一种新的径向基概率神经网络模型（I）：基本理论

文中在径向基函数网络（ＲＢＦＮ）和概率神经网络（ＰＮＮ）的基础上，提出了一种径向基概率神经网络（ＲＢＰＮＮ）模型，这种网络保留了前两种网络模型的优点，即可以减少网络连接权值的训练时间，又能减少网络隐单元的数目，同时，网络用于测试的时间也较ＲＢＦＮ明显一地下降。     

一类递归RBF神经网络模型的稳定性讨论

在径向基函数神经网络（RBFNN）和递归神经网络（RNN）的基础上,提出了一类新的递归径向基函数神经网络（RRBFNN）模型,它具有两种网络模型的优点。文中对它的渐近稳定性和学习算法进行了研究,并给出相关的定理和公式。仿真结果表明了该神经网络模型在控制不稳定非线性系统（如小车－倒摆系统）具有巨大潜力。     

一类非线性神经模糊控制系统

针对离散非线性系统,将神经网络和模糊技术有机结合,模糊神经网络与自适应控制方案相结合,设计了一种模糊神经网络自适应控制系统,它由模糊对向传播（FCP）网络辨识器和径向基函数（RBF）神经网络控制器组成,仿真结果表明了该方案的有效性。     

基于模糊对向传播网络的水中目标分类识别

把对向传播（CP）网络的竞争层神经元输出函数定义为模糊隶属度函数,将模糊C-均值（FCM）算法和对向传播网络相结合,提出了一种改进的模糊对向传播（MFCP）网络。在MFCP网络中解决了模糊隶属度函数的自动生成问题。对海上实录的三类水中目标辐射噪声进行了调制解调谱（DEMON谱）的线谱和连续谱分析,并进行了对应的特征提取和神经网络分类识别实验,结果证明：MFCP网络的分类能力及对未训练目标的适应性优于CP网络和误差反向传播（BP）网络。     

一种新的径向基概率神经网络模型(Ⅰ):基本理论

文中在径向基函数网络（ＲＢＦＮ）和概率神经网络（ＰＮＮ）的基础上，提出了一种径向基概率神经网络（ＲＢＰＮＮ）模型，这种网络保留了前两种网络模型的优点，既可以减少网络连接权值的训练时间，又能减少网络隐单元的数目，同时，网络用于测试的时间也较ＲＢＦＮ明显地下降．     

基于径向基神经网络的月降水量预测模型研究

针对月降水量高度非线性的特点,以合肥20年的月降水量为时间序列,综合运用径向基函数（RBF）神经网络,建立了一种基于径向基函数的神经网络预测模型。首先对RBF神经网络进行介绍,并将该网络应用于月降水量预测,应用归一化方法对原始数据进行预处理;然后运用MATLABR2008神经网络工具箱函数建立月降水量预测模型;最后进行仿真实验与分析,将RBF神经网络与传统的BP网络训练预测结果进行比较。结果显示,RBF神经网络模型训练的迭代次数和训练时间、预测结果明显好于传统BP神经网络。     

一种新型神经网络在自由曲面重构中的应用

以层次划分和模块化为思想基础,提出了一种新型神经网络模型对自由曲面进行重构,即基于径向基函数（RBF）神经网络的混合网络模型。先后运用减聚类方法、正交最小二乘法、最大似然法对网络进行有无监督的混合训练,旨在解决大样本集的简化建模和快速训练问题,提高混合网络输出精度。实验结果表明该网络模型使得曲面的拟合精度有了明显提高。     

多层反馈神经网络的FP学习和综合算法

本文给出多层反馈神经网络的ＦＰ学习和综合算法，并讨论此类网络的性质，指出将它应用于聚类分析能给出不粒度的聚类，且具有收敛速度快（是样本个数的线性函数）、算法计算量少（是样本个数和输入、输出维数的双线性函数）、网络元件个数少、权系数简单（只取３个值）、网络容易硬件实现等优点．作为聚类器的神经网络的学习和综合问题已得到较圆满地解决.     

基于粒子群算法的RBF网络参数优化算法

针对神经网络的一些缺陷,研究神经网络基于粒子群优化的学习算法,将粒子群优化算法用于RBF神经网络的学习训练。提出了一种基于粒子群优化（PSO）算法的径向基（RBF）网络参数优化算法,首先利用减聚类算法确定网络径向基函数中心的个数,再用PSO算法优化径向基函数的中心及宽度,最后用PSO算法训练隐含层到输出层的网络权值,找到神经网络权值的最优解,以达到优化神经网络学习的目的。最后,通过一个实验与最小二乘法优化的神经网络进行了比较,验证了算法的有效性。     

基于扩展卡尔曼滤波器的RBF神经网络学习算法

径向基函数（RBF）神经网络可广泛应用于解决信号处理与模式识别问题,目前存在一些学习算法用来确定RBF中心节点和训练网络,对于确定RBF中心节点向量值和网络权重值可以看作同一系统问题,因此该文提出把扩展卡尔曼滤波器（EKF）用于多输入多输出的径向基函数（RBF）神经网络作为其学习算法,当确定神经网络中网络节点的个数后,EKF可以同时确定中心节点向量值和网络权重矩阵,为提高收敛速度提出带有次优渐消因子的扩展卡尔曼滤波器（SFEKF）用于RBF神经网络学习算法,仿真结果说明了在学习过程中应用EKF比常规RBF神经网络有更好的效果,学习速度比梯度下降法明显加快,减少了计算负担。     

基于误差模型的自适应鲁棒主成分分析

研究了改善主成分分析(PCA)算法鲁棒性的一种实现途径.通过对误差函数的建 模分析,得到一种改进的目标函数.提出一种新的在线自适应式的鲁棒PCA运算规则.该方 法基于单层线性神经网络(NN)结构,但是权值的训练算法是非线性的.从而在迭代训练中对 "劣点"样本加以适当处理来排除对运算精度和收敛性的影响.     

Robust error measure for supervised neural network learning withoutliers

Most supervised neural networks (NNs) are trained by minimizing the mean squared error (MSE) of the training set. In the presence of outliers, the resulting NN model can differ significantly from the underlying system that generates the data. Two different approaches are used to study the mechanism by which outliers affect the resulting models: influence function and maximum likelihood. The mean log squared error (MLSE) is proposed as the error criteria that can be easily adapted by most supervised learning algorithms. Simulation results indicate that the proposed method is robust against outliers.     

Recurrent neural networks and robust time series prediction

We propose a robust learning algorithm and apply it to recurrent neural networks. This algorithm is based on filtering outliers from the data and then estimating parameters from the filtered data. The filtering removes outliers from both the target function and the inputs of the neural network. The filtering is soft in that some outliers are neither completely rejected nor accepted. To show the need for robust recurrent networks, we compare the predictive ability of least squares estimated recurrent networks on synthetic data and on the Puget Power Electric Demand time series. These investigations result in a class of recurrent neural networks, NARMA(p,q), which show advantages over feedforward neural networks for time series with a moving average component. Conventional least squares methods of fitting NARMA(p,q) neural network models are shown to suffer a lack of robustness towards outliers. This sensitivity to outliers is demonstrated on both the synthetic and real data sets. Filtering the Puget Power Electric Demand time series is shown to automatically remove the outliers due to holidays. Neural networks trained on filtered data are then shown to give better predictions than neural networks trained on unfiltered time series.     

The C-loss function for pattern classification

This paper presents a new loss function for neural network classification, inspired by the recently proposed similarity measure called Correntropy. We show that this function essentially behaves like the conventional square loss for samples that are well within the decision boundary and have small errors, and L₀ or counting norm for samples that are outliers or are difficult to classify. Depending on the value of the kernel size parameter, the proposed loss function moves smoothly from convex to non-convex and becomes a close approximation to the misclassification loss (ideal 0–1 loss). We show that the discriminant function obtained by optimizing the proposed loss function in the neighborhood of the ideal 0–1 loss function to train a neural network is immune to overfitting, more robust to outliers, and has consistent and better generalization performance as compared to other commonly used loss functions, even after prolonged training. The results also show that it is a close competitor to the SVM. Since the proposed method is compatible with simple gradient based online learning, it is a practical way of improving the performance of neural network classifiers.     

Evaluation of unsupervised feature extraction neural networks for face recognition

In this paper, new appearances based on neural networks (NN) algorithms are presented for face recognition. Face recognition is subdivided into two main stages: feature extraction and classifier. The suggested NN algorithms are the unsupervised Sanger principal component neural network (Sanger PCNN) and the self-organizing feature map (SOFM), which will be applied for features extraction of the frontal view of a face image. It is of interest to compare the unsupervised network with the traditional Eigenfaces technique. This paper presents an experimental comparison of the statistical Eigenfaces method for feature extraction and the unsupervised neural networks in order to evaluate the classification accuracies as comparison criteria. The classifier is done by the multilayer perceptron (MLP) neural network. Overcoming of the problem of the finite number of training samples per person is discussed. Experimental results are implemented on the Olivetti Research Laboratory database that contains variability in expression, pose, and facial details. The results show that the proposed method SOFM/MLP neural network is more efficient and robust than the Sanger PCNN/MLP and the Eigenfaces/MLP, when used a few number of training samples per person. As a result, it would be more applicable to utilize the SOFM/MLP NN in order to accomplish a higher level of accuracy within a recognition system.     

Function approximation using fuzzy neural networks with robustlearning algorithm

The paper describes a novel application of the B-spline membership functions (BMF's) and the fuzzy neural network to the function approximation with outliers in training data. According to the robust objective function, we use gradient descent method to derive the new learning rules of the weighting values and BMF's of the fuzzy neural network for robust function approximation. In this paper, the robust learning algorithm is derived. During the learning process, the robust objective function comes into effect and the approximated function will gradually be unaffected by the erroneous training data. As a result, the robust function approximation can rapidly converge to the desired tolerable error scope. In other words, the learning iterations will decrease greatly. We realize the function approximation not only in one dimension (curves), but also in two dimension (surfaces). Several examples are simulated in order to confirm the efficiency and feasibility of the proposed approach in this paper.     

Robust adaptive neural network control for environmental boundary tracking by mobile robots

The paper addresses the problem of environmental boundary tracking for the nonholonomic mobile robot with uncertain dynamics and external disturbances. To do environmental boundary tracking, a reference velocity is designed for the nonholonomic mobile robot. In this paper, a radial basis function neural network (NN) is used to approximate a nonlinear function containing the uncertain model terms and the elements of the Hessian matrix of the environmental concentration function. Then, the NN approximator is combined with a robust control to construct a robust adaptive NN control for the mobile robot to track the desired environment boundary. It is proved that the tracking error can be guaranteed to converge to zero in the ultimate. Simulation results are presented to illustrate the stability of the robust adaptive control. Copyright © 2011 John Wiley & Sons, Ltd.     

ARRBFNs with SVR for prediction of chaotic time series with outliers

In this article, annealing robust radial basis function networks (ARRBFNs), which consist of a radial basis function network and a support vector regression (SVR), and an annealing robust learning algorithm (ARLA) are proposed for the prediction of chaotic time series with outliers. In order to overcome the initial structural problems of the proposed neural networks, the SVR is utilized to determine the number of hidden nodes, the initial parameters of the kernel, and the initial weights for the proposed ARRBFNs. Then the ARLA that can conquer the outliers is applied to tune the parameters of the kernel and the weights in the proposed ARRBFNs under the initial structure with SVR. The simulation results of Mackey-Glass time series show that the proposed approach with different SVRs can cope with outliers and give a fast learning speed. The results of the simulation are also given to demonstrate the validity of proposed method for chaotic time series with outliers.     

Robust Adaptive Control of Robots Using Neural Network: Global Stability

A desired compensation adaptive law‐based neural network (DCAL‐NN) controller is proposed for the robust position control of rigid‐link robots. The NN is used to approximate a highly nonlinear function. The controller can guarantee the global asymptotic stability of tracking errors and boundedness of NN weights. In addition, the NN weights here are tuned on‐line, with no offline learning phase required. When compared with standard adaptive robot controllers, we do not require linearity in the parameters, or lengthy and tedious preliminary analysis to determine a regression matrix. The controller can be regarded as a universal reusable controller because the same controller can be applied to any type of rigid robots without any modifications. A comparative simulation study with different robust and adaptive controllers is included.     

Preliminary study on wilcoxon learning machines.

As is well known in statistics, the resulting linear regressors by using the rank-based Wilcoxon approach to linear regression problems are usually robust against (or insensitive to) outliers. This motivates us to introduce in this paper the Wilcoxon approach to the area of machine learning. Specifically, we investigate four new learning machines, namely Wilcoxon neural network (WNN), Wilcoxon generalized radial basis function network (WGRBFN), Wilcoxon fuzzy neural network (WFNN), and kernel-based Wilcoxon regressor (KWR). These provide alternative learning machines when faced with general nonlinear learning problems. Simple weights updating rules based on gradient descent will be derived. Some numerical examples will be provided to compare the robustness against outliers for various learning machines. Simulation results show that the Wilcoxon learning machines proposed in this paper have good robustness against outliers. We firmly believe that the Wilcoxon approach will provide a promising methodology for many machine learning problems.