Generalised Gaussian radial basis function neural networks

The mixed use of different shapes of radial basis functions (RBFs) in radial basis functions neural networks (RBFNNs) is investigated in this paper. For this purpose, we propose the use of a generalised version of the standard RBFNN, based on the generalised Gaussian distribution. The generalised radial basis function (GRBF) proposed in this paper is able to reproduce other different radial basis functions (RBFs) by changing a real parameter τ. In the proposed methodology, a hybrid evolutionary algorithm (HEA) is employed to estimate the number of hidden neuron, the centres, type and width of each RBF associated with each radial unit. In order to test the performance of the proposed methodology, an experimental study is presented with 20 datasets from the UCI repository. The GRBF neural network (GRBFNN) was compared to RBFNNs with Gaussian, Cauchy and inverse multiquadratic RBFs in the hidden layer and to other classifiers, including different RBFNN design methods, support vector machines (SVMs), a sparse probabilistic classifier (sparse multinominal logistic regression, SMLR) and other non-sparse (but regularised) probabilistic classifiers (regularised multinominal logistic regression, RMLR). The GRBFNN models were found to be better than the alternative RBFNNs for almost all datasets, producing the highest mean accuracy rank.     

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.     

Multiprocessor scheduling and neural network training methods using shuffled frog-leaping algorithm

In this paper, we designed novel methods for Neural Network (NN) and Radial Basis function Neural Networks (RBFNN) training using Shuffled Frog-Leaping Algorithm (SFLA). This paper basically deals with the problem of multi-processor scheduling in a grid environment. We, in this paper, introduce three novel approaches for the task scheduling problem using a recently proposed Shuffled Frog-Leaping Algorithm (SFLA). In a first attempt, the scheduling problem is structured as a problem of optimization and solved by SFLA. Next, this paper makes use of SFLA trained Artificial Neural Network (ANN) and Radial Basis function Neural Networks (RBFNN) for the problem of task scheduling. Interestingly, the proposed methods yield better performance than contemporary algorithms as evidenced by simulation results.     

一种基于模糊径向基神经网络的图像融合方法

传统的基于区域特征图像融合方法的一个难点是各源图像最佳权值的分配问题。该文利用径向基神经网络与T-S模糊推理模型具有函数等价性的特点,设计了一种模糊推理神经网络实现基于区域特征的图像融合,并用遗传算法优化网络参数。该网络能够自适应地动态获取优化的图像融合权值参数。仿真实验表明该算法有效可行,通过与传统的基于区域特征的图像融合算法相比,融合性能得到明显改善。     

The automatic model selection and variable kernel width for RBF neural networks

The Orthogonal Least Squares (OLS) algorithm has been extensively used in basis selection for RBF networks, but it is unable to perform model selection automatically because the tolerance ρ must be specified manually. This introduces noise and it is difficult to implement in the parametric complexity of real-time system. Therefore, a generic criterion that detects the optimum number of its basis functions is proposed. In this paper, not only the Bayesian Information Criterion (BIC) method, used for fitness calculation, is incorporated into the basis function selection process of the OLS algorithm for assigning its appropriate number, but also a new method is developed to optimize the widths of the Gaussian functions in order to improve the generalization performance. The augmented algorithm is employed to the Radial Basis Function Neural Networks (RBFNN) for known and unknown noise nonlinear dynamic systems and its performance is compared with the standard OLS; experimental results show that both the efficacy of BIC for fitness calculation and the importance of proper choice of basis function widths are significant.     

基于正则化RBF神经网络的钢包精炼炉电极系统智能建模

通过RBF神经网络和模糊推理系统的比较，得出正则化RBF神经网络的输出特性，在此基础上利用改进的最近邻聚类算法确定网络的隐层节点个数和高斯函数中心，并估计输出层权值。仿真结果表明了所提方案的有效性。     

Output value-based initialization for radial basis function neural networks

The use of Radial Basis Function Neural Networks (RBFNNs) to solve functional approximation problems has been addressed many times in the literature. When designing an RBFNN to approximate a function, the first step consists of the initialization of the centers of the RBFs. This initialization task is very important because the rest of the steps are based on the positions of the centers. Many clustering techniques have been applied for this purpose achieving good results although they were constrained to the clustering problem. The next step of the design of an RBFNN, which is also very important, is the initialization of the radii for each RBF. There are few heuristics that are used for this problem and none of them use the information provided by the output of the function, but only the centers or the input vectors positions are considered. In this paper, a new algorithm to initialize the centers and the radii of an RBFNN is proposed. This algorithm uses the perspective of activation grades for each neuron, placing the centers according to the output of the target function. The radii are initialized using the center’s positions and their activation grades so the calculation of the radii also uses the information provided by the output of the target function. As the experiments show, the performance of the new algorithm outperforms other algorithms previously used for this problem.     

Rule-Based Learning Systems for Support Vector Machines

In this article, we propose some methods for deriving symbolic interpretation of data in the form of rule based learning systems by using Support Vector Machines (SVM). First, Radial Basis Function Neural Networks (RBFNN) learning techniques are explored, as is usual in the literature, since the local nature of this paradigm makes it a suitable platform for performing rule extraction. By using support vectors from a learned SVM it is possible in our approach to use any standard Radial Basis Function (RBF) learning technique for the rule extraction, whilst avoiding the overlapping between classes problem. We will show that merging node centers and support vectors explanation rules can be obtained in the form of ellipsoids and hyper-rectangles. Next, in a dual form, following the framework developed for RBFNN, we construct an algorithm for SVM. Taking SVM as the main paradigm, geometry in the input space is defined from a combination of support vectors and prototype vectors obtained from any clustering algorithm. Finally, randomness associated with clustering algorithms or RBF learning is avoided by using only a learned SVM to define the geometry of the studied region. The results obtained from a certain number of experiments on benchmarks in different domains are also given, leading to a conclusion on the viability of our proposal.     

Designing RBF Networks Using the Agent-Based Population Learning Algorithm

Radial Basis Function Neural Networks (RBFNs) are nowadays quite popular due to their ability to discover and approximate complex nonlinear dependencies within the data under analysis. Performance of the RBF network depends on numerous factors related to its initialization and training. The paper proposes an approach to the radial basis function networks design, where initial parameters of the network, output weights and parameters of the transfer function are set using the proposed agent-based population learning algorithm (PLA). The algorithm is validated experimentally. Advantages and main features of the PLA-based RBF designs are discussed basing on results of the computational experiment.     

径向函数网络对国民经济生产总值预测研究

为了建立国民经济生产总值（GDP）神经网络预测模型,构造了双层网络结构的基于径向基网络,通过学习训练,确定径向基数神经网络参数和结构。仿真结果表明,生成的径向基函数模型应用于国民经济预测比BP神经网络模型具有更高的预测精度和良好的泛化能力。     

Improving project-profit prediction using a two-stage forecasting system

Accurate project-profit prediction is a crucial issue because it can provide an early feasibility estimate for the project. In order to achieve accurate project-profit prediction, this study developed a novel two-stage forecasting system. In stage one, the proposed forecasting system adopts fuzzy clustering technology, fuzzy c-means (FCM) and kernel fuzzy c-means (KFCM), for the correct grouping of different projects. In stage two, least-squares support vector regression (LSSVR) technology is employed for forecasting the project-profit in different project groups, respectively. Moreover, genetic algorithms (GA) were simultaneously used to select the parameters of the LSSVR. The project data come from a real enterprise in Taiwan. In this study, some forecasting methodologies are also compared, for instance Generalized Regression Neural Network (GRNN), Radial Basis Function Neural Networks (RBFNN), and Back Propagation Neural Network (BPNN), to predict project-profit in this real case. Empirical results indicate that the two-stage forecasting system (FCM+LSSVR and KFCM+LSSVR) has superior performance in terms of forecasting accuracy, compared to other methods. Furthermore, in observing the results of the two-stage forecasting system, it can be seen that FCM+LSSVR can achieve superior performance, and KFCM+LSSVR can achieve consistently good performance. Therefore, based on the empirical results, the two-stage forecasting system was verified to efficiently provide credible predictions for project-profit forecasting.     

基于RBF神经网络的传感器静态误差综合校正方法

以一受环境温度和电源波动影响的压力传感器为例,说明了具体实现方法和校正效果.并与采用BP神经网络进行误差校正的方法进行了比较.实验结果表明,采用RBF神经网络可以明显提高网络收敛速度,大大减小传感器静态误差,校正效果优于BP神经网络.     

RBF神经网络在柔性触觉传感器解耦中的应用

针对柔性触觉传感器模型高度非线性、解耦难度大等问题,提出一种有效的方法来模拟柔性触觉传感器在实际应用中含噪声的情形。首先在理想条件下的传感器模型上添加不同幅度的高斯白噪声并建立其数学模型,之后通过K-均值和递归最小二乘法优化RBF神经网络,并利用优化后的RBF神经网络算法逼近受噪声干扰的传感器阻值与形变之间的高维非线性映射关系,最后基于不同的展开幅度通过行列阻值解耦出传感器三维形变信息,获得了较好的解耦精度。解耦结果表明,RBF神经网络算法具有较强的鲁棒性和抗噪声能力,能够很好地逼近含噪声的传感器高维非线性数据之间的映射关系。     

基于改进型径向基函数网络的功放非线性建模

针对功率放大器(PA)的非线性建模,提出了改进型径向基函数神经网络(RBFNN)模型。首先,在该模型的输入端加入延迟交叉项和输出反馈项,利用正交最小二乘法提取模型的权值以及隐含层的中心;然后,采用15MHz带宽的宽带码分多址（WCDMA）三载波信号对Doherty功放进行测试,其归一化均方误差(NMSE)可以达到-45dB;最后,通过逆F类功放对模型的普遍适用性进行验证。仿真结果表明,该模型能够更加真实地拟合功率放大器的特性。     

基于集成RBF神经网络的小类别手写体汉字识别系统

该文介绍了RBF神经网络的模型,讨论了RBF网络分类器的机理和特点,提出了一种集成RBF神经网络并应用于小类别手写体汉字识别系统的设计,采用了组合重心分解网格特征方法来提取汉字特征,设计了遗传进化隐层节点自生成算法用于RBF的训练。实验表明该小类别手写体汉字识别系统有很高的识别率,具有一定的实用推广价值。     

径向基神经网络的汇率预测模型研究

针对BP网络存在着收敛速度慢和局部极小的问题,提出了一种基于径向基神经网络的汇率预测研究方法。将经济变量数据归一化处理,然后送入径向基神经网络（RBF）中训练,得出相应参数,再对汇率进行预测。详细的仿真实验以及与BP神经网络的比较表明,该方法不仅运算速度较快,且预测精度明显要高于传统BP神经网络所能达到的效果。     

Weighted Radial Basis Functions for improved pattern recognition and signal processing

The paper describes an improved version of the Radial Basis Function algorithm, which integrates the advantages of Multi-Layer Perceptrons and Radial Basis Functions alone. The proposed paradigm is more general in nature, since it has the other two as particular subcases. It finds applications in several pattern recognition and classification tasks. Furthermore it can also be used as a method to map Fuzzy Inference Systems on Artificial Neural Networks.     

糖厂澄清过程中和pH值控制的RBF神经网络建模研究

澄清工段是亚硫酸法生产蔗糖的关键过程之一,由于该过程是一个复杂的物理、化学过程,具有多输入、大滞后、强非线性、时变参数等特点,因此难以建立其精确的数学模型。为此本文采用径向基函数神经网络（Radial Basis Function NeuralNetwork,RBFNN）来建立该过程的神经网络模型。模型测试结果表明：采用该方法所建的模型精度较高、泛化能力较好,为解决复杂系统的建模问题提供了一种新途径。     

径向基函数神经网络用于复方氯丙嗪的含量测定

用径向基函数神经网络分光光度法测定了复方氯丙嗪中二组分盐酸氯丙嗪和盐酸异丙嗪的含量,回收主分别为：１００．２％和９９．９６％,变异系数分别为０．７８％和１．１２％,结果稍好于普通ＢＰ神经网络,但收敛速度大大加快。     

Using Radial Basis Function Neural Networks to identify river water data parameters

The complex conditions of water dynamics create a challenge in selecting an appropriate neuron structure for artificial neural networks to simulate real river parameters. This study proposes an identification model based on Radial Basis Function (RBF) Neural Networks. We applied this identification model to river water quality parameters with different neuron node size scenarios to test network structure characters. Simulation results reveal that the RBF Neural Networks model achieves convergence through neuron iterations and the simulation error is well controlled within a small margin. The adjusting effect is closely related to structure design and the neuron updating strategy.