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基于RBF神经网络PCA变换的识别技术左军;周灵;孙亚民【期刊名称】《中山大学学报（自然科学版）》【年(卷),期】2014(000)006【摘要】The RBF neural network for classification is applied in face recognition.With two important criterion for estimating the initial width of RBF unit,the width can control the generalization ability of RBF neural network classifier.PCA method to the training sample set the projection to the face space,to reduce dimension.On the basis of the PCA transform,an optimal subspace classification makes the dis-tance between the classes to maximize the ratio of the distance using FLD method.Simulation is conduc-ted on the ORL database,and its results show that the algorithm is efficiency and effectiveness.%应用RBF神经网络作为分类器用于人脸识别。
提出了两个重要的准则来估计RBF单元的初始宽度，这个宽度可以控制RBF神经网络分类器的泛化能力。
PCA方法把训练样本集投影到特征脸空间，以减少维数。
在PCA变换的基础上，作者进一步运用FLD方法，为分类找到一个最佳的子空间，使类间距离和类内距离之比最大化。
一种混沌混合粒子群优化RBF神经网络算法刘洁;李目;周少武【摘要】为了更精确地检测出混沌背景下的微弱目标信号，提高预测效果，文中提出了一种混沌混合粒子群优化RBF神经网络(CHPSO-RBFNN)算法。
本算法主要采用了基于群体自适应变异和个体退火操作的混沌粒子群优化RBF神经网络，利用群体自适应变异以及个体退火操作优化混沌粒子群，有效地提高了粒子群算法的全局收敛性，优化了RBF神经网络的结构和参数。
把该算法用于预测混沌时间序列、检测混沌背景下微弱目标信号，实验结果表明本算法有良好的非线性预测能力，可以有效地检测出混沌背景下的微弱目标信号。
%In order to detect the weak target signal accurately in the chaos background, and improve forecast result, a novel algorithm based on RBF Neural Network ( RBFNN) with Chaotic Hybrid Particle Swarm Optimization ( CHPSO) is presented. In this algorithm, the RBF neural network is optimized by chaotic particle swarm optimization with adaptive population mutation and individual annealing operation. In order to improve the global convergence ability of PSO,the colony adaptive mutation and individual annealing operation are used to adjust and optimize PSO. Then the parameters and structures of RBFNN are optimized. This novel algorithm is applied to predict chaotic time sequence and detect weak target signal in the chaos background. Simulation results show that the algorithm has preferable nonlinear prediction ability and can detect weak target signal effectively.【期刊名称】《计算机技术与发展》【年(卷),期】2013(000)008【总页数】4页(P181-184)【关键词】混沌;自适应变异;粒子群;模拟退火;RBF神经网络;目标检测【作者】刘洁;李目;周少武【作者单位】湖南工程学院设计艺术学院，湖南湘潭 411104;湖南科技大学信息与电气工程学院，湖南湘潭 411201;湖南科技大学信息与电气工程学院，湖南湘潭 411201【正文语种】中文【中图分类】TP390 引言粒子群算法是一种基于群体的优化算法，既具有进化算法的全局寻优能力，又避免了复杂的遗传操作，其参数调整简单，训练收敛速度快;而神经网络具有很强的自适应学习能力、并行处理能力和泛化能力，能够以任意精度逼近非线性函数。
改进的双模型结构RBF神经网络及其应用李全善;张义山;曹柳林;林晓琳;崔佳【期刊名称】《化工学报》【年(卷),期】2011(62)8【摘要】提出了离线结构学习和在线权值校正相结合的双模型结构RBF神经网络,以离线学习和在线校正相结合的方式实现网络的自学习和自校正,满足了软测量仪表现场应用的要求.针对应用过程中出现预测误差过大的现象,通过对网络算法进行分析,研究影响网络预测精度的因素,在此基础上,提出了以K均值聚类法和递推下降算法相结合的RBF神经网络建模改进算法,仿真结果和实际应用证明了改进算法的有效性.%A dual model RBF (radial basis function) neural network was proposed in this paper. One is used for self-learning, which learns one time a day. The other is used for on-line correcting, which is the running model currently. Both the self-learning model and the on-line correcting model are corrected six times every day and should track the current conditions of the system quickly. At the same time, the accuracy of the two models should be compared. If the accuracy of the on-line correcting model is less than the one of the self-learning model, the latter becomes the new currently running model instead of the old one. Otherwise, the currently model is maintained. To solve the problem of neural network large prediction errors, a network algorithm analysis is given and the influence factors of the network prediction accuracy are found. At last, an improved algorithm of RBF neural network modeling is proposed, which combines K-means clustering method with the recursive descent algorithm. Simulation and practical application proved the effectiveness of the improved method.【总页数】5页(P2345-2349)【作者】李全善;张义山;曹柳林;林晓琳;崔佳【作者单位】北京化工大学信息科学与技术学院,北京,100029;北京世纪隆博科技有限责任公司,北京,100020;中国石油辽阳石化分公司,辽宁,辽阳,111003;北京化工大学信息科学与技术学院,北京,100029;北京世纪隆博科技有限责任公司,北京,100020;北京世纪隆博科技有限责任公司,北京,100020【正文语种】中文【中图分类】TP183【相关文献】1.常减压蒸馏装置双模型结构RBF神经网络建模及其应用 [J], 王文新;潘立登;李荣;徐永新;闻光辉2.BL Lac天体PKS 0735+178的中心双黑洞模型结构研究 [J], 丁世学3.应用改进RBF神经网络的室内环境舒适度评价 [J], 杨亮;王谊4.基于降水量改进的PSO—RBF神经网络水质预测模型及应用研究 [J], 王晔5.双T板屋面体系单层工业厂房模型结构的地震模拟实验 [J], 王金国;廖健因版权原因，仅展示原文概要，查看原文内容请购买。
基于免疫算法的RBF神经网络盲均衡算法白伟【摘要】本文采用免疫算法来优化RBF神经网络,得到一种更加优化、更加合理的混合算法,即免疫神经网络,并将此算法用于盲均衡器的优化设计,MATLAB仿真实验结果表明,经此算法优化后的盲均衡器,其均衡效果显著提高.【期刊名称】《山西师范大学学报（自然科学版）》【年(卷),期】2014(028)001【总页数】5页(P33-37)【关键词】盲均衡;神经网络;免疫算法;仿真【作者】白伟【作者单位】太原广播电视大学,山西太原030002【正文语种】中文【中图分类】TP389.1RBF即径向基函数神经网络(Radical Basis Function)是神经网络中一种典型的前馈式网络模型，在理论研究、实践应用等方面有着丰硕的研究成果，它具有学习速度快、计算量小、逼近能力强、分类能力好等优点，在模式分类、系统辨识等方面应用广泛[1～3].人工免疫系统是一种非常复杂、并行分布的自适应系统，有自我识别和排斥异己等独特功能.虽然神经系统和免疫系统有各自不同的功能特性，但在维持机体正常运行方面，有类似的规律与调节方式.因此，免疫原理在优化RBF网络设计方面有巨大的潜力.免疫算法正是通过模拟免疫系统而构造的一种算法，在全局搜索、并行处理等方面具有一定的优势.1 免疫算法优化的RBF网络1.1 RBF神经网络RBF网络能够逼近任意的非线性曲线，可以处理系统内难以解析的规律性，具有良好的泛化能力，并有较快的学习收敛速度[4]，因此在非线性曲线逼近、模式识别、信息处理、数据分类、故障诊断等领域受到广泛的关注.RBF网络是一种具有单隐层的三层前馈神经网络，第一层即输入层，由信号源节点组成；第二层为隐含层，隐单元数视所描述问题的需要而定，隐单元的变换函数是RBF，它是中心径向对称且衰减的非线性函数；第三层为输出层，它对输入模式的作用作出响应.由于输入到输出的映射是非线性的，而隐含层空间到输出空间的映射是线性的，从而可以大大加快学习速度并避免局部极小问题[5].RBF的网络结构如图1所示.在RBF网络结构中，令网络的训练样本对为[Yn,Xn]，假设输入数据Y=[Y1,Y2,…,YN]，其中Yi=[Yi1,Yi2,…,Yip]T∈RP,i=1,2,…，N为网络输入，网络输出X=[x1,x2,…,xl]，其中图1 RBF神经网络结构模型Fig.1 The structure model of RBF neural network(1)Wi=[wi1,wi2,…,wim]T,i=1,2,…,l为隐含层到输出层的连接权值，G=[g1,g2,…,gm]为隐含层径向基函数向量.选择高斯函数为径向基函数(2)式中，ci是第i个基函数的中心，σi为函数的宽度参数，控制基函数的径向作用范围，‖x-ci‖是x-ci的范数，一般表示x和ci之间的欧氏距离，高斯函数形状如图2所示.根据模式识别理论，通过对低维空间到高维数空间的映射处理，可以使得非线性可分的问题在高维空间中实现线性可分.在RBF网络中，输入空间到隐含层空间的变换是非线性的，而从隐含层空间到输出层空间的变换是线性的，因此，通过选择合理的隐含层单元数，将非线性可分的问题变换为线性可分的问题，然后通过一个线性单元来解决问题，这种结构使得调节参数极为简单，在很大程度上加快了神经网络的学习速度，且不存在局部极小的问题[5～7].图 2 高斯函数示意图Fig.2 Gaussian function diagram1.2 免疫算法优化RBF网络RBF神经网络结构中对隐含层参数的确定学习了免疫系统中对抗原的识别过程，通过免疫算法来调节神经网络，由于约束条件少、能遍历整个解空间、容易得到全局最优解，因此本文使用免疫算法对RBF神经网络结构中的隐含层参数进行优化[8～10].免疫算法构造的RBF神经网络，其网络参数的确定分为两个步骤，首先是要确定RBF网络结构中隐含层的非线性参数；其次利用最小二乘法确定RBF网络结构中输出层的线性权值.在免疫算法优化RBF神经网络的设计中，其抗原相当于被优化RBF神经网络的目标函数和约束条件，抗体对应于RBF神经网络隐含层的参数编码.免疫算法优化RBF神经网络的具体过程按照图3进行学习优化.免疫算法优化RBF神经网络由以下三部分组成:(1)选取隐节点中心.将RBF神经网络中的样本数据作为动态聚类的处理数据，根据免疫模糊动态聚类算法进行动态聚类，所得最佳聚类数即为RBF神经网络的输入节点数，聚类中心即为RBF中心.(2)计算宽度.当确定RBF的网络中心后，即可通过对聚类的L个中心求平均值σi，即图3 基于免疫算法的RBF网络学习方法流程图Fig.3 Flow chart of learning methods by RBF network(3)(3)优化权值.在RBF神经网络中，输出层对权值是线性的，当隐含层节点数、函数类型和网络中心等参数确定之后，利用线性优化策略，获取使误差能量函数φ(‖xi-vi‖))2最小的权值参数.2 RBF网络盲均衡RBF神经网络是一个新颖有效的前馈式神经网络，它具有全局优化、局部逼近能力强等性能，在盲均衡算法中的应用，达到了优化均衡的效果.其原理框图如图4所示.在设计RBF网络的过程中，全局最优值很难快速确定，因此首先利用免疫算法对RBF神经网络进行优化，进一步改善网络的性能，再找到合适的权值，将优化后的RBF神经网络应用到盲均衡，最终达到优化均衡的目的.代价函数为图4 RBF神经网络盲均衡原理图Fig.4 The diagram of the RBF neural network blind equalization(4)式中(5)为RBF神经网络的输出.在均衡的过程中，随着J的减小，性能将逐渐提高，当J=0时，达到最佳状态，此时确定的网络参数、网络性能均为最佳.在RBF网络中需要确定的参数有网络权值W、扩展系数σ和中心数据C，利用求偏导的方法进行递推.(6)式中，η为迭代步长.(7)(8)(9)3 仿真结果以4QAM信号为例进行模拟仿真，仿真信道采用普通最小相位信道H1(z)和典型电话信道H2(z)，其传输函数分别为H1(z)=1+0.5z-1+0.25z-2+0.125z-3(10)H2(z)=0.005+0.009z-1-0.024z-2+0.854z-3-0.218z-4+0.049z-5-0.016z-6(11)免疫算法初始种群规模选取90，概率选择Ps=0.06，交叉概率Pc=0.85，变异概率Pm=0.01.图5和图6是盲均衡算法优化的RBF神经网络在最小相位信道和电话信道中的均衡收敛曲线.从图5可以看出，当迭代5 600次时算法达到收敛，剩余稳态误差约为0.01，从而得出当4QAM信号通过最小相位信道传输，经盲均衡均衡后，达到了较好的均衡效果，并且还原出了原始信号.从图6可以看出，当迭代6 200次时算法达到收敛，剩余稳态误差约为0.01左右，由此可知，4QAM信号通过典型电话信道传输，经免疫RBF神经网络盲均衡后，达到了较为理想的均衡效果，并且还原出了原始信号.图5 最小相位信道中的收敛曲线Fig.5 Minimum phase convergence curve in the channel图6 典型电话信道中的收敛曲线Fig.6 Convergence curves of typical phone channel图7为原始信号序列4QAM经过调制后成为发送序列，图8 为调制后的发送序列经过信道传输后的接收序列，由于受到码间干扰、高斯白噪声和信道干扰等因素的影响，接收序列呈现出杂乱无章的特点，看不到原始信号，此时如果直接进行判决，将会产生较大的误码率，如果误码率增大还有可能得到与原发送序列毫无关系的序列.图9是接收后的信号序列经过本文的盲均衡算法处理后得到的序列图，对比原始发送序列可看出，已经基本恢复到4个“星座”点附近，显著提高了正确判决率，并达到了盲均衡的目的.图7 发送序列调制后星座图Fig.7 Sending sequence modulation constellationdiagram图8 均衡前接收序列星座图Fig.8 Balance before receiving sequence diagram 图9 均衡后接收序列星座图Fig.9 Balance after receiving sequence diagram4 结论RBF神经网络是人工神经网络中一种比较新颖的前馈式网络结构，具有最佳逼近能力，且无局部极小问题.相比BP算法，计算量小、结构简单，因此在盲均衡器的设计中我们引入了该算法.本文将免疫算法优化后的RBF网络应用于盲均衡中，首先采用有较强全局搜索能力的免疫算法对RBF网络进行优化，使该网络呈现出较好的性能，再对盲均衡算法进行优化处理，最后通过MATLAB实验仿真验证了算法的有效性.【相关文献】[1] Meshref H，VanLandingham H．Artificial immune systems：application to Autonomous agents[C].IEEE International Conference on Systems Man and Cybernetics．2000,(1):61～66.[2] Jiao L c， Wang L．A novel genetic algorithm based on immunity[J].IEEE Trans on Systems Man And Cybernetics-part A Systems and Humans, 2000，30(5)：552～561. [3] Timmis J，Edmonds C，Kelsey J．Assessing the performance of two immune inspired algorithms and a hybrid genetic algorithm for function optimisation[J].Congress on Evolutionary Computation, 2004,(1)：1044～1051.[4] 李振兴，周连锋，肖瑛．能量匹配准则下的前馈神经网络盲均衡[J].通信技术，2008，12(41)：115～119.[5] 王军锋，张彬，宋国乡．复数RBF神经网络自适应均衡算法研究[J].系统工程与电子技术，2003，25(7)：848～850.[6] 张立毅，刘婷，孙云山,等．基于双线性神经网络盲均衡算法的研究[J].计算机工程与应用，2007，43(27)：142～151.[7] 赵建业，余道衡．用细胞神经网络实现盲均衡的一种新方法[J].电子科学学刊，2000，22(3)：423～428.[8] 郭丽华，庞伟正，张星宇．量化在基于正交小波的盲均衡算法上的应用[J].应用科技，2003，30(11)：16～18.[9] 孙云山，李艳琴，张立毅．模糊神经网络分类器在盲均衡算法中的应用[J].计算机工程与应用，2008，44(7):171～173.[10] 陈金召，郑鹏，尤春艳．用遗传算法求解基于高阶累积量的盲均衡问题[J].现代电子技术，2003，24：64～66.。
摘要当今人类社会已经进入了大数据时代，数据大多呈现出维数高、规模大、结构复杂等特性。
在大数据的研究当中，许多数据如媒体数据、遥感数据、生物医学数据、社交网络数据、金融数据等都是高维数据，尤其是在人类生产生活中，含高维数据的无解析模型或一次候选解的评价计算成本十分巨大的昂贵多目标问题，对其仿真求解势必面临维数灾难。
因此，寻找合适的降维方法处理高维数据已是迫切需求。
神经网络是模拟人脑的结构和功能而建立起来的分布式信息处理系统，面对高维多目标优化等非线性问题，与其他降维方法相比，神经网络具有巨大的优势，这得益于神经网络具有高度非线性、结构复杂、自学习、自适应等特点。
RBF神经网络是一种新颖有效的前馈式神经网络，它具有很强的非线性映射能力，能以任意精度全局逼近一个非线性函数，而且学习速度快。
利用RBF神经网络实现对高维数据的降维预处理，不仅有充分的理论依据，而且更具优越性。
本文在对RBF神经网络算法进行优化研究的基础上，研究了基于数据驱动的特征选择RBF 神经网络降维方法，并将其应用在高维多目标优化决策空间降维预处理及Pareto 优劣性预测中。
为了提高RBF神经网络的学习效率，本文首先对RBF神经网络进行改进研究。
通过自适应调节RBF神经网络的学习率和动量因子，加快了RBF神经网络的收敛速度；同时，利用遗传算法对RBF神经网络的三个参数初始值进行优化设计，提出了一种遗传自适应RBF神经网络算法。
将改进算法分别应用于故障诊断和UCI数据集的分类实验上，验证了改进RBF神经网络算法的有效性和优越性。
针对无解析模型的高维多目标优化问题，提出了一种最大信息系数与最大相关最小冗余相结合的特征选择方法，利用遗传自适应RBF神经网络算法在高维特征空间中选取出了一个低维的特征子集，从而实现对高维特征空间的降维。
通过在UCI数据集上的分类实验，证明了该降维算法在保证较好分类精度的前提下，大大减少了计算成本。
为了降低高维多目标优化的维数灾难，将本文提出的基于最大冗余最小相关的遗传自适应RBF神经网络特征选择算法用于多目标优化中的决策空间降维预处理，进行Pareto优劣性预测并将其嵌入MOEAs算法。
基于快速密度聚类的RBF神经网络设计蒙西;乔俊飞;李文静【期刊名称】《智能系统学报》【年(卷),期】2018(013)003【摘要】针对径向基函数(radial basis function,RBF)神经网络隐含层结构难以确定的问题,提出一种基于快速密度聚类的网络结构设计算法.该算法将快速密度聚类算法良好的聚类特性用于RBF神经网络结构设计中,通过寻找密度最大的点并将其作为隐含层神经元,进而确定隐含层神经元个数和初始参数;同时,引入高斯函数的特性,保证了每个隐含层神经元的活性;最后,用一种改进的二阶算法对神经网络进行训练,提高了神经网络的收敛速度和泛化能力.利用典型非线性函数逼近和非线性动态系统辨识实验进行仿真验证,结果表明,基于快速密度聚类设计的RBF神经网络具有紧凑的网络结构、快速的学习能力和良好的泛化能力.%To design a hidden layer structure in radial-basis-function (RBF) neural networks,a novel algorithm based on fast density clustering is proposed.The algorithm searches for the point with the highest density and then uses it as the neuron of the hidden layer,thereby ascertaining the number of neurons in the hidden layer and the initial parameters.Moreover,the activity of each hidden neuron is ensured by introducing the Gaussian function.An improved second-order algorithm is used to train the designed network,increasing the training speed and improving the generalization performance.In addition,two benchmark simulations-the typical nonlinear function approximation and the nonlinear dynamic system identification experiment-are used to testthe effectiveness of the proposed RBF neural network.The results suggest that the proposed RBF neural network based on fast density clustering offers improved generalization performance,has a compact structure,and requires shorter training time.【总页数】8页(P331-338)【作者】蒙西;乔俊飞;李文静【作者单位】北京工业大学信息学部,北京 100124;北京工业大学计算智能与智能系统北京市重点实验室,北京 100124;北京工业大学信息学部,北京 100124;北京工业大学计算智能与智能系统北京市重点实验室,北京 100124;北京工业大学信息学部,北京 100124;北京工业大学计算智能与智能系统北京市重点实验室,北京100124【正文语种】中文【中图分类】TP273【相关文献】1.基于密度聚类的能耗数据采集网关设计 [J], 王平;于祥春2.基于快速密度聚类的电力通信网节点重要性评估 [J], 狄立;郑征;夏旻;胡凯3.基于图过滤的快速密度聚类双层网络推荐算法 [J], 陈晋音;吴洋洋;林翔4.基于引力核密度聚类算法的作物病害叶片区域的快速检测 [J], 刘哲;黄文准;王利平5.一种基于参考点的快速密度聚类算法 [J], 闫安;刘琪林因版权原因，仅展示原文概要，查看原文内容请购买。
城市空气质量的BP和RBF人工神经网络建模及分类评价刘杰;杨鹏;吕文生;刘阿古达木【摘要】根据MATLAB提供的人工神经网络模型,将其应用到城市空气质量评价,研究并对比分析BP和RBF两种人工神经网络的建模方法及评价结果.首先构建BP 神经网络模型,确定输入层、隐含层和输出层的神经元数,选择Sigmoid型函数作为激励函数,应用内插扩展出的训练样本对BP网络进行学习,再用训练成熟的BP网络对待评价样本进行仿真;其次构建RBF神经网络模型,确定其输入层和输出层的神经元数,选择Gauss函数作为隐含层激励函数,再用同样的训练样本进行学习和仿真;最终进行归一化论证,验证归一化预处理在空气质量评价中的必要性.结果表明:应用BP和RBF人工神经网络可以得出较好的城市空气质量分类评价结果,其中RBF神经网络模型与改进的灰色聚类法评价结果一致,具有较高的准确率,是一种快捷、有效的综合评价方法.【期刊名称】《安全与环境工程》【年(卷),期】2014(021)006【总页数】7页(P129-134,139)【关键词】城市空气质量;分类评价;BP神经网络;RBF神经网络【作者】刘杰;杨鹏;吕文生;刘阿古达木【作者单位】北京科技大学土木与环境工程学院,北京100083;北京联合大学北京市信息服务重点实验室,北京100101;北京科技大学土木与环境工程学院,北京100083;北京科技大学土木与环境工程学院,北京100083【正文语种】中文【中图分类】X823区域生态安全以人类赖以生存的环境为主体[1—2]，城市空气质量安全则是保障城市居民身体健康的首要条件。
当前城市空气质量评价是环境管理与决策的重点，2012年我国颁布的《环境空气质量标准》(GB 3095—2012)和《环境空气质量指数技术规定(试行)》(HJ 633—2012)[3]国家标准，明确规定了6类基本污染物的浓度限值及其对人体健康的影响情况。
目前对城市空气质量进行评价的方法主要为单污染指数影响评价法(AQI)，该方法以保障人体健康为出发点，主要突出单一污染物的影响因素。
基于结构最优化RBF神经网络的润滑油金属含量预测石宏;张帅;李昂【摘要】航空发动机的磨损机制十分复杂且受诸多不确定因素影响,传统预测方法难以对其磨损趋势进行有效预测.提出一种结构最优化RBF(径向基函数)网络预测模型,采用改进的粒子群算法同时优化模型嵌入维数、核函数宽度及训练误差目标值,实现了RBF网络预测模型最优结构的自动获取.将该方法用于某型航空发动机润滑油金属含量预测,并与传统自回归模型对比,结果证明了该方法的有效性及优越性.%The wear mechanism of aero-engine is complex and affected by many complicated factors,therefore traditional method is difficult to forecast the wear trend effectively. An optimal RBF (radial basis function) neural network forecasting model was put forward. An improved PSO was used to optimize the network embedded dimension, the kernel function width,and the training error,in order to obtain the optimum structure of RBF network forecasting model automatically. The method was applied to forecast the metal content in an aero-engine lubricating oil,and the forecasted result was compared with that of traditional regression model. The superiority and effectiveness of the new method was validated.【期刊名称】《润滑与密封》【年(卷),期】2012(037)011【总页数】4页(P35-38)【关键词】航空发动机;金属含量;神经网络;粒子群算法【作者】石宏;张帅;李昂【作者单位】沈阳航空航天大学航空宇航工程学部辽宁沈阳110136;沈阳航空航天大学航空宇航工程学部辽宁沈阳110136;沈阳航空航天大学航空宇航工程学部辽宁沈阳110136【正文语种】中文【中图分类】TP181;V263.5航空发动机的零部件长期工作于高温、高负荷的条件下，容易发生磨损故障，严重影响发动机的安全工作。
rbf神经网络原理RBF神经网络是一种对输入输出非线性关系的建模方法，它能够有效地提取非线性的特征。
RBF神经网络的全称是“基于径向基函数的神经网络”（radial basis function neural network），它是一种基于模式识别、计算机视觉以及语音识别等任务的有效工具。
它有多种不同的应用，包括控制系统设计、语音识别、机器学习、数据挖掘等。
RBF神经网络的基本原理是将输入空间划分到多个互不重叠的子空间，每个子空间由一个独立的RBF函数来描述。
RBF函数是一种非线性函数，它可以有效地提取输入信号的非线性特征，从而实现非线性输入输出关系的建模。
RBF神经网络的基本结构由三部分组成：输入层、隐层和输出层。
输入层首先接收输入信号，并将输入信号传递到隐层。
然后，隐层根据RBF函数的参数计算出响应信号，并将其传递到输出层。
最后，输出层将响应信号进行综合处理，并计算出最终的输出结果。
作为一种有效的建模方法，RBF神经网络在模式识别、计算机视觉、语音识别等多个领域的应用越来越广泛。
它的基本原理是通过将输入空间划分为多个互不重叠的子空间，每个子空间由一个RBF函数来描述，从而有效地提取数据中的非线性特征，并通过输入层、隐层和输出层之间的联系实现非线性输入输出关系的建模，从而解决复杂的任务。
RBF神经网络的优点在于它能够有效地提取非线性的特征和信息，它能够高效地处理大规模的输入输出数据，而且它的计算量较小，可以实现快速的计算。
此外，RBF神经网络还具有良好的学习能力和泛化能力，因此，它可以对输入输出关系进行更准确的建模，从而实现更好的效果。
尽管RBF神经网络有很多优点，但它也存在一些缺点。
首先，它受到输入数据规模的限制，在处理大规模的输入信号时，效率会很低。
其次，它的训练过程复杂，需要调整多个参数，因此，它的训练时间较长。
最后，它还存在可靠性的问题，因为它的训练决定了它的计算结果的可靠性，因此，在某些特定情况下，可能无法实现可靠的计算结果。
基于改进的粒子群径向基神经网络的目标识别袁艳;叶俊浩;苏丽娟【摘要】为了提高径向基(RBF)神经网络对航拍影像目标的识别率,提出了一种权重改进的粒子群优化(PSO)算法优化径向基神经网络,进行目标识别.首先,运用权重改进的PSO算法求解RBF神经网络隐含层中心,获取优化的径向基神经网络的权值和阈值;合理地选择待识别目标的样本图像;最后,采用训练过的径向基神经网络对航拍疑似目标图像进行识别.分别采用该算法、经正交最小二乘(OLS)算法和基本PSO算法优化的RBF神经网络对航拍影像进行疑似目标提取和识别,实验结果表明,所提算法对隐含层节点较少的RBF神经网络,识别正确率达到98％,识别效果最好.【期刊名称】《计算机应用》【年(卷),期】2018(038)0z1【总页数】4页(P6-8,23)【关键词】粒子群优化算法;径向基;神经网络;识别【作者】袁艳;叶俊浩;苏丽娟【作者单位】北京航空航天大学仪器科学与光电工程学院,北京100191;北京航空航天大学仪器科学与光电工程学院,北京100191;北京航空航天大学仪器科学与光电工程学院,北京100191【正文语种】中文【中图分类】TP1830 引言随着计算机技术、测绘技术、信息技术与无人机技术的发展,航拍影像在经济、民生、国防安全等领域的应用越来越广泛。
而航拍图像目标识别作为当前遥感图像应用领域的主要研究内容之一,具有广泛的应用价值。
目前有许多学者专注于对目标的检测和识别。
其中：模板匹配[1]利用模板的像素和特征信息对待识别图像进行搜索,方法简单、直接,但不具有尺度不变性和旋转不变性,要求背景的复杂度低,局限性强。
统计模式识别[2-3]采用不同的决策规则,对低维特征向量建立最优的判别函数,进行分类决策。
句法识别[4]以形式语言理论的概念为基础,采用基元定性的描述目标的最基本性质,但是,提取目标图像的基元特征比较困难,目前应用并不广泛。
模糊模式识别[5]用模糊集合的概念代替需要确定的子集,通过模糊集合限制进行调整模糊隶属函数的形状,进行识别分类,适用于类别分界不明的情况。
Improved RBF Neural Network for NonlinearIdentification System1Jian Guo, Jing Gong 1 ,and Jinbang Xu 21Wuhan Polytechnic University, Wuhan, ChinaEmail:guojianxh@2Huazhong University of Science and Technology /Country Department of Controlled Science and Engineering, ,Wuhan, ChinaEmail: { Jing Gong, Jinbang Xu }@Abstract—Standard particle swarm optimization (SPSO)algorithm was modified by escape strategy of the particle velocity, and an escape PSO (EPSO) was proposed to overcome the shortcomings of being trapped in local optima because of premature convergence. To enhance the performance of radial basis function (RBF) neural network, the EPSO is combined with RBF neural network to form a EPSON hybrid algorithm. Compared with the hybrid algorithm of BP neural network (PSOBP), the experiment results show that EPSON has less adjustable parameters, faster convergence speed and higher precision in the nondifferentiableII.R ADIAL B ASIS F UNCTION N ETWORKArtificial neural network (ANN)ˈwhich is composed of a large number of neuronsˈis a complex system of nonlinear dynamic and adaptive organizationˊIt has a highly nonlinear mapping capabilityˊRBF network is better than BP network in approximation capabilityˈclassification and learning velocity.RBF was first proposed by Powell[9] and introduced into neural network literature. It has been widely used in pattern recognition, parameter identification, clustering analysis, etc. [10]. The topological structure of RBF network is commonly divided into three layers. The input node of the RBF network sends signals to the hidden layerˈand the output node is usually a simple linear functionˊAs input to output is nonlinear, and the network output is linear to adjustable parameter mappingˈthe weight value of the network can be recursively calculated. The RBF network mathematica1 model is described asfunction identification.Index Terms—escape strategy, non-differentiable function identification, EPSO, radial basis functionI.I NTRODUCTIONRecently, the intelligent techniques, such as particle swarm optimization (PSO), genetic algorithm (GA) and ant colony algorithm (ACA), have been developed rapidly. They have achieved important progresses in parameter optimization, fuzzy simulation and problem-solving of acceptableness observation data, etc[1].Artificial neural network (ANN) has also been applied in parameter identification and classification [2-4]. The significant research achievements are obtained without any complicated mathematical analyses. Howevr, when BP and RBF are employed to identify parameter, some problems exist, such as local optimization, slow convergence and low precision[5]. To overcome these shortcomings, a combination of an intelligent evolutionary algorithm was used to train and optimize the neural networks structure [6]. The research results show that the hybrid algorithm can improve ANN performances in generalization ability, convergence velocity and learning ability [7-8].TVM¦h niiiicxwxf1N),()( (1) xwhere is the input value;iw is the weight value fromthe i th hidden layer to the output layer;ic is the center of the i th hidden layer node; Vis the Euclid norm;is the spread of Gaussian function; is the number of the hidden layer nodes;hnT is neuron threshold; )(M is the radial basis function, namely]2exp[)(2iiicxVM(2)In this paper, a new algorithm, called escape PSO (EPSO), is presented to modify original PSO by using a escape velocity method. In this algorithm, the EPSO combines RBF network, which has the characteristics of dynamic recursion, to form a EPSON hybrid algorithm. Then, a EPSON system is constructed, and is employed stochastic global optimization and nonlinear dynamic identification.ċ.SAVPSON I DENTIFICATION S YSTEM A.PSO Principle and Escape MethodPSO is a simple evolutionary stochastic technique[11].It finds optimal solutions through interaction ofindividuals in a population of particles. It is an effectivemethod to solve optimizing problems in complex multi-dimensional functions[12]. Based on the concept offitness degree, the evolution equations are described asfollowsISBN 978-952-5726-06-0 Proceedings of the 2009 International Workshop on Information Security and Application (IWISA 2009)Qingdao, China, November 21-22, 2009)(111k id k id k id k id x p r c v w v)(22kid k id x p r c (3)kidk id k id v x x 1 (4) where and are the velocity and position of theth dimension of the i th particle respectively at the k -iteration respectively;gdand are the global and previous best position of the d th dimensional at the k -iteration respectively; 1c and 2are constants named acceleration coefficients, whose values are assumed as 2.0; r k id v kid x d k p kid p c 1and r 2 are two independent random numbers uniformly distributed in the range of (0,1); w is an inertia weight, whose value decaying from a maximum value 0.9 towards a minimum value 0.4 in the iterative process.However, PSO is easily to get into local optimum value during solving the multi-model and highly complicated nonlinear function problems. It induces the particles in a state of premature convergence.At present, many researchers have modified PSO algorithms to alleviate the problems ˈand a great deal of research findings have been gained[13]. Based on previous research[14], the strategy of variation velocity is employed to modify PSO, and the new algorithm is called EPSO. In the proposed method, if the absolute velocity of a particle is smaller than a threshold v th (>0), increase it with a larger value. In this way, the particle has a large probability to escape from the local minimum point. A new equation of the particle velocity is defined asmax 3)1(v r v id [ (5)where [is a variation coefficient, max v is a designated maximum velocity; r 3 is a random number in the range of (0,1).B.Step of SAVPSON Hybrid AlgorithmThe identification steps of EPSON system is as follows:Step1.Construct and initialize RBF topological structure. The network node numbers of each layer are set, initial node numbers of the hidden are zero.Step2. Confirm an population size k and the maximum iteration number iter . Initialize pbest and gbest .Step3. Map the network weight, threshold and hidden node numbers to a group of particle. Initialize particles position and velocity v .i i Step4. Normalize and train the input samples.x Step5. Evaluate the individual fitness degree of each particle according to the fitness function. Update the position and velocity v .i i Step6. Distinguish the variation condition of each particle according to equation(6). If this is satisfied, the particles positions i and velocities i would be randomly reinitialized. Then, a new population is produced, and goes back to step 3.x x v Step7. Judge whether the error or the iterative number meets the algorithm terminate rule. If this is satisfied, global optimal particle is mapped to the network weight,threshold and hidden node numbers. And then, RBF optimal structure is gained according to optimal output result. If this fails, go back to step 3.Step8. Input the lithology test samples to verify whether the identification system could meet the requirements of function and generalization.C.SAVPSON Hybrid SystemThe off-line training of RBF adopts mainly the methods as follows: BP algorithm, gradient descent and GA. This would cause the trained weights and thresholds of RBF to be fixed. Once system orders or hidden-layer units are changed, the problems of weak adaptive ability and low approximate precision would be caused.To improve RBF real-time performance, EPSO is employed to train and optimize RBF structure online. Then, EPSON hybrid algorithm is formed. The system of EPSON global optimization and dynamic identification isconstructed, shown in figure 1.Figure 1. System of EPSON optimization and identificationThe EPSON system is described asT i i i i f y ],,[V X Y (8)where )( f is a nonlinear function; i Y and i are the output and input vectors of the system at the time respectively;is the random noise vectors. X i i The RBF function V )( N f is used to approximate the nonlinear relation function and can map the input/output of the network, namely)( f T i i i N i N f y ],,[,V X Y (9)In order to realize the nonlinear dynamic identification, the network output value i is trained to approximate actual value , i.e. .N y ,i i i N The fitness function of the particle is used by the reciprocal of the system performance index , namelyy y y |,i E ¦ 4 4pi i i N ii i x y yE F 12,)],([1)(1(10)p where is the particle number; 4is its parameter, ; is neural output values, and is denoted asThe programs of the EPSON and PSOBP are compiled using MATLAB7.0.The EPSON T ][i i i c w T ˈˈ 4i N y ,parameters are as follows: the size populations are 20; the maximum iterations are 1000; the acceleration constants c 1=c 2=2.0; the inertia weight w decreases linearly from a maximum value 0.9 towards a minimum value 0.4 during the evolution process; the random noise v ¦ 4pi i i i i i i i N c x w x y 1,),(),(V M (11)i is randomly distributedin the range (0,1); velocity threshold v Based on dynamic identification principle, the output value k i N of network can be used to replace system output value after k -step is identified.th =0.1;and variation coefficient y ,[=0.6. The input and output nodes are 2 and 3, respectively, and the optimal node numbers of the hidden is dynamically chosen as 12 by the EPSON algorithm. After trial calculation, the PSOBP k i y Č.N UMERICAL E XPERIMENTparameters are as follows: the size populations are 20. The structure parameter of BP neural network is 2-20-3; the learning operator evaluate To the performance of the hybrid algorithm, four famous Benchmark optimization problems are used, which are respectively described as K is 0.45; the momentum coefficient D is 0.01.The multi-model Benchmark has been identified by EPSON and PSOBP, respectively. The global minimum of four functions are shown in Tab.1. According to the average results of 100 test, the particle convergence velocity curves are shown in figures.3-4. Bohachevsky function)3(cos 3.0)(221x y x y x f S ˈ3.0)4cos(3.0 y S ˈ (12)]1 1[ˈˈ y x Form figures 3-4, it can be seen that the convergence velocity of EPSON is more rapid than that of PSOBP. Shown in figure 8, the EPSON Rastriginr function fitness values are much less than 1×10 ,) 10)2(cos 10()(122¦ Ni i i x xx f S -10 after about 200-steps,.Form the results in Table 1, it is obvious that the accuracy of EPSON is higher than of PSOBP.]12.5 12.5[ˈ i x(14)The two Benchmark functions consist of severalmaxima and minima distributed over the parameter space,as illustrated in figure 2.(a)BohachevskyFigure 3. Comparison of the algorithms for Bohachevsky function(b)Rastrigin3D graph of multi-model Benchmark functionFigure 2.Figure 4. Comparison of the algorithms for Rastrigin functionsuperior to PSOBP hybrid algorithm in stochastic global optimization. EPSON can find global optima with very high probability for every function even with small function evaluation number. Besides, for those valid runs, EPSON costs the smallest average function evaluation number. So, it is concluded that EPSON is much effective and reliable for complex numerical optimization.č.C ONCLUSIONSPSO has been modified by escape method of particle velocity in this paper, and EPSO algorithm is proposed. The new algorithm can overcome the shortcomings of conventional PSO: premature convergence and local optimization.EPSO can solve the RBF problems of the weak adaptive ability, and can improve the RBF performance of the online global optimization. Therefore, EPSO was combined with the RBF to form a EPSON hybrid algorithm. Compared with PSOBP, EPSON has less adjustable parameters, faster convergence velocity and global optimization in the numerical experiment.Based on EPSON algorithm, an system of global optimization was established. The results show that the EPSON system can successfully escape local minimal point, with a successful rate being larger than 90%.A CKNOWLEDGMENTThis paper is partially supported by The National Natural Science Foundation of China (No:E50774076).R EFERENCES[1]J. Kennedy, R.C. Eberhart, and Y. H. Shi, Swarmintelligence, San Francisco: Morgan Kaufman Publishers, 2001.[2]R.Y. Cui, B.R.Hong, and X.F.Piao, “Study on hidden layerevaluation for feed-forward neural networks,” Journal of China University of Mining & Technology, vol. 33, pp.668-672, June 2004.[3]X.W. Lu and Z.D. Jin. “Method of lithologic recognizingbased on feed forward neural network,” Oil and Gas Geology, vol. 20, pp. 82-84, January 1999.[4]Y. J. Ma, and R. S. Zhou, “The lithology discriminationwith neural network method,” Computing Techniques for Geophysical and Geochemical Exploration, vol. 26, pp.220-223, March 2004.[5] D. E. Rumelhart, G. E. Hinton, and Williams R J,“Learning representations by back propagating errors,”Nature, vol. 323, pp. 533 -536, November 1986.[6]R. S. Sexton, and R. E. Dorsey, “Reliable classificationusing neural networks: a genetic algorithm and back-propagation comparison,” Decision Support Systems, vol.30, pp. 11-22, January 2000.[7]H. B. Gao, L. Gao, and C. Zhou, et al. ,“Particle swarmoptimization based algorithm for neural network learning,”Acta Electronica Sinica, vol. 32, pp. 1572-1574 , September 2004.[8]M.Vittorio, “Genetic evolution of the topology and weightdistribution of networks,” IEEE Trans. on Neural Networks, vol. 5, pp. 39-53, January 1994.[9]J. D. Powell, “Radial basis function approximations topolynomials,” In: Proceedings of the Numerical analysis.Dundee, 1987, pp. 223-241.[10]D. T. Pham, and X. Liu, “Dynamic system identifycationusing partially recurrent neural networks,” Journal of Systems Engineering, vol. 2, pp. 90-97, February 1992. [11]J. Kennedy, and R. C. Eberhart, “Particle swarmoptimization,” In: Proceedings of IEEE International Conference on Neural Network. Piscataway: IEEE Press, 1995, pp. 1942-1948.[12]T. L. Vincent, and W. J. Grantham, “Optimality inParametric Systems,” Wiley: New York, 1981.[13]Y. H. Shi, and R.C. Eberhart, “Experimental study ofparticle swarm optimization,” In: Proceedings of SCI Conference. Piscataway: IEEE Press, 1999, pp. 1945-1950.[14]D. Y. Zhu, and H. Shi, Principle and application ofartificial neural network, Beijing: Science Press, 2006.。
