Basis Functions Neural Networks with a Hybrid Algorithm for binary classification

A classification problem is a decision-making task that many researchers have studied. A number of techniques have been proposed to perform binary classification. Neural networks are one of the artificial intelligence techniques that has had the most successful results when applied to this problem. Our proposal is the use of q-Gaussian Radial Basis Function Neural Networks (q-Gaussian RBFNNs). This basis function includes a supplementary degree of freedom in order to adapt the model to the distribution of data. A Hybrid Algorithm (HA) is used to search for a suitable architecture for the q-Gaussian RBFNN. The use of this type of more flexible kernel could greatly improve the discriminative power of RBFNNs. In order to test performance, the RBFNN with the q-Gaussian basis functions is compared to RBFNNs with Gaussian, Cauchy and Inverse Multiquadratic RBFs, and to other recent neural networks approaches. An experimental study is presented on 11 binary-classification datasets taken from the UCI repository. Moreover, aerial imagery taken in mid-May, mid-June and mid-July was used to evaluate the potential of the methodology proposed for discriminating Ridolfia segetum patches (one of the most dominant and harmful weeds in sunflower crops) in two naturally infested fields in southern Spain.     

一种改进PSO优化RBF神经网络的新方法

为了克服神经网络模型结构和参数难以设置的缺点,提出了一种改进粒子群优化的径向基函数(RBF)神经网络的新方法.首先将最近邻聚类用于RBF神经网络隐层中心向量的确定,同时对引入适应度值择优选取的原则对基本粒子群算法进行改进,采用改进粒子群(IMPSO)算法对最近邻聚类的聚类半径进行优化,合理的确定了RBF神经网络的隐层结构.将改进PSO优化的RBF神经网络应用于非线性函数逼近和混沌时间序列预测,经实验仿真验证.与基本粒子群(PSO)算法,收缩因子粒子群(CFA PSO)算法优化的RBF神经网络相比较,其在识别精度和收敛速度上都有了显著的提高.     

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.     

基于神经元特性的径向基函数神经网络自组织设计方法

针对径向基神经函数(RBF)网络隐层结构难以确定的问题, 本文介绍了一种基于神经元特性的RBF神经网 络自组织设计方法, 该方法将神经元的激活活性、显著性、相关性相结合设计RBF(ASC–RBF)神经网络. 首先利用 神经元的激活活性, 实现隐含层神经元的自适应增加, 结合神经元的显著性以及神经元之间的相关性, 实现神经元 的自适应替换和合并, 完成网络自组织设计并提高网络的紧凑性, 然后利用二阶梯度算法对网络参数进行修正学 习, 保证了RBF网络的精度; 另外, 针对网络结构自组织机制给出了稳定性分析; 最后通过两个基准非线性系统建模 仿真实验以及实际污水处理过程水质参数预测实验验证, 证明该算法的有效性. 对比实验结果表明, ASC–RBF神经 网络与现有的自组织网络相比, 在保证泛化性能的同时, 该网络的训练速度更快, 而且有更紧凑的网络结构.     

Research on an online self-organizing radial basis function neural network

A new growing and pruning algorithm is proposed for radial basis function (RBF) neural network structure design in this paper, which is named as self-organizing RBF (SORBF). The structure of the RBF neural network is introduced in this paper first, and then the growing and pruning algorithm is used to design the structure of the RBF neural network automatically. The growing and pruning approach is based on the radius of the receptive field of the RBF nodes. Meanwhile, the parameters adjusting algorithms are proposed for the whole RBF neural network. The performance of the proposed method is evaluated through functions approximation and dynamic system identification. Then, the method is used to capture the biochemical oxygen demand (BOD) concentration in a wastewater treatment system. Experimental results show that the proposed method is efficient for network structure optimization, and it achieves better performance than some of the existing algorithms.     

基于AQPSO的RBF神经网络自组织学习

针对径向基函数(RBF)神经网络的结构设计及参数优化问题,提出一种自适应量子粒子群优化(AQPSO)算法.将RBF神经网络的网络规模及参数映射到粒子的空间位置,定义权值平均最优位置,从而对量子粒子群优化(QPSO)中$L_{i,j     

基于模糊RBF神经网络的非线性滤波

该文从基本的智能技术——神经网络(NN)和模糊系统(FS)技术出发,探讨了神经网络与模糊系统相结合的基本理论,提出了一种基于模糊RBF神经网络的非线性滤波的方法。该方法将模糊逻辑的知识表达以及推理能力和RBF网络的快速学习和泛化能力结合起来,网络结构参数可按实际问题调整,对信号中有色噪声进行较高精度的逼近,来达到非线性滤波的目的。该滤波方法显示出很强的处理问题的能力,学习速度快,仿真结果表明了这种方法的有效性和可性行。     

径向基函数神经网络的一种两级学习方法

建立RBF(radial basis function)神经网络模型关键在于确定网络隐中心向量、基宽度参数和隐节点数.为设计结构简单,且具有良好泛化性能径向基网络结构,本文提出了一种RBF网络的两级学习新设计方法.该方法在下级由正则化正交最小二乘法与D-最优试验设计结合算法自动构建结构节俭的RBF网络模型;在上级通过粒子群优化算法优选结合算法中影响网络泛化性能的3个学习参数,即基宽度参数、正则化系数和D-最优代价系数的最佳参数组合.仿真实例表明了该方法的有效性.     

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.     

Communication channel equalization using complex-valued minimalradial basis function neural networks

A complex radial basis function neural network is proposed for equalization of quadrature amplitude modulation (QAM) signals in communication channels. The network utilizes a sequential learning algorithm referred to as complex minimal resource allocation network (CMRAN) and is an extension of the MRAN algorithm originally developed for online learning in real-valued radial basis function (RBF) networks. CMRAN has the ability to grow and prune the (complex) RBF network's hidden neurons to ensure a parsimonious network structure. The performance of the CMRAN equalizer for nonlinear channel equalization problems has been evaluated by comparing it with the functional link artificial neural network (FLANN) equalizer of J.C. Patra et al. (1999) and the Gaussian stochastic gradient (SG) RBF equalizer of I. Cha and S. Kassam (1995). The results clearly show that CMRANs performance is superior in terms of symbol error rates and network complexity.     

基于径向基函数神经网络的混沌背景谐波提取

为提高强混沌背景下谐波信号的提取能力,给出混沌系统的单步预测模型,提出了一种新的径向基函数神经网络模型.由混沌吸引子的维数来确定网络的输入,并给出了基于卡尔曼滤波器的动态学习算法,利用学习算法可以在网络训练时同时确定径向基神经网络隐层中心和输出层权值,提高了网络的收敛速度和预测性能.通过对Bossler混沌背景下低信噪比谐波信号的提取进行计算机认真实验,并且实验表明信噪比最低达一27dB时,仍能有效提取出谐波信号,验证了算法的有效性和可行性.     

基于RBF网络的模拟电路故障诊断算法

针对BP神经网络在模拟电路故障诊断上存在的收敛速度慢、易陷入局部最小等不足,提出了一种基于多层小波分解和RBF神经网络的模拟电路故障诊断算法。为提高诊断效率,用多层小波分解能有效提取电路故障特征;用RBF网络优良的泛化能力和快速的非线性逼近能力可以较好的解决模拟电路中存在的容差和非线性问题。故障诊断仿真实验表明,在保证较高故障诊断正确率的情况下,RBF网络的训练次数得到了极大地缩小,有效克服了基于BP网络算法存在的上述不足,极大地提高了模拟电路故障诊断的时间效率。     

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.     

Support vector machine with adaptive parameters in financial time series forecasting

A novel type of learning machine called support vector machine (SVM) has been receiving increasing interest in areas ranging from its original application in pattern recognition to other applications such as regression estimation due to its remarkable generalization performance. This paper deals with the application of SVM in financial time series forecasting. The feasibility of applying SVM in financial forecasting is first examined by comparing it with the multilayer back-propagation (BP) neural network and the regularized radial basis function (RBF) neural network. The variability in performance of SVM with respect to the free parameters is investigated experimentally. Adaptive parameters are then proposed by incorporating the nonstationarity of financial time series into SVM. Five real futures contracts collated from the Chicago Mercantile Market are used as the data sets. The simulation shows that among the three methods, SVM outperforms the BP neural network in financial forecasting, and there are comparable generalization performance between SVM and the regularized RBF neural network. Furthermore, the free parameters of SVM have a great effect on the generalization performance. SVM with adaptive parameters can both achieve higher generalization performance and use fewer support vectors than the standard SVM in financial forecasting.     

一种应用ARPSO优化RBF神经网络的方法

针对径向基函数神经网络参数难以设置以及因此而导致的网络隐层结构不明朗的问题,提出了一种应用控制种群多样性的微粒群（ ARPSO）优化径向基函数神经网络（ RBF）的方法。通过引入“吸引”和“扩散”因子对基本微粒群算法进行改进,并将改进的微粒群算法用于RBF聚类半径的优化,进而能够合理地确定RBF的隐层结构。将用ARPSO优化的RBF神经网络应用于非线性函数逼近,经实验仿真验证,与基本微粒群（ PSO）算法、收缩因子微粒群（ CFA PSO）算法优化的RBF神经网络相比较,在收敛速度和识别精度上有了显著的提高。