Stable weighted multiple model adaptive control- discretetime stochastic plant
深度优先局部聚合哈希
Vol.48，No.6Jun. 202 1第48卷第6期2 0 2 1年6月湖南大学学报)自然科学版)Journal of Hunan University (Natural Sciences )文章编号：1674-2974(2021 )06-0058-09 DOI ： 10.16339/ki.hdxbzkb.2021.06.009深度优先局艺B 聚合哈希龙显忠g,程成李云12(1.南京邮电大学计算机学院，江苏南京210023；2.江苏省大数据安全与智能处理重点实验室，江苏南京210023)摘 要：已有的深度监督哈希方法不能有效地利用提取到的卷积特征，同时，也忽视了数据对之间相似性信息分布对于哈希网络的作用，最终导致学到的哈希编码之间的区分性不足.为了解决该问题，提出了一种新颖的深度监督哈希方法，称之为深度优先局部聚合哈希(DeepPriority Local Aggregated Hashing , DPLAH ). DPLAH 将局部聚合描述子向量嵌入到哈希网络 中，提高网络对同类数据的表达能力，并且通过在数据对之间施加不同权重，从而减少相似性 信息分布倾斜对哈希网络的影响.利用Pytorch 深度框架进行DPLAH 实验，使用NetVLAD 层 对Resnet18网络模型输出的卷积特征进行聚合，将聚合得到的特征进行哈希编码学习.在CI-FAR-10和NUS-WIDE 数据集上的图像检索实验表明，与使用手工特征和卷积神经网络特征的非深度哈希学习算法的最好结果相比,DPLAH 的平均准确率均值要高出11%，同时，DPLAH 的平均准确率均值比非对称深度监督哈希方法高出2%.关键词：深度哈希学习；卷积神经网络；图像检索；局部聚合描述子向量中图分类号:TP391.4文献标志码:ADeep Priority Local Aggregated HashingLONG Xianzhong 1，覮，CHENG Cheng1,2,LI Yun 1,2(1. School of Computer Science & Technology ,Nanjing University of Posts and Telecommunications ,Nanjing 210023, China ;2. Key Laboratory of Jiangsu Big Data Security and Intelligent Processing ,Nanjing 210023, China )Abstract : The existing deep supervised hashing methods cannot effectively utilize the extracted convolution fea tures, but also ignore the role of the similarity information distribution between data pairs on the hash network, result ing in insufficient discrimination between the learned hash codes. In order to solve this problem, a novel deep super vised hashing method called deep priority locally aggregated hashing (DPLAH) is proposed in this paper, which em beds the vector of locally aggregated descriptors (VLAD) into the hash network, so as to improve the ability of the hashnetwork to express the similar data, and reduce the impact of similarity distribution skew on the hash network by im posing different weights on the data pairs. DPLAH experiment is carried out by using the Pytorch deep framework. Theconvolution features of the Resnet18 network model output are aggregated by using the NetVLAD layer, and the hashcoding is learned by using the aggregated features. The image retrieval experiments on the CIFAR-10 and NUS - WIDE datasets show that the mean average precision (MAP) of DPLAH is11 percentage points higher than that of* 收稿日期：2020-04-26基金项目：国家自然科学基金资助项目(61906098,61772284),National Natural Science Foundation of China(61906098, 61772284);国家重 点研发计划项目(2018YFB 1003702) , National Key Research and Development Program of China (2018YFB1003702)作者简介:龙显忠(1985—),男，河南信阳人，南京邮电大学讲师，工学博士，硕士生导师覮 通信联系人,E-mail ： *************.cn第6期龙显忠等:深度优先局部聚合哈希59non-deep hash learning algorithms using manual features and convolution neural network features,and the MAP of DPLAH is2percentage points higher than that of asymmetric deep supervised hashing method.Key words:deep Hash learning;convolutional neural network;image retrieval;vector of locally aggregated de-scriptors(VLAD)随着信息检索技术的不断发展和完善，如今人们可以利用互联网轻易获取感兴趣的数据内容，然而，信息技术的发展同时导致了数据规模的迅猛增长.面对海量的数据以及超大规模的数据集，利用最近邻搜索［1(Nearest Neighbor Search,NN)的检索技术已经无法获得理想的检索效果与可接受的检索时间.因此,近年来,近似最近邻搜索［2(Approximate Nearest Neighbor Search,ANN)变得越来越流行,它通过搜索可能相似的几个数据而不再局限于返回最相似的数据，在牺牲可接受范围的精度下提高了检索效率.作为一种广泛使用的ANN搜索技术，哈希方法(Hashing)［3］将数据转换为紧凑的二进制编码(哈希编码)表示，同时保证相似的数据对生成相似的二进制编码.利用哈希编码来表示原始数据，显著减少了数据的存储和查询开销，从而可以应对大规模数据中的检索问题.因此，哈希方法吸引了越来越多学者的关注.当前哈希方法主要分为两类：数据独立的哈希方法和数据依赖的哈希方法，这两类哈希方法的区别在于哈希函数是否需要训练数据来定义.局部敏感哈希(Locality Sensitive Hashing,LSH)［4］作为数据独立的哈希代表，它利用独立于训练数据的随机投影作为哈希函数•相反，数据依赖哈希的哈希函数需要通过训练数据学习出来，因此，数据依赖的哈希也被称为哈希学习，数据依赖的哈希通常具有更好的性能.近年来，哈希方法的研究主要侧重于哈希学习方面.根据哈希学习过程中是否使用标签，哈希学习方法可以进一步分为：监督哈希学习和无监督哈希学习.典型的无监督哈希学习包括:谱哈希［5(Spectral Hashing,SH);迭代量化哈希［6］(Iterative Quantization, ITQ);离散图哈希［7(Discrete Graph Hashing,DGH);有序嵌入哈希［8］(Ordinal Embedding Hashing,OEH)等.无监督哈希学习方法仅使用无标签的数据来学习哈希函数，将输入的数据映射为哈希编码的形式.相反,监督哈希学习方法通过利用监督信息来学习哈希函数,由于利用了带有标签的数据,监督哈希方法往往比无监督哈希方法具有更好的准确性，本文的研究主要针对监督哈希学习方法.传统的监督哈希方法包括：核监督哈希［9］(Supervised Hashing with Kernels,KSH);潜在因子哈希［10］(Latent Factor Hashing,LFH);快速监督哈希［11］(Fast Supervised Hashing,FastH);监督离散哈希［1(Super-vised Discrete Hashing,SDH)等.随着深度学习技术的发展［13］,利用神经网络提取的特征已经逐渐替代手工特征，推动了深度监督哈希的进步.具有代表性的深度监督哈希方法包括:卷积神经网络哈希［1(Convolutional Neural Networks Hashing,CNNH);深度语义排序哈希［15］(Deep Semantic Ranking Based Hash-ing,DSRH);深度成对监督哈希［16］(Deep Pairwise-Supervised Hashing,DPSH);深度监督离散哈希［17］(Deep Supervised Discrete Hashing,DSDH);深度优先哈希［18］(Deep Priority Hashing,DPH)等.通过将特征学习和哈希编码学习(或哈希函数学习)集成到一个端到端网络中，深度监督哈希方法可以显著优于非深度监督哈希方法.到目前为止，大多数现有的深度哈希方法都采用对称策略来学习查询数据和数据集的哈希编码以及深度哈希函数.相反，非对称深度监督哈希［19］(Asymmetric Deep Supervised Hashing,ADSH)以非对称的方式处理查询数据和整个数据库数据，解决了对称方式中训练开销较大的问题，仅仅通过查询数据就可以对神经网络进行训练来学习哈希函数，整个数据库的哈希编码可以通过优化直接得到.本文的模型同样利用了ADSH的非对称训练策略.然而，现有的非对称深度监督哈希方法并没有考虑到数据之间的相似性分布对于哈希网络的影响,可能导致结果是:容易在汉明空间中保持相似关系的数据对,往往会被训练得越来越好;相反,那些难以在汉明空间中保持相似关系的数据对，往往在训练后得到的提升并不显著.同时大部分现有的深度监督哈希方法在哈希网络中没有充分有效利用提60湖南大学学报(自然科学版)2021年取到的卷积特征.本文提出了一种新的深度监督哈希方法，称为深度优先局部聚合哈希(Deep Priority Local Aggregated Hashing,DPLAH).DPLAH的贡献主要有三个方面:1)DPLAH采用非对称的方式处理查询数据和数据库数据，同时DPLAH网络会优先学习查询数据和数据库数据之间困难的数据对，从而减轻相似性分布倾斜对哈希网络的影响.2)DPLAH设计了全新的深度哈希网络，具体来说,DPLAH将局部聚合表示融入到哈希网络中，提高了哈希网络对同类数据的表达能力.同时考虑到数据的局部聚合表示对于分类任务的有效性.3)在两个大型数据集上的实验结果表明，DPLAH在实际应用中性能优越.1相关工作本节分别对哈希学习［3］、NetVLAD［20］和Focal Loss［21］进行介绍.DPLAH分别利用NetVLAD和Focal Loss提高哈希网络对同类数据的表达能力及减轻数据之间相似性分布倾斜对于哈希网络的影响. 1.1哈希学习哈希学习［3］的任务是学习查询数据和数据库数据的哈希编码表示，同时要满足原始数据之间的近邻关系与数据哈希编码之间的近邻关系相一致的条件.具体来说，利用机器学习方法将所有数据映射成{0,1}r形式的二进制编码(r表示哈希编码长度)，在原空间中不相似的数据点将被映射成不相似)即汉明距离较大)的两个二进制编码，而原空间中相似的两个数据点将被映射成相似(即汉明距离较小)的两个二进制编码.为了便于计算，大部分哈希方法学习{-1,1}r形式的哈希编码，这是因为{-1,1}r形式的哈希编码对之间的内积等于哈希编码的长度减去汉明距离的两倍，同时{-1,1}r形式的哈希编码可以容易转化为{0,1}r形式的二进制编码.图1是哈希学习的示意图.经过特征提取后的高维向量被用来表示原始图像，哈希函数h将每张图像映射成8bits的哈希编码,使原来相似的数据对(图中老虎1和老虎2)之间的哈希编码汉明距离尽可能小，原来不相似的数据对(图中大象和老虎1)之间的哈希编码汉明距离尽可能大.h（大象）=10001010h（老虎1）=01100001h（老虎2）=01100101相似度尽可能小相似度尽可能大图1哈希学习示意图Fig.1Hashing learning diagram1.2NetVLADNetVLAD的提出是用于解决端到端的场景识别问题［20(场景识别被当作一个实例检索任务),它将传统的局部聚合描述子向量(Vector of Locally Aggregated Descriptors,VLAD［22］)结构嵌入到CNN网络中，得到了一个新的VLAD层.可以容易地将NetVLAD 使用在任意CNN结构中，利用反向传播算法进行优化，它能够有效地提高对同类别图像的表达能力，并提高分类的性能.NetVLAD的编码步骤为：利用卷积神经网络提取图像的卷积特征;利用NetVLAD层对卷积特征进行聚合操作.图2为NetVLAD层的示意图.在特征提取阶段,NetVLAD会在最后一个卷积层上裁剪卷积特征，并将其视为密集的描述符提取器，最后一个卷积层的输出是H伊W伊D映射，可以将其视为在H伊W空间位置提取的一组D维特征,该方法在实例检索和纹理识别任务［23別中都表现出了很好的效果.NetVLAD layer（KxD）x lVLADvectorh------->图2NetVLAD层示意图⑷Fig.2NetVLAD layer diagram1201NetVLAD在特征聚合阶段，利用一个新的池化层对裁剪的CNN特征进行聚合，这个新的池化层被称为NetVLAD层.NetVLAD的聚合操作公式如下：NV((，k)二移a(x)(血⑺-C((j))(1)i=1式中:血(j)和C)(j)分别表示第i个特征的第j维和第k个聚类中心的第j维；恣&)表示特征您与第k个视觉单词之间的权.NetVLAD特征聚合的输入为：NetVLAD裁剪得到的N个D维的卷积特征,K个聚第6期龙显忠等:深度优先局部聚合哈希61类中心.VLAD的特征分配方式是硬分配,即每个特征只和对应的最近邻聚类中心相关联，这种分配方式会造成较大的量化误差，并且，这种分配方式嵌入到卷积神经网络中无法进行反向传播更新参数.因此,NetVLAD采用软分配的方式进行特征分配，软分配对应的公式如下：-琢II Xi-C*II 2=—e(2)-琢II X-Ck，II2k，如果琢寅+肄,那么对于最接近的聚类中心,龟&)的值为1,其他为0.aS)可以进一步重写为：w j X i+b ka(x i)=—e-)3)w J'X i+b kk，式中:W k=2琢C k；b k=-琢||C k||2.最终的NetVLAD的聚合表示可以写为：N w；x+b kv(j，k)=移—----(x(j)-Ck(j))(4)i=1w j.X i+b k移ek，1.3Focal Loss对于目标检测方法,一般可以分为两种类型:单阶段目标检测和两阶段目标检测,通常情况下，两阶段的目标检测效果要优于单阶段的目标检测.Lin等人［21］揭示了前景和背景的极度不平衡导致了单阶段目标检测的效果无法令人满意,具体而言，容易被分类的背景虽然对应的损失很低，但由于图像中背景的比重很大,对于损失依旧有很大的贡献,从而导致收敛到不够好的一个结果.Lin等人［21］提出了Focal Loss应对这一问题，图3是对应的示意图.使用交叉爛作为目标检测中的分类损失，对于易分类的样本,它的损失虽然很低，但数据的不平衡导致大量易分类的损失之和压倒了难分类的样本损失,最终难分类的样本不能在神经网络中得到有效的训练.Focal Loss的本质是一种加权思想，权重可根据分类正确的概率p得到，利用酌可以对该权重的强度进行调整.针对非对称深度哈希方法，希望难以在汉明空间中保持相似关系的数据对优先训练,具体来说,对于DPLAH的整体训练损失，通过施加权重的方式,相对提高难以在汉明空间中保持相似关系的数据对之间的训练损失.然而深度哈希学习并不是一个分类任务,因此无法像Focal Loss一样根据分类正确的概率设计权重，哈希学习的目的是学到保相似性的哈希编码，本文最终利用数据对哈希编码的相似度作为权重的设计依据具体的权重形式将在模型部分详细介绍.正确分类的概率图3Focal Loss示意图［21】Fig.3Focal Loss diagram12112深度优先局部聚合哈希2.1基本定义DPLAH模型采用非对称的网络设计.Q={0},=1表示n张查询图像,X={X i}m1表示数据库有m张图像；查询图像和数据库图像的标签分别用Z={Z i},=1和Y ={川1表示；i=［Z i1，…,zj1,i=1，…,n;c表示类另数；如果查询图像0属于类别j,j=1，…,c;那么z”=1,否则=0.利用标签信息，可以构造图像对的相似性矩阵S沂{-1,1}"伊”,s”=1表示查询图像q,和数据库中的图像X j语义相似,S j=-1表示查询图像和数据库中的图像X j语义不相似.深度哈希方法的目标是学习查询图像和数据库中图像的哈希编码，查询图像的哈希编码用U沂{-1,1}""，表示,数据库中图像的哈希编码用B沂{-1,1}m伊r表示，其中r表示哈希编码的长度.对于DPLAH模型,它在特征提取部分采用预训练好的Resnet18网络［25］.图4为DPLAH网络的结构示意图，利用NetVLAD层聚合Resnet18网络提取到的卷积特征，哈希编码通过VLAD编码得到，由于VLAD编码在分类任务中被广泛使用，于是本文将NetVLAD层的输出作为分类任务的输入，利用图像的标签信息监督NetVLAD层对卷积特征的利用.事实上，任何一种CNN模型都能实现图像特征提取的功能，所以对于选用哪种网络进行特征学习并不是本文的重点.62湖南大学学报(自然科学版)2021年conv1图4DPLAH结构Fig.4DPLAH structure图像标签soft-max1,0,1,1,0□1,0,0,0,11,1,0,1,0---------*----------VLADVLAD core)c)l・>:i>数据库图像的哈希编码2.2DPLAH模型的目标函数为了学习可以保留查询图像与数据库图像之间相似性的哈希编码，一种常见的方法是利用相似性的监督信息S e{-1,1}n伊"、生成的哈希编码长度r,以及查询图像的哈希编码仏和数据库中图像的哈希编码b三者之间的关系[9],即最小化相似性的监督信息与哈希编码对内积之间的L损失.考虑到相似性分布的倾斜问题，本文通过施加权重来调节查询图像和数据库图像之间的损失，其公式可以表示为：min J=移移(1-w)(u T b j-rs)专,B i=1j=1s.t.U沂{-1,1}n伊r,B沂{-1,1}m伊r,W沂R n伊m(5)受FocalLoss启发,希望深度哈希网络优先训练相似性不容易保留图像对，然而Focal Loss利用图像的分类结果对损失进行调整，因此，需要重新进行设计，由于哈希学习的目的是为了保留图像在汉明空间中的相似性关系，本文利用哈希编码的余弦相似度来设计权重,其表达式为：1+。
预测控制
g11=poly2tfd(12.8,[16.7,1],0,1);%POL Y2TFD Create transfer functions in 3 row representation将通用的传递函数模型转换为MPC传递函数模型% g = poly2tfd(num,den,delt,delay)% POL Y2TFD creates a MPC toolbox transfer function in following format:%g为对象MPC传递函数模型% g = [ b0 b1 b2 ... ] (numerator coefficients)% | a0 a1 a2 ... | (denominator coefficients)% [ delt delay 0 ... ] (only first 2 elements used in this row)%% Inputs:% num : Coefficients of the transfer function numerator.% den : Coefficients of the transfer function denominator.% delt : Sampling time. Can be 0 (for continuous-time system)% or > 0 (for discrete-time system). Default is 0.% delay : Pure time delay (dead time). Can be >= 0.% If omitted or empty, set to zero.% For discrete-time systems, enter as PERIODS of pure% delay (an integer). Otherwise enter in time units.g21=poly2tfd(6.6,[10.9,1],0,7);g12=poly2tfd(-18.9,[21.0,1],0,3);g22=poly2tfd(-19.4,[14.4,1],0,3);delt=3;ny=2;tfinal=90;model=tfd2step(tfinal,delt,ny,g11,g21,g12,g22)%对于这个例子,N=90/3=30figure(3)plot(model)%TFD2STEP Determines the step response model of a transfer function model.传递函数模型转换成阶跃响应模型% plant = tfd2step(tfinal, delt2, nout, g1)% plant = tfd2step(tfinal, delt2, nout, g1, ..., g25)% The transfer function model can be continuous or discrete.%% Inputs:% tfinal: truncation time for step response model.% delt2: desired sampling interval for step response model.% nout: output stability indicator. For stable systems, this% argument is set equal to number of outputs, ny.% For systems with one or more integrating outputs,% this argument is a column vector of length ny with% nout(i)=0 indicating an integrating output and% nout(i)=1 indicating a stable output.% g1, g2,...: SISO transfer function described above ordered% to be read in columnwise (by input). The number of % transfer functions required is ny*nu. (nu=number of % inputs). Limited to ny*nu <= 25.%% Output:% plant: step response coefficient matrix in MPC step format. plant=model;P=6;M=2;ywt=[];uwt=[1 1];Kmpc=mpccon(model,ywt,uwt,M,P)%ywt,uwt : 相当于Q,R%MPCCON Calculate MPC controller gains for unconstrained case.% Kmpc = mpccon(model,ywt,uwt,M,P)% MPCCON uses a step-response model of the process.% Inputs:% model : Step response coefficient matrix of model.% ywt,uwt : matrices of constant or time-varying weights.相当于Q,R% If the trajectory is too short, they are kept constant% for the remaining time steps.% M : number of input moves and blocking specification. If% M contains only one element it is the input horizon% length. If M contains more than one element% then each element specifies blocking intervals.% P : output (prediction) horizon length. P = Inf indicates the% infinite horizon.%% Output:% Kmpc : Controller gain matrixtend=30;r=[0 1];[y,u]=mpcsim(plant,model,Kmpc,tend,r);%plan为开环对象的实际阶跃响应模型%model为辨识得到的开环阶跃响应模型%Kmpc相当于D阵%Tend仿真的结束时间.%R输出设定值和参考轨迹%r=[r1(1) r2(1)...rny(1);r1(2) r2(2)....rny(2);... r1(N) r2(N) ...rny(N)]%y:控制输出%u:控制变量%ym:模型预测输出%MPCSIM Simulation of the unconstrained Model Predictive Controller.% [y,u,ym] = mpcsim(plant, model, Kmpc, tend, r,usat, tfilter,% dplant, dmodel, dstep)% REQUIRED INPUTS:% plant(model): the step response coefficient matrix of the plant (model)% generated by the function tfd2step% Kmpc: the constant control law matrix computed by the function mpccon% (closed-loop simulations).For open-loop simulation, controller=[].% tend: final time of simulation.% r: for the closed-loop simulation, it is a constant or time-varying% reference trajectory. For the open-loop simulation, it is the% trajectory of the manipulated variable u.% OPTIONAL INPUTS:% usat: the matrix of manipulated variable constraints.It is a constant% or time-varying trajectory of the lower limits (Ulow), upper limits% (Uhigh) and rate of change limits (DelU) on the manipulated % variables. Default=[].% tfilter: time constants for noise filter and unmeasured disturbance lags.% Default is no filtering and step disturbance.% dplant: step response coefficient matrix for the disturbance effect on the% plant output generated by the function tfd2step. If distplant is% provided, dstep is also required. Default = [].% dmodel: step response coefficient matrix for the measured disturbance% effect on the model output generated by the function tfd2step.% If distmodel is provided, dstep is also required. Default=[].% dstep: matrix of disturbances to the plant. For output step disturbances% it is a constant or time-varying trajectory of disturbance values% For disturbances through step response models,it is a constant or% time-varying trajectory of disturbance model inputs.Default=[].% OUTPUT ARGUMENTS: y (system response), u (manipulated variable) and% ym (model response)plotall(y,u,delt)figure(2)plot(y,'*')南通大学毕业设计（论文）任务书题目锅炉液位系统的DMC-PID控制学生姓名朱养兵学院电气工程学院专业自动化班级自051学号0512012010起讫日期2009.2 －2009.6指导教师李俊红职称讲师发任务书日期2009 年2 月18 日●MATLAB 软件●JX-300X组态监控软件●浙大中控DCS●上海齐鑫公司过程控制对象●PC机。
统计学专业名词中英对照
统计学专业名词中英对照Lane某y我大学毕业已经多年，这些年来，越发感到外刊的重要性。
读懂外刊要有不错的英语功底，同时，还需要掌握一定的专业词汇。
掌握足够的专业词汇，在国内外期刊的阅读和写作中会游刃有余。
abcia横坐标abencerate缺勤率Abolutedeviation绝对离差Abolutenumber绝对数abolutevalue绝对值Abolutereidual绝对残差accidenterror偶然误差Accelerationarray加速度立体阵Accelerationinanarbitrarydirection任意方向上的加速度Accelerationnormal法向加速度Accelerationpacedimenion加速度空间的维数Accelerationtangential切向加速度Accelerationvector加速度向量Acceptablehypothei可接受假设Accumulation累积Accumulatedfrequency累积频数Accuracy准确度Actualfrequency实际频数Adaptiveetimator自适应估计量Addition相加Additiontheorem加法定理AdditiveNoie加性噪声Additivity可加性Adjutedrate调整率Adjutedvalue校正值Admiibleerror容许误差Aggregation聚集性Alphafactoringα因子法Alternativehypothei备择假设Amonggroup组间Amount总量ANOVA（analyiofvariance）方差分析ANOVAModel方差分析模型ANOVAtableandeta分组计算方差分析Arcing弧/弧旋Arcinetranformation反正弦变换Area区域图Areaunderthecurve曲线面积AREG评估从一个时间点到下一个时间点回归相关时的误差ARIMA季节和非季节性单变量模型的极大似然估计Arithmeticgridpaper算术格纸Arithmeticmean算术平均数Arithmeticweightedmean加权算术均数Arrheniurelation艾恩尼斯关系Aeingfit拟合的评估Aociativelaw结合律Aumedmean假定均数Aymmetricditribution非对称分布Autocorrelationofreidual残差的自相关Average平均数Averageconfidenceintervallength平均置信区间长度averagedeviation平均差Averagegrowthrate平均增长率BBarchart/graph条形图Baeperiod基期Baye'theoremBaye定理Bell-hapedcurve钟形曲线Bernoulliditribution伯努力分布Bet-trimetimator最好切尾估计量Bia偏性Biometric生物统计学Binarylogiticregreion二元逻辑斯蒂回归Binomialditribution二项分布Biquare双平方BivariateCorrelate二变量相关Bivariatenormalditribution双变量正态分布Bivariatenormalpopulation双变量正态总体Biweightinterval双权区间BiweightM-etimator双权M估计量Block区组/配伍组Canonicalcorrelation典型相关Caption纵标目Cartogram统计图Caefatalityrate病死率Cae-controltudy病例对照研究Categoricalvariable分类变量Catenary悬链线Cauchyditribution柯西分布Caue-and-effectrelationhip因果关系Cell单元Cenoring终检cenu普查Centerofymmetry对称中心Centeringandcaling中心化和定标Centraltendency集中趋势Centralvalue中心值CHAID-χ2AutomaticInteractionDetector卡方自动交互检测Chance 机遇Chanceerror随机误差Chancevariable随机变量Characteriticequation特征方程Characteriticroot特征根Characteriticvector特征向量Chebhevcriterionoffit拟合的切比雪夫准则Chernoffface切尔诺夫脸谱图Claifiedvariable分类变量Cluteranalyi聚类分析Cluterampling 整群抽样Code代码Codeddata编码数据Coding编码Coefficientofmultiplecorrelation多重相关系数Coefficientofpartialcorrelation偏相关系数Columneffect列效应Columnfactor列因素Conditionale某pectation条件期望Conditionallikelihood条件似然Conditionalprobability条件概率Conditionallylinear依条件线性Confidenceinterval置信区间Confidencelevel可信水平，置信水平Confidencelimit置信限Confidencelowerlimit置信下限Confidenceupperlimit置信上限ConfirmatoryFactorAnalyi验证性因子分析Confirmatoryreearch 证实性实验研究Confoundingfactor混杂因素Conjoint联合分析Conitency相合性Conitencycheck一致性检验Conitentaymptoticallynormaletimate相合渐近正态估计Conitentetimate相合估计Contituentratio构成比，结构相对数Contrainednonlinearregreion受约束非线性回归Contraint约束Contaminatedditribution污染分布ContaminatedGauian污染高斯分布Contaminatednormalditribution污染正态分布Contamination污染Contaminationmodel污染模型Continuity连续性Contingencytable 列联表Contour边界线Contributionrate贡献率Control对照质量控制图Controlgroup对照组Controllede某periment对照实验Conventionaldepth常规深度Convolution卷积Coordinate坐标Correctedfactor校正因子Correctedmean校正均值Correctioncoefficient校正系数Correctionforcontinuity连续性校正Correctionforgrouping归组校正Correctionnumber校正数Correctionvalue校正值Correctne正确性Equalun-clanumber相等次级组含量Equallylikely等可能Equationoflinearregreion线性回归方程Equivariance同变性Error误差/错误Errorofetimate估计误差Errorofreplication重复误差ErrortypeI 第一类错误ErrortypeII第二类错误Etimand被估量Etimatederrormeanquare估计误差均方Etimatederrorumofquare估计误差平方和Euclideanditance欧式距离Event事件E某ceptionaldatapoint异常数据点E某pectationplane期望平面E某pectationurface期望曲面E某pectedvalue期望值E某periment 实验E某perimentdeign实验设计E某perimenterror实验误差E某perimentalgroup实验组E某perimentalampling试验抽样E某perimentalunit试验单位E某plainedvariance（已说明方差）E某planatoryvariable说明变量E某ploratorydataanalyi探索性数据分析E某ploreSummarize探索-摘要E某ponentialcurve指数曲线E某ponentialgrowth指数式增长E某SMOOTH指数平滑方法E某tendedfit扩充拟合E某traparameter附加参数E某trapolation外推法E某tremeobervation末端观测值E某treme极端值/极值FFditributionF分布FtetF检验Factor因素/因子Factoranalyi因子分析FactorAnalyi因子分析Factorcore因子得分Factorial阶乘Factorialdeign析因试验设计Falenegative假阴性Falenegativeerror假阴性错误Familyofditribution分布族Familyofetimator估计量族Fanning扇面Fatalityrate病死率Fieldinvetigation现场调查Fieldurvey现场调查Finitepopulation有限总体Finite-ample有限样本Firtderivative一阶导数Forecat预测Fourfoldtable四格表Fourth四分点Fractionblow左侧比率Fractionalerror相对误差Frequency频率Freguencyditribution频数分布Frequencypolygon频数多边图Frontierpoint界限点Functionrelationhip泛函关系GGammaditribution伽玛分布Gauincrement高斯增量Gauianditribution高斯分布/正态分布Gau-Newtonincrement高斯-牛顿增量Generalcenu全面普查Generalizedleatquare综合最小平方法GENLOG(Generalizedlinermodel)广义线性模型Geometricmean几何平均数Gini'meandifference基尼均差GLM(Generallinermodel)通用线性模型Goodneoffit拟和优度/配合度Gradientofdeterminant行列式的梯度Graeco-Latinquare希腊拉丁方Grandmean总均值Groerror重大错误Half-life半衰期HampelM-etimator汉佩尔M估计量Happentance偶然事件Harmonicmean调和均数Hazardfunction风险均数Hazardrate风险率Heading标目Heavy-tailedditribution重尾分布Heianarray海森立体阵Heterogeneity不同质Heterogeneityofvariance方差不齐Hierarchicalclaification组内分组Hierarchicalcluteringmethod系统聚类法High-leveragepoint高杠杆率点High-Low低区域图HigherOrderInteractionEffect，高阶交互作用HILOGLINEAR多维列联表的层次对数线性模型Hinge折叶点Hitogram直方图Hitoricalcohorttudy历史性队列研究Hole空洞HOMALS多重响应分析Homogeneityofvariance方差齐性Homogeneitytet齐性检验HuberM-etimator休伯M估计量Hyperbola双曲线Hypotheiteting假设检验Hypotheticalunivere假设总体IImagefactoring多元回归法Impoibleevent不可能事件Independence独立性Independentvariable自变量Inde某指标/指数Indirecttandardization间接标准化法Individual个体Inferenceband推断带Infinitepopulation无限总体Infinitelygreat无穷大Infinitelymall无穷小Influencecurve影响曲线Informationcapacity信息容量Initialcondition初始条件Initialetimate初始估计值Initiallevel最初水平Interaction交互作用Interactionterm交互作用项Intercept截距Interpolation内插法Interquartilerange四分位距Intervaletimation区间估计Intervalofequalprobability等概率区间Intriniccurvature固有曲率Invariance不变性Inverematri某逆矩阵Invereprobability逆概率Invereinetranformation反正弦变换Iteration迭代JJacobiandeterminant雅可比行列式Jointditributionfunction分布函数Jointprobability联合概率Jointprobabilityditribution联合概率分布KK-MeanCluter逐步聚类分析Kmeanmethod逐步聚类法Kaplan-Meier 评估事件的时间长度Kaplan-MerierchartKaplan-Merier图Kendall'rankcorrelationKendall等级相关Kinetic动力学Kolmogorov-Smirnovetet柯尔莫哥洛夫-斯米尔诺夫检验KrukalandWallitetKrukal及Walli检验/多样本的秩和检验/H检验Kurtoi峰度LLackoffit失拟Ladderofpower幂阶梯Lag滞后Largeample大样本Largeampletet大样本检验Latinquare拉丁方Latinquaredeign拉丁方设计Leakage泄漏Leatfavorableconfiguration最不利构形Leatfavorableditribution最不利分布Leatignificantdifference最小显著差法Leatquaremethod最小二乘法LeatSquaredCriterion，最小二乘方准则Leat-abolute-reidualetimate最小绝对残差估计Leat-abolute-reidualfit最小绝对残差拟合Leat-abolute-reidualline最小绝对残差线Legend图例L-etimatorL估计量L-etimatoroflocation位置L估计量L-etimatorofcale尺度L估计量Level水平LeveageCorrection，杠杆率校正Lifee某pectance预期期望寿命Lifetable寿命表Lifetablemethod生命表法Light-tailedditribution轻尾分布Likelihoodfunction似然函数Likelihoodratio似然比linegraph 线图Linearcorrelation直线相关Linearequation线性方程Linearprogramming线性规划Linearregreion直线回归LinearRegreion 线性回归Lineartrend线性趋势Loading载荷Locationandcaleequivariance位置尺度同变性Locationequivariance位置同变性Locationinvariance位置不变性Locationcalefamily位置尺度族Logranktet时序检验Logarithmiccurve 对数曲线Logarithmicnormalditribution对数正态分布Logarithmiccale对数尺度Logarithmictranformation对数变换Logiccheck逻辑检查Logiticditribution逻辑斯特分布LogittranformationLogit转换Outlier极端值OVERALS多组变量的非线性正规相关Overhoot迭代过度PPaireddeign配对设计Pairedample配对样本Pairwielope成对斜率Parabola抛物线Paralleltet平行试验Parameter参数Parametrictatitic参数统计Parametrictet参数检验Pareto直条构成线图（佩尔托图）Partialcorrelation偏相关Partialregreion偏回归Partialorting偏排序Partialreidual偏残差Pattern模式PCA（主成分分析）Pearoncurve皮尔逊曲线Peeling退层Percentbargraph百分条形图Percentage百分比Percentile百分位数Percentilecurve百分位曲线Periodicity周期性Permutation排列P-etimatorP估计量Piegraph 构成图饼图Pitmanetimator皮特曼估计量Pivot枢轴量Planar平坦Planaraumption平面的假设PLANCARDS生成试验的计划卡PLS（偏最小二乘法）Pointetimation点估计Poionditribution泊松分布Polihing 平滑Polledtandarddeviation合并标准差Polledvariance合并方差Polygon多边图Polynomial多项式Polynomialcurve多项式曲线Population总体Probabilitydenity概率密度Productmoment乘积矩/协方差Profiletrace截面迹图Proportion比/构成比Proportionallocationintratifiedrandomampling按比例分层随机抽样Proportionate成比例Proportionateub-clanumber成比例次级组含量Propectivetudy前瞻性调查Pro某imitie亲近性PeudoFtet近似F检验Peudomodel近似模型Peudoigma伪标准差Purpoiveampling有目的抽样QQuantile-quantileplot分位数-分位数图/Q-Q图Quantitativeanalyi定量分析Quartile四分位数QuickCluter快速聚类RRadi某ort基数排序Randomallocation随机化分组Randomblockdeign随机区组设计Randomevent随机事件Randomization随机化Range极差/全距Rankcorrelation等级相关Reciprocaltranformation倒数变换Recording记录Redecendingetimator回降估计量Reducingdimenion降维Re-e某preion重新表达Referenceet标准组Regionofacceptance接受域Regreioncoefficient回归系数Regreionumofquare回归平方和Rejectionpoint拒绝点Relativediperion相对离散度Relativenumber 相对数Reliability可靠性Reparametrization重新设置参数Replication重复ReportSummarie 报告摘要Reidualumofquare剩余平方和reidualvariance(剩余方差)Reitance耐抗性Reitantline耐抗线Reitanttechnique耐抗技术R-etimatoroflocation位置R估计量R-etimatorofcale尺度R估计量Retropectivetudy回顾性调查Ridgetrace岭迹RiditanalyiRidit分析Rotation旋转Rounding舍入Row行Roweffect行效应Rowfactor行因素R某CtableR某C表SSample样本Sampleregreioncoefficient样本回归系数Sampleize样本量Sampletandarddeviation样本标准差Samplingerror抽样误差SAS(Statiticalanalyiytem)SAS统计软件包Scale尺度/量表Scatterdiagram散点图Schematicplot示意图/简图Scoretet计分检验Screening筛检SEASON季节分析Secondderivative二阶导数SEM(Structuralequationmodeling)结构化方程模型Semi-logarithmicgraph半对数图Semi-logarithmicpaper半对数格纸Senitivitycurve敏感度曲线Sequentialanalyi贯序分析Sequence普通序列图Sequentialdataet顺序数据集Sequentialdeign贯序设计Sequentialmethod贯序法Sequentialtet贯序检验法Serialtet系列试验Short-cutmethod简捷法SigmoidcurveS形曲线Signfunction正负号函数Signtet符号检验Signedrank符号秩SignificantLevel显著水平Significancetet显著性检验Significantfigure有效数字Simplecluterampling简单整群抽样Simplecorrelation简单相关Simplerandomampling简单随机抽样Simpleregreion简单回归impletable简单表Sineetimator正弦估计量Single-valuedetimate单值估计Singularmatri某奇异矩阵Skewedditribution偏斜分布Skewne 偏度Slahditribution斜线分布Slope斜率Spearmanrankcorrelation斯皮尔曼等级相关Specificfactor特殊因子Specificfactorvariance特殊因子方差Spectra频谱Sphericalditribution球型正态分布Spread展布SPSS(Statiticalpackagefortheocialcience)Spurioucorrelation 假性相关Squareroottranformation平方根变换Stabilizingvariance稳定方差Standarddeviation标准差Standarderror标准误Standarderrorofdifference差别的标准误Standarderrorofetimate 标准估计误差Standarderrorofrate率的标准误Standardnormalditribution标准正态分布Standardization标准化Startingvalue起始值Statitic统计量Statiticalcontrol统计控制Statiticalgraph统计图Statiticalinference统计推断SPSS统计软件包Statiticaltable统计表Steepetdecent最速下降法Stemandleafdiplay茎叶图Stepfactor步长因子Stepwieregreion逐步回归Storage存Strata层（复数）Stratifiedampling分层抽样Stratifiedampling分层抽样Strength 强度Stringency严密性Structuralrelationhip结构关系Studentizedreidual学生化残差/t化残差Sub-clanumber次级组含量Subdividing分割Sufficienttatitic充分统计量Sumofproduct积和Sumofquare离差平方和Sumofquareaboutregreion回归平方和Sumofquarebetweengroup组间平方和Sumofquareofpartialregreion偏回归平方和Sureevent必然事件Survey调查。
基于本福特定律和机器学习的网络入侵检测研究
基于贝叶斯优化算法（BOA）的 XGBoost 检测模型对第一层中的异常窗口进一
步分析以实现精确到单条流的细粒度检测。与单独的检测模型对比，
Filter-XGBoost 充 分 结 合 了 两 种 检 测 模 型 各 自 的 优 点 。 与 其 他 算 法 对 比 ，
1.4 本文组织结构 .............................................................................................. 11
1.5 本章小结 ...................................................................................................... 11
摘 要
互联网的普及在造福人们的同时，也带来了巨大的安全隐患。不断升级的
网络入侵行为可能会导致个人隐私泄露、系统瘫痪等一系列重大安全问题。相
关入侵检测技术已日臻完善，诸如机器学习等新技术的使用解决了传统入侵检
测中存在的方法僵化、自适应性差等问题，同时也在一定程度上提高了检测率。
但机器学习算法自身的局限性使得现有解决方案仍面临两大主要问题：一是如
accurate to a single flow. Compared with the separate detection models,
Filter-XGBoost combines the advantages of both detection models. Compared with
other algorithms, Filter-XGBoost performs well in detection rate and false alarm rate.
最优加权几何平均组合预测在短期电价预测中的应用
成熟的理论，因此，电价预测方法可以适当借鉴电 力负荷预测的思想， 由于电价预测的影响因素较多， 规律性弱，所以准确地电价预测要比负荷预测困难 的多。 目前，国内外的众多研究者在这一领域做了大 量的工作，短期电价预测是研究的重点。 要的预 性 测方法有趋势外推法、时间序列法、人工神经网络 法、灰色预测等，其中有的方法考虑了电价变化的 时间特征， 有的方法在详细分析电价特性的基础上，
Abstr act A veracious short-term electricity price forecasting can help a market effective bidding decisions.1t inf uences the participant' s profits directly.To improve the accuracy of electricity l price forecasting, the paper presents a optimal weighted geometric combined forecasting method, wh ich m ak es u se of th e in form atio n of second-index f atness, adaptive neuron-fuzzy inference system l and grey model of modification comprehensively. The sum of squared errors of combined forecasting method is less than the ones of unitary forecasting method.So the forecasting accuracy is improved. A calculation instance proves the feasibility of this method finally. Key words: short-term electricity price forecasting; second-index f atness; adaptive neuron-fuzzy l inference system; grey model of modification; optimal weighted geometric combined forecasting method
基于交互式多模型无迹卡尔曼滤波的锂电池荷电状态估计
基于交互式多模型无迹卡尔曼滤波的锂电池荷电状态估计谭霁宬;颜学龙【摘要】为了提高传统卡尔曼滤波法估计锂电池荷电状态(SOC)的精度,在锂电池二阶RC等效电路模型基础上,根据隐马尔科夫模型(HMM)理论并采用遗传算法优化构造出了不同参数状态的电池模型.结合交互式多模型(IMM)算法与无迹卡尔曼滤波(UKF)算法进行SOC估计,提出了一种基于HMM的IMM-UKF算法估计锂电池SOC的方法.锂电池在线SOC估计实验表明,该方法比较其他估计方法有着更高的估计精度,平均绝对误差仅为1％.【期刊名称】《科学技术与工程》【年(卷),期】2019(019)012【总页数】6页(P170-175)【关键词】荷电状态;隐马尔科夫模型;交互式多模型;无迹卡尔曼滤波;遗传算法【作者】谭霁宬;颜学龙【作者单位】桂林电子科技大学电子工程与自动化学院,桂林541004;桂林电子科技大学电子工程与自动化学院,桂林541004【正文语种】中文【中图分类】TM912当前，全球汽车工业正面临着金融危机和能源环境问题的双重挑战，它促进了传统汽车向电动汽车的转变，实现汽车能源动力系统的电气化在中国乃至国际社会都达成了广泛共识[1]。
锂电池因能量密度大、循环寿命长、高工作电压、环保无污染等优良性能成为电动汽车的理想电动源首选[2]。
电池荷电状态(state of charge，SOC)描述电池剩余电量的数量，是电池使用过程中的重要参数。
电池SOC的估计对电动汽车动力锂电池放电和均衡管理上起到关键的作用，直接影响到电池的使用寿命与安全。
电动汽车动力锂电池性能是高度非线性的，很难准确估计其SOC。
估计SOC的方法有很多，但是都具有一定的缺陷，例如，放电实验法适用于所有电池，但是需要大量时间且电池工作时需要被迫中断；安时积分法存在初值问题，若电流测量不准确，长时间容易形成累积误差；开路电压法则需要电池长时间静置；神经网络方法的训练需要大量的参考数据；卡尔曼滤波算法适合于各种电池，但是非常依赖电池等效模型[3]。
金融工程常用术语(中英对照)
金融工程常用术语中英对照AABS Asset-Backed Security 资产支持证券ABS CDO 由ABS所派生出的份额产品Accrual Swap 计息互换Accrued Interest 应计利息Actuaries 保险精算师Adaptive Mesh Model 自适应网格模型Adjusted Present Value 调整现值法Adverse Selection 逆向选择After-tax Interest Rate 税后利润Agency Costs 代理费用American Option 美式期权Amortization 分期偿付Amortization Schedule 分期偿付时间表Amortizing Swap 分期偿还互换Analytic Result 解析结果APR Annual Percentage Rate 年度百分率Annualized Capital Cost 按年折算的资本成本Arbitrage 套利Arbitrageur 套利者Asian Option 亚式期权Ask Price 卖盘价Asset 资产Asset Allocation 资产分配Asset-or-Nothing Call Option 资产或空手看涨期权Asset-or-Nothing Put Option 资产或空手看跌期权Asset Swap 资产互换As-You-Like-It Option 任选期权At-the-Money Option 平值期权Average Price Call Option 平均价格看涨期权Average Price Put Option 平均价格看跌期权Average Strike Option 平均执行价格期权BBackdating 倒填日期Back Testing 回顾测试Backwards Induction 倒推归纳Barrier Option 障碍期权Base Correlation 基础相关系数Basel Committee 巴塞尔委员会Basis 基差Basis Point 基点Basis Risk 基差风险Basis Swap 基差互换Basket Credit Default Swap 篮筐式信用违约互换Basket Option 篮筐式期权Bear Spread 熊市差价Bermudan Option 百慕大式期权Before-tax Interest Rate 税前利率Beta 贝塔Bid-Ask Spread 买入卖出差价Bid Price 买入价Bilateral Clearing 双边结算Binary Credit Default Swap 两点式信用违约互换Binary Option 两值期权Binomial Model 二项式模型Binomial Option Pricing Model 二项期权定价模型Binomial Tree 二叉树Bivariate Normal Distribution 二元正态分布Black’s Approximation 布莱克近似Black’s Model 布莱克模型Black-Scholes-Merton Model 布莱克-斯科尔斯-莫顿模型Bond Option 债券期权Bond Yield 债券收益率Book Value 账面价值Bootstrap Method 票息剥离方法Boston Option 波士顿期权BOT Build-Operate-Transfer 建设-经营-转让Box Spread 合式差价Break-even point 盈亏平衡点Break Forward 断点远期Brownian Motion 布朗运动Bull Spread 牛市差价Butterfly Spread 蝶式差价CCalendar Spread 日历差价Calibration 校正Callable Bond 可赎回债券Call Option 看涨期权Cancelable Swap 可取消互换Cap 上限Cap Rate 上限利率CAPM Capital Asset Pricing Model 资本资产定价模型Caplet 上限单元Capital gain 资本收藏Capital less 资本损失Capital Market 资本市场Capital Market Line 资本市场线Caps 赔付限额Case-Shiller Index 凯斯-席勒指数Cash budget 现金预算Cash cycle time 现金周转时间Cash Dividend 现金股利Cash Flow Mapping 现金流映射Cash-or-Nothing Call Option 现金或空手看涨期权Cash-or-Nothing Put Option 现金或空手看跌期权Cash Settlement 现金交割或现金清算CCP Central Clearing Party 中央结算对手CDD Cooling Degree Days 降温天数CDO Collateralized Debt Obligation 债务抵押债券CDS Credit Default Swap 信用违约互换CEBO Credit Event Binary Option 信用事件两点式期权Central Clearing 中心结算Central Clearing Party 中央结算对手Central Counterparty 中央交易对手CEV Model Constant Elasticity of Variance Model 常方差弹性模型Cheapest-to-Deliver Bond 最便宜可交割债券Cholesky Decomposition 乔里斯基分解Chooser Option 选择人期权Class of Options 期权分类Clean Price of Bond 债券除息价格Clearing House 结算中心Clearing Margin 结算保证金Cliquet Option 棘轮期权CMO Collateralized Mortgage Obligation 见房产抵押债券CMS Constant Maturity Swap 固定期限国债互换Collar 双限Collateral 抵押品Collateralization 抵押品策略Collateralized Debt Obligation 债务抵押债券Collateralized Mortgage Obligation 房产抵押债券Combination 组合Commercial Banks 商业银行Commercial Loan Rate 商业贷款利率Commodity Futures Trading Commission 商品期货交易管理委员会Commodity Swap 商品互换Compound Interest 复利Compounding 复利计息Compounding Frequency 复利利率Compound Correlation 复合相关系数Compound Option 复合期权Confidence interval 置信区间Continuous Probability Distribution 连续概率分布Confirmation 交易确认书Consumption Asset 消费资产Contango 期货溢价Continuous Compounding 连续复利Control Variate Technique 控制变量技术Convenience Yield 便利收益率Conversion Factor 转换因子Convertible Bond 可转换债券Convexity 曲率Convexity Adjustment 曲率调整Cornish-Fisher Expansion 科尼什-费雪展开Copayments 赔付比例Corporation 公司Correlation 相关性Cost of Capital 资本成本Cost of Carry 持有成本Controller 审计官Counterparty 交易对手Coupon 券息Coupon bond 付息债券Covariance 协方差Covarance Matrix 协方差矩阵Covered Call 备保看涨期权Crash phobia 暴跌恐惧症Credit Contagion 信用蔓延Credit Default Swap 信用违约互换Credit Derivative 信用衍生产品Credit Event 信用事件Credit Event Binary Option 信用事件两点式期权Credit Index 信用指数Credit Rating 信用等级Credit Ratings Transition Matrix 信用评级转移矩阵Credit Risk 信用风险Credit Spread Option 信用差价期权CSA Credit Support Annex 信用支持附约CVA Credit Value Adjustment 信用价值调节量Credit Value at Risk 信用风险价值度Cross Hedging 交叉对冲Currency Swap 货币互换Current yield 本期收益率DDay Count 计天方式Day Trade 即日交易DCF Discounted Cash flow Model 现金流折现模型DDM Dividend Discount Model 股利贴现模型DVA Debt Value Adjustment 债务价值调节量Decision Tree 决策树Deductible 免赔额Default Risk 违约风险Defined-benefit Pension Plan 规定受益型养老金计划Defined-contribution Pension Plan 规定缴费型养老金计划Delivery Price 交割价格Delta Hedging Delta对冲Delta-Neutral Portfolio Delta 中性交易组合Derivative 衍生产品Deterministic Variable 确定性变量Diagonal Spread 对角差价Differential Swap 交叉货币度量互换Diffusion Process 扩散过程Dirty Price of Bond 带息价格Discount Bond 折扣债券Discount Instrument 折扣产品Discounted Cash Flow Analysis 贴现现金流分析Discounted Dividend Model 股利贴现模型Diversifiable Risk 可分散风险Diversification 分散化Diversification Principle 分散化原则Diversifying 分散投资Discount Rate 贴现率Dividend 股息Dividend Yield 股息收益率Dodd-Frank Act 多德-弗兰克法案Dollar Duration 绝对额久期DOOM Option DOOM期权Down-and-In Option 下降-敲入期权Down-and-Out Option 下降-敲出期权Downgrade Trigger 降级触发Drift Rate 漂移变化率Duration 久期Duration Matching 久期匹配Dynamic Hedging 动态对冲EEAR/ EFF Effective Annual Rate 实际年利率Early Exercise 提前行使EBIT Earnings Before Interest and Tax 息税前利润Effective Federal Funds Rate 有效联邦基金利率Efficient Portfolio 有效投资组合Efficient Portfolio Frontier 有效投资组合边界Electronic Trading 电子交易Embedded Option 内含期权EMH Efficient Markets Hypothesis 有效市场假说Empirical Research 实证研究Employee Stock Option 雇员股票期权Equilibrium Model 均衡模型Equity Swap 股权互换Equity Tranche 股权份额Equivalent Annual Interest Rate 等价年利率Eurocurrency 欧洲货币Eurodollar 欧洲美元Eurodollar Futures Contract 欧洲美元期货合约Eurodollar Interest Rate 欧洲美元利率Euro LIBOR 欧元同业拆借利率European Option 欧式期权Exchange Option 互换期权Exchange Rate 汇率Exclusions 免赔条款Ex-dividend Date 除息日Exercise Limit 行使限额Exercise Multiple 行使倍数Exercise Price 执行价格Exotic Option 特种期权Expectations Theory 预期理论Expected Shortfall 预期亏损Expected Rate of Return 预期回报率Expected Value of a Variable 变量的期望值Expiration Date 到期日Explicit Finite Difference Method 显式有限差分方法Exponentially Weighted Moving Average Model 指数加权移动平均模型Exponential Weighting 指数加权Exposure 风险敞口Extendable Bond 可展期债券Extendable Swap 可延期互换External Financing 外部投资FFace Value 面值Factor 因子Factor Analysis 因子分析Federal Funds Rate 联邦基金利率FEI Financial Executives Institute 财务执行官组织Finance 金融学Financial Futures 金融期货Financial Guarantees 财务担保Financial Intermediary 金融媒介Financial System 金融系统Finite Difference Method 有限差分法Fixed-Income Instrument 固定收益证券Flat Volatility 单一波动率Flex Option 灵活期权Flexi Cap Flexi上限Floor 下限Floor-Ceiling Agreement 下限上限协议Floor let 下限单元Floor Rate 下限利率Flow of funds 资金流Foreign Currency Option 外汇期权Forward Contract 远期合约Forward Exchange Rate 远期汇率Forward Interest Rate 远期利率Forward Price 远期价格Forward Rate 远期率FRA Forward Rate Agreement 远期利率合约Forward Risk-Neutral World 远期风险中性世界Forward Start Option 远期开始期权Forward Swap 远期互换Fundamental Value 基本价值Futures Commission Merchants 期货佣金经纪人Futures Contract 期货合约Futures Option 期货期权Futures-Style Option 期货式期权FV Final Value 终值GGrowth annuity 增长年金GAP Management 制品管理Gap Option 缺口期权Gaussian Copula Model 高斯Copula 模型Gaussian Quadrature 高斯求积公式Generalize Wiener Process 广义维纳过程Geometric Average 几何平均Geometric Brownian Motion 几何布朗运动Girsanov’s Theorem 哥萨诺夫定理Guaranty Fund 担保基金HHaircut 折扣Hazard Rate 风险率Hedge 对冲Hedge Funds 对冲基金Hedger 对冲者Hedge Ratio 对冲比率Hedgers 套期保值者Historical Simulation 历史模拟Historical Volatility 历史波动率Holiday Calendar 假期日历Human Capital 人力资本IImmediate Annuity 即时年金Implicit Finite Difference Method 隐式有限差分Implied Correlation 隐含相关系数Implied Distribution 隐含分布Implied Dividend 隐含股利Implied Tree 隐含树形Implied Volatility 隐含波动率Inception Profit 起始盈利Index Amortizing Swap 指数递减互换Index Arbitrage 指数套利Index Futures 指数期货Index-linked Bonds 指数化债券Index Option 指数期权Index Principal Swap 指数本金互换Initial Margin 初始保证金Instantaneous Forward Rate 瞬时远期利率Insuring 保险Intangible Assets 无形资产Interest-rate Arbitrage 利率套利Interest Rate Cap 利率上限Interest Rate Collar 利率双限Interest Rate Derivative 利率衍生产品Interest Rate Floor 利率下限Interest Rate Swap 利率互换Internal Financing 内部融资International Swap and Derivatives Association 国际互换和衍生产品协会In-the-Money Option 实值期权Intrinsic Value 内涵价值Inverted Market 反向市场Investment Asset 投资资产Investment Banks 投资银行ISDA International Swap and Derivatives Association 国际互换和衍生产品协会IRR Internal Rate of Return 内部收益率JJump-Diffusion Model 跳跃扩散模型Jump Process 跳跃过程LLaw of One Price 一价原则Liability 负债LIBID London Inter Bank Bid Rate 伦敦同业借款利率LIBOR London Inter Bank Offered Rate 伦敦同业拆出利率LIBOR Curve LIBOR曲线LIBOR-in-Arrears Swap LIBOR后置互换Life Annuity 人寿年金Limited Liability 有限责任Limit Move 涨跌停版变动Limit Order 限价指令Liquidity 流动性Liquidity Preference Theory 流动性偏好理论Liquidity Premium 流动性溢价Liquidity Risk 流动性风险Locals 自营经纪人Lognormal Distribution 对数正态分布Long Hedge 多头对冲Long Position 多头Look back option 回望期权Low Discrepancy Sequence 低偏差序列MMaintenance Margin 维持保证金Margin 保证金Margin Call 保证金催付Market Capitalization Rate 市场资本化利率MSU Market-Leveraged Stock Unit 市场股票凭据Market Maker 做市商Market Model 市场模型Market Portfolio 市场投资组合Market Price of Risk 风险市场价格Market Segmentation Theory 市场分隔理论Market-weighted Stock Indexes 市场加权股票指数Marking to Market 按市场定价Markov Process 马尔科夫过程Martingale 鞅Maturity 期限Maturity Date 到期日Maximum Likelihood Method 极大似然方法Mean Reversion 均值回归Measure 测度Merger 合并Mezzanine Tranche 中层份额Minimum Variance 最小方差组合Modified Duration 修正久期Money Market 货币市场Money Market Account 货币市场帐户Monte Carlo Simulation 蒙特卡罗模拟Moral Hazard 道德风险Mortgage-Backed Security 房产抵押贷款证券Mutual Fund 共同基金NNaked Position 裸露期权Netting 净额结算Net Present Value 净现值Net Worth 净资产No-Arbitrage Assumption 无套利假设No-Arbitrage Interest Rate Model 无套利假设Nominal Future Value 名义终值Nominal Interest Rate 名义利率Nominal Prices 名义价格Nondiversifiable Risk 不可分割风险Nonstationary Model 非平稳模型Non Systemic Risk 非系统风险Normal Backwardation 正常现货溢价NPV Net Present Value 净现值Normal Distribution 正态分布Normal Market 正常市场Notional Principal 面值（本金）Numeraire 计价单位Numerical Procedure 数值方法OOCC Option Clearing Corporation 期权结算中心Offer Price 卖出价格Open Interest 未平仓合约Open Outcry 公开喊价Opportunity Cost of Capital 资金的机会成本Optimal Combination of risky assets 风险资产的最优组合Option 期权Option-Adjusted Spread 期权调整差价Option Class 期权种类Ordinary Annuity 普通年金Out-of-the-Money Option 虚值期权Overnight Indexed Swap 隔夜指数互换Over-the-Counter Market 场外交易市场PPackage 组合期权Par bonds 等价债券Par Value 面值Par Yield 面值收益Parallel Shift 平行移动Parisian Option 巴黎期权Partnership 合伙制Path-Dependent Option 路径依赖型期权Payoff 收益Pay off Diagram 收益图Percent-of-sales method 销售收入百分比法Permanent Income 持久收入Perpetuity 永续年金Perpetual Derivatives 永续衍生品Portfolio Immunization 组合免疫Portfolio Insurance 证券组合保险Portfolio selection 投资组合选择Portfolio theory 投资组合理论Position Limit 头寸限额Premium 期权付费Premium Bond 溢价债券Present Value 现值Principal-agent Problem 委托人-代理人问题Prepayment Function 提前偿付函数Principal 本金Principal Components Analysis 主因子分析Principal Protected Notes 保本型证券Probability Distributions 概念分布Program Trading 程序交易Protective Put 保护看跌期权Pull-to-Par 收敛于面值现象Purchasing-power Parity 购买力评价Pure Discount Bonds 纯贴现债券Put-Call Parity 看跌-看涨期权平价关系式Put Option 看跌期权Puttable Bond 可提前退还债券Puttable Swap 可赎回互换President 总裁PMT Payment（Returns the periodic payment for an annuity）年金PPP Public-Private Partnership 政府和社会资本合作PV Present Value 现值QQuansi-Random Sequences 伪随机序列RRate of Return on capital 资本收益率Rainbow Option 彩虹期权Range-Forward Contract 远期范围合约Ratchet Cap 执行价格调整上限Real Future Value 实际终值Real Interest Rate 实际利率Real Option 实物期权Real Prices 实际价格Rebalancing 再平衡Recovery Rate 回收率Reference Entity 参考实体Reinvestment Rate 再投资利率Residual Claim 剩余索取权Repo 再回购Repo Rate 再回购利率Reset Date 重置日（定息日）RSU Restricted Stock Unit 受限股票单位Reversion Level 回归水平Risk Aversion 风险厌恶Risk-adjusted discount rate 风险调整贴现率Risk Exposure 风险暴露Rights Issue 优先权证Risk-Free Rate 无风险利率Risk Management 风险管理Risk Management Process 风险管理过程Risk-Neutral Valuation 风险中性定价Risk-Neutral World 风险中性世界Roll Back 倒推ROS Ratio of income as percentage of sales 销售利润率ROA Return On Assets 资产收益率ROE Rate of Return on Common Stockholders’ Equity 净资产收益率SScalper 投机者Scenario Analysis 情形分析Securitization 证券化Security Market Line 证券市场线Sensitivity Analysis 敏感性分析Self-financing Investment Strategy 自筹资金投资策略Settlement Price 结算价格Share Repurchase 股票回购Short Hedge 空头头寸对冲Short Position 空头头寸Short Rate 短期利率Short Selling 卖空交易Short-Term Risk-Free Rate 短期无风险利率Shout Option 喊价期权Simple Interest 单利Sole Proprietorship 独资企业Specialist 专家Speculator 投机者Spot futures price parity relation 现货期货价格平价关系。
基于自适应多尺度注意力机制的CNN-GRU矿用电动机健康状态评估
基于自适应多尺度注意力机制的CNN−GRU矿用电动机健康状态评估谭东贵， 袁逸萍， 樊盼盼（新疆大学 智能制造现代产业学院，新疆 乌鲁木齐 830017）摘要：利用多传感器信息融合技术进行电动机健康状态评估时，矿用电动机监测数据中存在异常值和缺失值，而卷积神经网络和循环神经网络等深度学习模型在数据质量下降严重的情况下难以有效提取数据特征和更新网络权重，导致梯度消失或爆炸等问题。
针对上述问题，提出了一种基于自适应多尺度注意力机制的CNN−GRU （CNN−GRU−AMSA ）模型，用于评估矿用电动机健康状态。
首先，对传感器采集的电动机运行数据进行填补、剔除和标准化处理，并以环境温度变化作为依据对矿用电动机运行数据进行工况划分。
然后，根据马氏距离计算出电动机电流、电动机三相绕组温度、电动机前端轴承温度和电动机后端轴承温度等健康评估指标的健康指数（HI ），采用Savitzky–Golay 滤波器对指标HI 进行降噪、平滑、归一化处理，并结合主成分分析法计算的不同指标对矿用电动机的贡献度，对指标HI 进行加权融合得到矿用电动机HI 。
最后，将矿用电动机HI 输入CNN−GRU−AMSA 模型中，该模型通过动态调整注意力权重，实现对不同尺度特征的信息融合，从而准确输出电动机健康状态评估结果。
实验结果表明，与其他常见的深度学习模型CNN ，CNN−GRU ，CNN−LSTM ，CNN−LSTM−Attention 相比，CNN−GRU−AMSA 模型在均方根误差、平均绝对误差、准确率、Macro F1及Micro F1等评价指标上更优，且预测残差的波动范围更小，稳定性更优。
关键词：电动机健康状态评估；自适应多尺度注意力机制；CNN−GRU ；多传感器信息融合；主成分分析中图分类号：TD614 文献标志码：AHealth status evaluation of CNN-GRU mine motor based on adaptive multi-scale attention mechanismTAN Donggui, YUAN Yiping, FAN Panpan(Intelligent Manufacturing Modern Industry College, Xinjiang University, Urumqi 830017, China)Abstract : When using multi-sensor information fusion technology to evaluate the health status of motors,there are outliers and missing values in the monitoring data of mine motors. However, deep learning models such as convolutional neural networks and recurrent neural networks find it difficult to effectively extract data features and update network weights when the data quality is severely degraded, resulting in problems such as vanishing or exploding gradients. In order to solve the above problems, A CNN-GRU (CNN-GRU-AMSA) model based on adaptive multi-scale attention mechanism is proposed to evaluate the health status of mine motors. Firstly, the model fills in, removes, and standardizes the motor operation data collected by sensors, and classifies the operating conditions of mine motors based on environmental temperature changes. Secondly, based on the Mahalanobis distance, the health index (HI) of health evaluation indicators such as motor current, three-phase收稿日期：2023-11-08；修回日期：2024-02-25；责任编辑：盛男。
α稳定分布噪声下基于梯度范数的VSS-NLMP算法
α稳定分布噪声下基于梯度范数的VSS-NLMP算法郝燕玲;单志明;沈锋【摘要】针对α稳定分布噪声环境下的自适应滤波问题,提出一种新的基于梯度范数的变步长归一化最小平均p范数(variable step-size normalized least mean p-norm,VSS-NLMP)算法.该算法首先对梯度矢量进行加权平滑,以减小梯度噪声的影响,然后利用梯度矢量能够跟踪自适应过程的均方偏差这一特点,利用梯度矢量的欧氏范数控制步长的变化.给出了新算法的迭代过程,然后对其收敛性进行分析,仿真结果表明本算法较现有变步长NLMP算法有更好的性能.%According to the problem of adaptive filtering in α stable environments, a gradient-norm based variable step-size normalized least mean p-norm (VSS-NLMP) algorithm is proposed. The squared norm of the smoothed gradient vector, which can track the variation of the mean square deviation at iteration, is used to update the step-size parameter in the algorithm. The weighted average of the gradient vector reduces the noise effectively and results in a more stable and less noisy adaptation of the step-size parameter. The update and convergence of the proposed algorithm are formulated. The simulation results indicate that the proposed algorithm has a better performance compared with the existing VSS-NLMP algorithms.【期刊名称】《系统工程与电子技术》【年(卷),期】2012(034)004【总页数】5页(P652-656)【关键词】信号处理;α稳定分布;分数低阶统计量;自适应滤波;变步长归一化最小平均p范数算法【作者】郝燕玲;单志明;沈锋【作者单位】哈尔滨工程大学自动化学院,黑龙江哈尔滨150001;哈尔滨工程大学自动化学院,黑龙江哈尔滨150001;哈尔滨工程大学自动化学院,黑龙江哈尔滨150001【正文语种】中文【中图分类】TN911.70 引言高斯分布白噪声是最常用的接收机背景噪声模型，这是因为理想的高斯模型可以简化信号处理算法和接收机结构设计，并且这种假设的合理性由中心极限定理得到证明［1］。
基于加权多新息H∞滤波的锂离子电池SOC估计
基于加权多新息滤波的锂离子电池SOC 估计丁 洁，姚建鑫，万佑红，凤 良（南京邮电大学自动化学院、人工智能学院，江苏南京210023 ）摘要：采用具有自适应遗忘因子的递归最小二乘法辨识二阶RC 模型，改进的H ”滤波（HIF ）提高锂离子电池荷电状态（SOC ）的估计精度。
提出具有加权的H ”滤波（WI-HIF ）算法，考虑当前新息及历史信息，通过粒子滤波的权重计算思想，根据重要性对每个新息点加权。
相对于HIF ,WI-HIF 估计SOC 的误差在放电测试中降低71%，在动态应力测试中降低19%。
关键词:锂离子电池；荷电状态（SOC ）；在线参数辨识；加权H ”滤波（WI-HIF ）中图分类号:TM912. 9 文献标志码:A 文章编号：1001-1579（2020）05-0432-04SOC estimation for Li-ion battery based on weighted innovation H ^filterDING Jie,YAO Jian-xin , WAN You-hong , FENG Liang( College of Automation & College of Artificial Intelligence , Nanjing University of Postsand Telecommunications , Nanjing , Jiangsu 210023, China )Abstract ：A second-order RC model was identified by the recursive least squares method with adaptive forgetting factor. Animproved H ^ filter ( HIF ) was used to improve the estimation accuracy of state of charge(SOC ) of Li-ion battery. Taking the currentinnovation and previous information in considered, H ^ filter algorithm with weighted innovation ( WI-HIF ) was proposed. Each innovation point was weighted according to its importance by employing the weight calculation idea of particle filter. Compared withHIF , the SOC estimation error of WI-HIF was reduced by 71% in discharge test , reduced by 19% in dynamic stress test.Key words :Li-ion battery ； state of charge ( SOC ) ； online parameter identification ； weighted innovation H ^ filter( WI-HIF )锂离子电池的安全性和可靠性是电动汽车技术的核心， 需要良好的电池管理系统来检测系统状态和平衡电荷放电。
统计学专业名词·中英对照
统计学专业名词·中英对照Lansexyhttp：//hi。
baidu。
com/new/lansexy我大学毕业已经多年,这些年来,越发感到外刊的重要性.读懂外刊要有不错的英语功底，同时,还需要掌握一定的专业词汇。
掌握足够的专业词汇，在国内外期刊的阅读和写作中会游刃有余。
在此小结，按首字母顺序排列。
这些词汇的来源，一是专业书籍，二是网上查找，再一个是比较重要的期刊。
当然,这些仅是常用专业词汇的一部分，并且由于个人精力、文献查阅的限制，难免有不足和错误之处，希望读者批评指出.Aabscissa 横坐标absence rate 缺勤率Absolute deviation 绝对离差Absolute number 绝对数absolute value 绝对值Absolute residuals 绝对残差accident error 偶然误差Acceleration array 加速度立体阵Acceleration in an arbitrary direction 任意方向上的加速度Acceleration normal 法向加速度Acceleration space dimension 加速度空间的维数Acceleration tangential 切向加速度Acceleration vector 加速度向量Acceptable hypothesis 可接受假设Accumulation 累积Accumulated frequency 累积频数Accuracy 准确度Actual frequency 实际频数Adaptive estimator 自适应估计量Addition 相加Addition theorem 加法定理Additive Noise 加性噪声Additivity 可加性Adjusted rate 调整率Adjusted value 校正值Admissible error 容许误差Aggregation 聚集性Alpha factoring α因子法Alternative hypothesis 备择假设Among groups 组间Amounts 总量Analysis of correlation 相关分析Analysis of covariance 协方差分析Analysis of data 分析资料Analysis Of Effects 效应分析Analysis Of Variance 方差分析Analysis of regression 回归分析Analysis of time series 时间序列分析Analysis of variance 方差分析Angular transformation 角转换ANOVA （analysis of variance）方差分析ANOVA Models 方差分析模型ANOVA table and eta 分组计算方差分析Arcing 弧/弧旋Arcsine transformation 反正弦变换Area 区域图Area under the curve 曲线面积AREG 评估从一个时间点到下一个时间点回归相关时的误差ARIMA 季节和非季节性单变量模型的极大似然估计Arithmetic grid paper 算术格纸Arithmetic mean 算术平均数Arithmetic weighted mean 加权算术均数Arrhenius relation 艾恩尼斯关系Assessing fit 拟合的评估Associative laws 结合律Assumed mean 假定均数Asymmetric distribution 非对称分布Asymmetry coefficient 偏度系数Asymptotic bias 渐近偏倚Asymptotic efficiency 渐近效率Asymptotic variance 渐近方差Attributable risk 归因危险度Attribute data 属性资料Attribution 属性Autocorrelation 自相关Autocorrelation of residuals 残差的自相关Average 平均数Average confidence interval length 平均置信区间长度average deviation 平均差Average growth rate 平均增长率BBar chart/graph 条形图Base period 基期Bayes’ theorem Bayes 定理Bell—shaped curve 钟形曲线Bernoulli distribution 伯努力分布Best—trim estimator 最好切尾估计量Bias 偏性Biometrics 生物统计学Binary logistic regression 二元逻辑斯蒂回归Binomial distribution 二项分布Bisquare 双平方Bivariate Correlate 二变量相关Bivariate normal distribution 双变量正态分布Bivariate normal population 双变量正态总体Biweight interval 双权区间Biweight M-estimator 双权M 估计量Block 区组/配伍组BMDP(Biomedical computer programs) BMDP 统计软件包Box plot 箱线图/箱尾图Breakdown bound 崩溃界/崩溃点CCanonical correlation 典型相关Caption 纵标目Cartogram 统计图Case fatality rate 病死率Case—control study 病例对照研究Categorical variable 分类变量Catenary 悬链线Cauchy distribution 柯西分布Cause-and—effect relationship 因果关系Cell 单元Censoring 终检census 普查Center of symmetry 对称中心Centering and scaling 中心化和定标Central tendency 集中趋势Central value 中心值CHAID -χ2 Automatic Interaction Detector 卡方自动交互检测Chance 机遇Chance error 随机误差Chance variable 随机变量Characteristic equation 特征方程Characteristic root 特征根Characteristic vector 特征向量Chebshev criterion of fit 拟合的切比雪夫准则Chernoff faces 切尔诺夫脸谱图chi—sguare(X2) test 卡方检验卡方检验/χ2 检验Choleskey decomposition 乔洛斯基分解Circle chart 圆图Class interval 组距Classification 分组、分类Class mid-value 组中值Class upper limit 组上限Classified variable 分类变量Cluster analysis 聚类分析Cluster sampling 整群抽样Code 代码Coded data 编码数据Coding 编码Coefficient of contingency 列联系数Coefficient of correlation 相关系数Coefficient of determination 决定系数Coefficient of multiple correlation 多重相关系数Coefficient of partial correlation 偏相关系数Coefficient of production-moment correlation 积差相关系数Coefficient of rank correlation 等级相关系数Coefficient of regression 回归系数Coefficient of skewness 偏度系数Coefficient of variation 变异系数Cohort study 队列研究Collection of data 资料收集Collinearity 共线性Column 列Column effect 列效应Column factor 列因素Combination pool 合并Combinative table 组合表Combined standard deviation 合并标准差Combined variance 合并方差Common factor 共性因子Common regression coefficient 公共回归系数Common value 共同值Common variance 公共方差Common variation 公共变异Communality variance 共性方差Comparability 可比性Comparison of bathes 批比较Comparison value 比较值Compartment model 分部模型Compassion 伸缩Complement of an event 补事件Complete association 完全正相关Complete dissociation 完全不相关Complete statistics 完备统计量Complete survey 全面调查Completely randomized design 完全随机化设计Composite event 联合事件Composite events 复合事件Concavity 凹性Conditional expectation 条件期望Conditional likelihood 条件似然Conditional probability 条件概率Conditionally linear 依条件线性Confidence interval 置信区间Confidence level 可信水平，置信水平Confidence limit 置信限Confidence lower limit 置信下限Confidence upper limit 置信上限Confirmatory Factor Analysis 验证性因子分析Confirmatory research 证实性实验研究Confounding factor 混杂因素Conjoint 联合分析Consistency 相合性Consistency check 一致性检验Consistent asymptotically normal estimate 相合渐近正态估计Consistent estimate 相合估计Constituent ratio 构成比，结构相对数Constrained nonlinear regression 受约束非线性回归Constraint 约束Contaminated distribution 污染分布Contaminated Gausssian 污染高斯分布Contaminated normal distribution 污染正态分布Contamination 污染Contamination model 污染模型Continuity 连续性Contingency table 列联表Contour 边界线Contribution rate 贡献率Control 对照质量控制图Control group 对照组Controlled experiments 对照实验Conventional depth 常规深度Convolution 卷积Coordinate 坐标Corrected factor 校正因子Corrected mean 校正均值Correction coefficient 校正系数Correction for continuity 连续性校正Correction for grouping 归组校正Correction number 校正数Correction value 校正值Correctness 正确性Correlation 相关，联系Correlation analysis 相关分析Correlation coefficient 相关系数Correlation 相关性Correlation index 相关指数Correspondence 对应Counting 计数Counts 计数/频数Covariance 协方差Covariant 共变Cox Regression Cox 回归Criteria for fitting 拟合准则Criteria of least squares 最小二乘准则Critical ratio 临界比Critical region 拒绝域Critical value 临界值Cross—over design 交叉设计Cross-section analysis 横断面分析Cross—section survey 横断面调查Crosstabs 交叉表Crosstabs 列联表分析Cross—tabulation table 复合表Cube root 立方根Cumulative distribution function 分布函数Cumulative frequency 累积频率Cumulative probability 累计概率Curvature 曲率/弯曲Curvature 曲率Curve Estimation 曲线拟合Curve fit 曲线拟和Curve fitting 曲线拟合Curvilinear regression 曲线回归Curvilinear relation 曲线关系Cut—and—try method 尝试法Cycle 周期Cyclist 周期性DD test D 检验data 资料Data acquisition 资料收集Data bank 数据库Data capacity 数据容量Data deficiencies 数据缺乏Data handling 数据处理Data manipulation 数据处理Data processing 数据处理Data reduction 数据缩减Data set 数据集Data sources 数据来源Data transformation 数据变换Data validity 数据有效性Data—in 数据输入Data—out 数据输出Dead time 停滞期Degree of freedom 自由度degree of confidence 可信度，置信度degree of dispersion 离散程度Degree of precision 精密度Degree of reliability 可靠性程度degree of variation 变异度Degression 递减Density function 密度函数Density of data points 数据点的密度Dependent variableDepth 深度Derivative matrix 导数矩阵Derivative-free methods 无导数方法Design 设计design of experiment 实验设计Determinacy 确定性Determinant 行列式Determinant 决定因素Deviation 离差Deviation from average 离均差diagnose accordance rate 诊断符合率Diagnostic plot 诊断图Dichotomous variable 二分变量Differential equation 微分方程Direct standardization 直接标准化法Direct Oblimin 斜交旋转Discrete variable 离散型变量DISCRIMINANT 判断Discriminant analysis 判别分析Discriminant coefficient 判别系数Discriminant function 判别值Dispersion 散布/分散度Disproportional 不成比例的Disproportionate sub-class numbers 不成比例次级组含量Distribution free 分布无关性/免分布Distribution shape 分布形状Distribution—free method 任意分布法Distributive laws 分配律Disturbance 随机扰动项Dose response curve 剂量反应曲线Double blind method 双盲法Double blind trial 双盲试验Double exponential distribution 双指数分布Double logarithmic 双对数Downward rank 降秩Dual-space plot 对偶空间图DUD 无导数方法Duncan’s new multiple range method 新复极差法/Duncan 新法EError Bar 均值相关区间图Effect 实验效应Effective rate 有效率Eigenvalue 特征值Eigenvector 特征向量Ellipse 椭圆Empirical distribution 经验分布Empirical probability 经验概率单位Enumeration data 计数资料Equal sun-class number 相等次级组含量Equally likely 等可能Equation of linear regression 线性回归方程Equivariance 同变性Error 误差/错误Error of estimate 估计误差Error of replication 重复误差Error type I 第一类错误Error type II 第二类错误Estimand 被估量Estimated error mean squares 估计误差均方Estimated error sum of squares 估计误差平方和Euclidean distance 欧式距离Event 事件Exceptional data point 异常数据点Expectation plane 期望平面Expectation surface 期望曲面Expected values 期望值Experiment 实验Experiment design 实验设计Experiment error 实验误差Experimental group 实验组Experimental sampling 试验抽样Experimental unit 试验单位Explained variance （已说明方差) Explanatory variable 说明变量Exploratory data analysis 探索性数据分析Explore Summarize 探索-摘要Exponential curve 指数曲线Exponential growth 指数式增长EXSMOOTH 指数平滑方法Extended fit 扩充拟合Extra parameter 附加参数Extrapolation 外推法Extreme observation 末端观测值Extremes 极端值/极值FF distribution F 分布F test F 检验Factor 因素/因子Factor analysis 因子分析Factor Analysis 因子分析Factor score 因子得分Factorial 阶乘Factorial design 析因试验设计False negative 假阴性False negative error 假阴性错误Family of distributions 分布族Family of estimators 估计量族Fanning 扇面Fatality rate 病死率Field investigation 现场调查Field survey 现场调查Finite population 有限总体Finite—sample 有限样本First derivative 一阶导数First principal component 第一主成分First quartile 第一四分位数Fisher information 费雪信息量Fitted value 拟合值Fitting a curve 曲线拟合Fixed base 定基Fluctuation 随机起伏Forecast 预测Four fold table 四格表Fourth 四分点Fraction blow 左侧比率Fractional error 相对误差Frequency 频率Freguency distribution 频数分布Frequency polygon 频数多边图Frontier point 界限点Function relationship 泛函关系GGamma distribution 伽玛分布Gauss increment 高斯增量Gaussian distribution 高斯分布/正态分布Gauss-Newton increment 高斯-牛顿增量General census 全面普查Generalized least squares 综合最小平方法GENLOG (Generalized liner models) 广义线性模型Geometric mean 几何平均数Gini’s mean difference 基尼均差GLM （General liner models）通用线性模型Goodness of fit 拟和优度/配合度Gradient of determinant 行列式的梯度Graeco-Latin square 希腊拉丁方Grand mean 总均值Gross errors 重大错误Gross-error sensitivity 大错敏感度Group averages 分组平均Grouped data 分组资料Guessed mean 假定平均数HHalf—life 半衰期Hampel M-estimators 汉佩尔M 估计量Happenstance 偶然事件Harmonic mean 调和均数Hazard function 风险均数Hazard rate 风险率Heading 标目Heavy-tailed distribution 重尾分布Hessian array 海森立体阵Heterogeneity 不同质Heterogeneity of variance 方差不齐Hierarchical classification 组内分组Hierarchical clustering method 系统聚类法High—leverage point 高杠杆率点High-Low 低区域图Higher Order Interaction Effects，高阶交互作用HILOGLINEAR 多维列联表的层次对数线性模型Hinge 折叶点Histogram 直方图Historical cohort study 历史性队列研究Holes 空洞HOMALS 多重响应分析Homogeneity of variance 方差齐性Homogeneity test 齐性检验Huber M-estimators 休伯M 估计量Hyperbola 双曲线Hypothesis testing 假设检验Hypothetical universe 假设总体IImage factoring 多元回归法Impossible event 不可能事件Independence 独立性Independent variable 自变量Index 指标/指数Indirect standardization 间接标准化法Individual 个体Inference band 推断带Infinite population 无限总体Infinitely great 无穷大Infinitely small 无穷小Influence curve 影响曲线Information capacity 信息容量Initial condition 初始条件Initial estimate 初始估计值Initial level 最初水平Interaction 交互作用Interaction terms 交互作用项Intercept 截距Interpolation 内插法Interquartile range 四分位距Interval estimation 区间估计Intervals of equal probability 等概率区间Intrinsic curvature 固有曲率Invariance 不变性Inverse matrix 逆矩阵Inverse probability 逆概率Inverse sine transformation 反正弦变换Iteration 迭代JJacobian determinant 雅可比行列式Joint distribution function 分布函数Joint probability 联合概率Joint probability distribution 联合概率分布KK-Means Cluster 逐步聚类分析K means method 逐步聚类法Kaplan—Meier 评估事件的时间长度Kaplan-Merier chart Kaplan-Merier 图Kendall's rank correlation Kendall 等级相关Kinetic 动力学Kolmogorov-Smirnove test 柯尔莫哥洛夫—斯米尔诺夫检验Kruskal and Wallis test Kruskal 及Wallis 检验/多样本的秩和检验/H 检验Kurtosis 峰度LLack of fit 失拟Ladder of powers 幂阶梯Lag 滞后Large sample 大样本Large sample test 大样本检验Latin square 拉丁方Latin square design 拉丁方设计Leakage 泄漏Least favorable configuration 最不利构形Least favorable distribution 最不利分布Least significant difference 最小显著差法Least square method 最小二乘法Least Squared Criterion，最小二乘方准则Least-absolute—residuals estimates 最小绝对残差估计Least—absolute—residuals fit 最小绝对残差拟合Least-absolute—residuals line 最小绝对残差线Legend 图例L—estimator L 估计量L—estimator of location 位置L 估计量L—estimator of scale 尺度L 估计量Level 水平Leveage Correction，杠杆率校正Life expectance 预期期望寿命Life table 寿命表Life table method 生命表法Light—tailed distribution 轻尾分布Likelihood function 似然函数Likelihood ratio 似然比line graph 线图Linear correlation 直线相关Linear equation 线性方程Linear programming 线性规划Linear regression 直线回归Linear Regression 线性回归Linear trend 线性趋势Loading 载荷Location and scale equivariance 位置尺度同变性Location equivariance 位置同变性Location invariance 位置不变性Location scale family 位置尺度族Log rank test 时序检验Logarithmic curve 对数曲线Logarithmic normal distribution 对数正态分布Logarithmic scale 对数尺度Logarithmic transformation 对数变换Logic check 逻辑检查Logistic distribution 逻辑斯特分布Logit transformation Logit 转换LOGLINEAR 多维列联表通用模型Lognormal distribution 对数正态分布Lost function 损失函数Low correlation 低度相关Lower limit 下限Lowest—attained variance 最小可达方差LSD 最小显著差法的简称Lurking variable 潜在变量MMain effect 主效应Major heading 主辞标目Marginal density function 边缘密度函数Marginal probability 边缘概率Marginal probability distribution 边缘概率分布Matched data 配对资料Matched distribution 匹配过分布Matching of distribution 分布的匹配Matching of transformation 变换的匹配Mathematical expectation 数学期望Mathematical model 数学模型Maximum L—estimator 极大极小L 估计量Maximum likelihood method 最大似然法Mean 均数Mean squares between groups 组间均方Mean squares within group 组内均方Means (Compare means）均值-均值比较Median 中位数Median effective dose 半数效量Median lethal dose 半数致死量Median polish 中位数平滑Median test 中位数检验Minimal sufficient statistic 最小充分统计量Minimum distance estimation 最小距离估计Minimum effective dose 最小有效量Minimum lethal dose 最小致死量Minimum variance estimator 最小方差估计量MINITAB 统计软件包Minor heading 宾词标目Missing data 缺失值Model specification 模型的确定Modeling Statistics 模型统计Models for outliers 离群值模型Modifying the model 模型的修正Modulus of continuity 连续性模Morbidity 发病率Most favorable configuration 最有利构形MSC(多元散射校正）Multidimensional Scaling (ASCAL）多维尺度/多维标度Multinomial Logistic Regression 多项逻辑斯蒂回归Multiple comparison 多重比较Multiple correlation 复相关Multiple covariance 多元协方差Multiple linear regression 多元线性回归Multiple response 多重选项Multiple solutions 多解Multiplication theorem 乘法定理Multiresponse 多元响应Multi—stage sampling 多阶段抽样Multivariate T distribution 多元T 分布Mutual exclusive 互不相容Mutual independence 互相独立NNatural boundary 自然边界Natural dead 自然死亡Natural zero 自然零Negative correlation 负相关Negative linear correlation 负线性相关Negatively skewed 负偏Newman—Keuls method q 检验NK method q 检验No statistical significance 无统计意义Nominal variable 名义变量Nonconstancy of variability 变异的非定常性Nonlinear regression 非线性相关Nonparametric statistics 非参数统计Nonparametric test 非参数检验Nonparametric tests 非参数检验Normal deviate 正态离差Normal distribution 正态分布Normal equation 正规方程组Normal P-P 正态概率分布图Normal Q—Q 正态概率单位分布图Normal ranges 正常范围Normal value 正常值Normalization 归一化Nuisance parameter 多余参数/讨厌参数Null hypothesis 无效假设Numerical variable 数值变量OObjective function 目标函数Observation unit 观察单位Observed value 观察值One sided test 单侧检验One—way analysis of variance 单因素方差分析Oneway ANOVA 单因素方差分析Open sequential trial 开放型序贯设计Optrim 优切尾Optrim efficiency 优切尾效率Order statistics 顺序统计量Ordered categories 有序分类Ordinal logistic regression 序数逻辑斯蒂回归Ordinal variable 有序变量Orthogonal basis 正交基Orthogonal design 正交试验设计Orthogonality conditions 正交条件ORTHOPLAN 正交设计Outlier cutoffs 离群值截断点Outliers 极端值OVERALS 多组变量的非线性正规相关Overshoot 迭代过度PPaired design 配对设计Paired sample 配对样本Pairwise slopes 成对斜率Parabola 抛物线Parallel tests 平行试验Parameter 参数Parametric statistics 参数统计Parametric test 参数检验Pareto 直条构成线图（佩尔托图）Partial correlation 偏相关Partial regression 偏回归Partial sorting 偏排序Partials residuals 偏残差Pattern 模式PCA（主成分分析)Pearson curves 皮尔逊曲线Peeling 退层Percent bar graph 百分条形图Percentage 百分比Percentile 百分位数Percentile curves 百分位曲线Periodicity 周期性Permutation 排列P—estimator P 估计量Pie graph 构成图饼图Pitman estimator 皮特曼估计量Pivot 枢轴量Planar 平坦Planar assumption 平面的假设PLANCARDS 生成试验的计划卡PLS(偏最小二乘法）Point estimation 点估计Poisson distribution 泊松分布Polishing 平滑Polled standard deviation 合并标准差Polled variance 合并方差Polygon 多边图Polynomial 多项式Polynomial curve 多项式曲线Population 总体Population attributable risk 人群归因危险度Positive correlation 正相关Positively skewed 正偏Posterior distribution 后验分布Power of a test 检验效能Precision 精密度Predicted value 预测值Preliminary analysis 预备性分析Principal axis factoring 主轴因子法Principal component analysis 主成分分析Prior distribution 先验分布Prior probability 先验概率Probabilistic model 概率模型probability 概率Probability density 概率密度Product moment 乘积矩/协方差Profile trace 截面迹图Proportion 比/构成比Proportion allocation in stratified random sampling 按比例分层随机抽样Proportionate 成比例Proportionate sub—class numbers 成比例次级组含量Prospective study 前瞻性调查Proximities 亲近性Pseudo F test 近似F 检验Pseudo model 近似模型Pseudosigma 伪标准差Purposive sampling 有目的抽样QQR decomposition QR 分解Quadratic approximation 二次近似Qualitative classification 属性分类Qualitative method 定性方法Quantile-quantile plot 分位数-分位数图/Q—Q 图Quantitative analysis 定量分析Quartile 四分位数Quick Cluster 快速聚类RRadix sort 基数排序Random allocation 随机化分组Random blocks design 随机区组设计Random event 随机事件Randomization 随机化Range 极差/全距Rank correlation 等级相关Rank sum test 秩和检验Rank test 秩检验Ranked data 等级资料Rate 比率Ratio 比例Raw data 原始资料Raw residual 原始残差Rayleigh's test 雷氏检验Rayleigh's Z 雷氏Z 值Reciprocal 倒数Reciprocal transformation 倒数变换Recording 记录Redescending estimators 回降估计量Reducing dimensions 降维Re—expression 重新表达Reference set 标准组Region of acceptance 接受域Regression coefficient 回归系数Regression sum of square 回归平方和Rejection point 拒绝点Relative dispersion 相对离散度Relative number 相对数Reliability 可靠性Reparametrization 重新设置参数Replication 重复Report Summaries 报告摘要Residual sum of square 剩余平方和residual variance （剩余方差)Resistance 耐抗性Resistant line 耐抗线Resistant technique 耐抗技术R-estimator of location 位置R 估计量R-estimator of scale 尺度R 估计量Retrospective study 回顾性调查Ridge trace 岭迹Ridit analysis Ridit 分析Rotation 旋转Rounding 舍入Row 行Row effects 行效应Row factor 行因素RXC table RXC 表SSample 样本Sample regression coefficient 样本回归系数Sample size 样本量Sample standard deviation 样本标准差Sampling error 抽样误差SAS(Statistical analysis system ) SAS 统计软件包Scale 尺度/量表Scatter diagram 散点图Schematic plot 示意图/简图Score test 计分检验Screening 筛检SEASON 季节分析Second derivative 二阶导数Second principal component 第二主成分SEM （Structural equation modeling) 结构化方程模型Semi-logarithmic graph 半对数图Semi—logarithmic paper 半对数格纸Sensitivity curve 敏感度曲线Sequential analysis 贯序分析Sequence 普通序列图Sequential data set 顺序数据集Sequential design 贯序设计Sequential method 贯序法Sequential test 贯序检验法Serial tests 系列试验Short-cut method 简捷法Sigmoid curve S 形曲线Sign function 正负号函数Sign test 符号检验Signed rank 符号秩Significant Level 显著水平Significance test 显著性检验Significant figure 有效数字Simple cluster sampling 简单整群抽样Simple correlation 简单相关Simple random sampling 简单随机抽样Simple regression 简单回归simple table 简单表Sine estimator 正弦估计量Single-valued estimate 单值估计Singular matrix 奇异矩阵Skewed distribution 偏斜分布Skewness 偏度Slash distribution 斜线分布Slope 斜率Smirnov test 斯米尔诺夫检验Source of variation 变异来源Spearman rank correlation 斯皮尔曼等级相关Specific factor 特殊因子Specific factor variance 特殊因子方差Spectra 频谱Spherical distribution 球型正态分布Spread 展布SPSS（Statistical package for the social science) SPSS 统计软件包Spurious correlation 假性相关Square root transformation 平方根变换Stabilizing variance 稳定方差Standard deviation 标准差Standard error 标准误Standard error of difference 差别的标准误Standard error of estimate 标准估计误差Standard error of rate 率的标准误Standard normal distribution 标准正态分布Standardization 标准化Starting value 起始值Statistic 统计量Statistical control 统计控制Statistical graph 统计图Statistical inference 统计推断Statistical table 统计表Steepest descent 最速下降法Stem and leaf display 茎叶图Step factor 步长因子Stepwise regression 逐步回归Storage 存Strata 层(复数）Stratified sampling 分层抽样Stratified sampling 分层抽样Strength 强度Stringency 严密性Structural relationship 结构关系Studentized residual 学生化残差/t 化残差Sub-class numbers 次级组含量Subdividing 分割Sufficient statistic 充分统计量Sum of products 积和Sum of squares 离差平方和Sum of squares about regression 回归平方和Sum of squares between groups 组间平方和Sum of squares of partial regression 偏回归平方和Sure event 必然事件Survey 调查Survival 生存分析Survival rate 生存率Suspended root gram 悬吊根图Symmetry 对称Systematic error 系统误差Systematic sampling 系统抽样TTags 标签Tail area 尾部面积Tail length 尾长Tail weight 尾重Tangent line 切线Target distribution 目标分布Taylor series 泰勒级数Test（检验)Test of linearity 线性检验Tendency of dispersion 离散趋势Testing of hypotheses 假设检验Theoretical frequency 理论频数Time series 时间序列Tolerance interval 容忍区间Tolerance lower limit 容忍下限Tolerance upper limit 容忍上限Torsion 扰率Total sum of square 总平方和Total variation 总变异Transformation 转换Treatment 处理Trend 趋势Trend of percentage 百分比趋势Trial 试验Trial and error method 试错法Tuning constant 细调常数Two sided test 双向检验Two—stage least squares 二阶最小平方Two—stage sampling 二阶段抽样Two-tailed test 双侧检验Two—way analysis of variance 双因素方差分析Two—way table 双向表Type I error 一类错误/α错误Type II error 二类错误/β错误UUMVU 方差一致最小无偏估计简称Unbiased estimate 无偏估计Unconstrained nonlinear regression 无约束非线性回归Unequal subclass number 不等次级组含量Ungrouped data 不分组资料Uniform coordinate 均匀坐标Uniform distribution 均匀分布Uniformly minimum variance unbiased estimate 方差一致最小无偏估计Unit 单元Unordered categories 无序分类Unweighted least squares 未加权最小平方法Upper limit 上限Upward rank 升秩VVague concept 模糊概念Validity 有效性V ARCOMP （Variance component estimation）方差元素估计Variability 变异性Variable 变量Variance 方差Variation 变异Varimax orthogonal rotation 方差最大正交旋转V olume of distribution 容积WW test W 检验Weibull distribution 威布尔分布Weight 权数Weighted Chi—square test 加权卡方检验/Cochran 检验Weighted linear regression method 加权直线回归Weighted mean 加权平均数Weighted mean square 加权平均方差Weighted sum of square 加权平方和Weighting coefficient 权重系数Weighting method 加权法W—estimation W 估计量W-estimation of location 位置W 估计量Width 宽度Wilcoxon paired test 威斯康星配对法/配对符号秩和检验Wild point 野点/狂点Wild value 野值/狂值Winsorized mean 缩尾均值Withdraw 失访X此组的词汇还没找到YYouden's index 尤登指数ZZ test Z 检验Zero correlation 零相关Z—transformation Z 变换。
机器学习英语词汇
目录第一部分 (3)第二部分 (12)Letter A (12)Letter B (14)Letter C (15)Letter D (17)Letter E (19)Letter F (20)Letter G (21)Letter H (22)Letter I (23)Letter K (24)Letter L (24)Letter M (26)Letter N (27)Letter O (29)Letter P (29)Letter R (31)Letter S (32)Letter T (35)Letter U (36)Letter W (37)Letter Z (37)第三部分 (37)A (37)B (38)C (38)D (40)E (40)F (41)G (41)H (42)L (42)J (43)L (43)M (43)N (44)O (44)P (44)Q (45)R (46)S (46)U (47)V (48)第一部分[ ] intensity 强度[ ] Regression 回归[ ] Loss function 损失函数[ ] non-convex 非凸函数[ ] neural network 神经网络[ ] supervised learning 监督学习[ ] regression problem 回归问题处理的是连续的问题[ ] classification problem 分类问题处理的问题是离散的而不是连续的回归问题和分类问题的区别应该在于回归问题的结果是连续的，分类问题的结果是离散的。
[ ]discreet value 离散值[ ] support vector machines 支持向量机,用来处理分类算法中输入的维度不单一的情况（甚至输入维度为无穷）[ ] learning theory 学习理论[ ] learning algorithms 学习算法[ ] unsupervised learning 无监督学习[ ] gradient descent 梯度下降[ ] linear regression 线性回归[ ] Neural Network 神经网络[ ] gradient descent 梯度下降监督学习的一种算法，用来拟合的算法[ ] normal equations[ ] linear algebra 线性代数原谅我英语不太好[ ] superscript上标[ ] exponentiation 指数[ ] training set 训练集合[ ] training example 训练样本[ ] hypothesis 假设，用来表示学习算法的输出，叫我们不要太纠结H的意思，因为这只是历史的惯例[ ] LMS algorithm “least mean squares” 最小二乘法算法[ ] batch gradient descent 批量梯度下降，因为每次都会计算最小拟合的方差，所以运算慢[ ] constantly gradient descent 字幕组翻译成“随机梯度下降” 我怎么觉得是“常量梯度下降”也就是梯度下降的运算次数不变，一般比批量梯度下降速度快，但是通常不是那么准确[ ] iterative algorithm 迭代算法[ ] partial derivative 偏导数[ ] contour 等高线[ ] quadratic function 二元函数[ ] locally weighted regression局部加权回归[ ] underfitting欠拟合[ ] overfitting 过拟合[ ] non-parametric learning algorithms 无参数学习算法[ ] parametric learning algorithm 参数学习算法[ ] other[ ] activation 激活值[ ] activation function 激活函数[ ] additive noise 加性噪声[ ] autoencoder 自编码器[ ] Autoencoders 自编码算法[ ] average firing rate 平均激活率[ ] average sum-of-squares error 均方差[ ] backpropagation 后向传播[ ] basis 基[ ] basis feature vectors 特征基向量[50 ] batch gradient ascent 批量梯度上升法[ ] Bayesian regularization method 贝叶斯规则化方法[ ] Bernoulli random variable 伯努利随机变量[ ] bias term 偏置项[ ] binary classfication 二元分类[ ] class labels 类型标记[ ] concatenation 级联[ ] conjugate gradient 共轭梯度[ ] contiguous groups 联通区域[ ] convex optimization software 凸优化软件[ ] convolution 卷积[ ] cost function 代价函数[ ] covariance matrix 协方差矩阵[ ] DC component 直流分量[ ] decorrelation 去相关[ ] degeneracy 退化[ ] demensionality reduction 降维[ ] derivative 导函数[ ] diagonal 对角线[ ] diffusion of gradients 梯度的弥散[ ] eigenvalue 特征值[ ] eigenvector 特征向量[ ] error term 残差[ ] feature matrix 特征矩阵[ ] feature standardization 特征标准化[ ] feedforward architectures 前馈结构算法[ ] feedforward neural network 前馈神经网络[ ] feedforward pass 前馈传导[ ] fine-tuned 微调[ ] first-order feature 一阶特征[ ] forward pass 前向传导[ ] forward propagation 前向传播[ ] Gaussian prior 高斯先验概率[ ] generative model 生成模型[ ] gradient descent 梯度下降[ ] Greedy layer-wise training 逐层贪婪训练方法[ ] grouping matrix 分组矩阵[ ] Hadamard product 阿达马乘积[ ] Hessian matrix Hessian 矩阵[ ] hidden layer 隐含层[ ] hidden units 隐藏神经元[ ] Hierarchical grouping 层次型分组[ ] higher-order features 更高阶特征[ ] highly non-convex optimization problem 高度非凸的优化问题[ ] histogram 直方图[ ] hyperbolic tangent 双曲正切函数[ ] hypothesis 估值，假设[ ] identity activation function 恒等激励函数[ ] IID 独立同分布[ ] illumination 照明[100 ] inactive 抑制[ ] independent component analysis 独立成份分析[ ] input domains 输入域[ ] input layer 输入层[ ] intensity 亮度/灰度[ ] intercept term 截距[ ] KL divergence 相对熵[ ] KL divergence KL分散度[ ] k-Means K-均值[ ] learning rate 学习速率[ ] least squares 最小二乘法[ ] linear correspondence 线性响应[ ] linear superposition 线性叠加[ ] line-search algorithm 线搜索算法[ ] local mean subtraction 局部均值消减[ ] local optima 局部最优解[ ] logistic regression 逻辑回归[ ] loss function 损失函数[ ] low-pass filtering 低通滤波[ ] magnitude 幅值[ ] MAP 极大后验估计[ ] maximum likelihood estimation 极大似然估计[ ] mean 平均值[ ] MFCC Mel 倒频系数[ ] multi-class classification 多元分类[ ] neural networks 神经网络[ ] neuron 神经元[ ] Newton’s method 牛顿法[ ] non-convex function 非凸函数[ ] non-linear feature 非线性特征[ ] norm 范式[ ] norm bounded 有界范数[ ] norm constrained 范数约束[ ] normalization 归一化[ ] numerical roundoff errors 数值舍入误差[ ] numerically checking 数值检验[ ] numerically reliable 数值计算上稳定[ ] object detection 物体检测[ ] objective function 目标函数[ ] off-by-one error 缺位错误[ ] orthogonalization 正交化[ ] output layer 输出层[ ] overall cost function 总体代价函数[ ] over-complete basis 超完备基[ ] over-fitting 过拟合[ ] parts of objects 目标的部件[ ] part-whole decompostion 部分-整体分解[ ] PCA 主元分析[ ] penalty term 惩罚因子[ ] per-example mean subtraction 逐样本均值消减[150 ] pooling 池化[ ] pretrain 预训练[ ] principal components analysis 主成份分析[ ] quadratic constraints 二次约束[ ] RBMs 受限Boltzman机[ ] reconstruction based models 基于重构的模型[ ] reconstruction cost 重建代价[ ] reconstruction term 重构项[ ] redundant 冗余[ ] reflection matrix 反射矩阵[ ] regularization 正则化[ ] regularization term 正则化项[ ] rescaling 缩放[ ] robust 鲁棒性[ ] run 行程[ ] second-order feature 二阶特征[ ] sigmoid activation function S型激励函数[ ] significant digits 有效数字[ ] singular value 奇异值[ ] singular vector 奇异向量[ ] smoothed L1 penalty 平滑的L1范数惩罚[ ] Smoothed topographic L1 sparsity penalty 平滑地形L1稀疏惩罚函数[ ] smoothing 平滑[ ] Softmax Regresson Softmax回归[ ] sorted in decreasing order 降序排列[ ] source features 源特征[ ] sparse autoencoder 消减归一化[ ] Sparsity 稀疏性[ ] sparsity parameter 稀疏性参数[ ] sparsity penalty 稀疏惩罚[ ] square function 平方函数[ ] squared-error 方差[ ] stationary 平稳性（不变性）[ ] stationary stochastic process 平稳随机过程[ ] step-size 步长值[ ] supervised learning 监督学习[ ] symmetric positive semi-definite matrix 对称半正定矩阵[ ] symmetry breaking 对称失效[ ] tanh function 双曲正切函数[ ] the average activation 平均活跃度[ ] the derivative checking method 梯度验证方法[ ] the empirical distribution 经验分布函数[ ] the energy function 能量函数[ ] the Lagrange dual 拉格朗日对偶函数[ ] the log likelihood 对数似然函数[ ] the pixel intensity value 像素灰度值[ ] the rate of convergence 收敛速度[ ] topographic cost term 拓扑代价项[ ] topographic ordered 拓扑秩序[ ] transformation 变换[200 ] translation invariant 平移不变性[ ] trivial answer 平凡解[ ] under-complete basis 不完备基[ ] unrolling 组合扩展[ ] unsupervised learning 无监督学习[ ] variance 方差[ ] vecotrized implementation 向量化实现[ ] vectorization 矢量化[ ] visual cortex 视觉皮层[ ] weight decay 权重衰减[ ] weighted average 加权平均值[ ] whitening 白化[ ] zero-mean 均值为零第二部分Letter A[ ] Accumulated error backpropagation 累积误差逆传播[ ] Activation Function 激活函数[ ] Adaptive Resonance Theory/ART 自适应谐振理论[ ] Addictive model 加性学习[ ] Adversarial Networks 对抗网络[ ] Affine Layer 仿射层[ ] Affinity matrix 亲和矩阵[ ] Agent 代理/ 智能体[ ] Algorithm 算法[ ] Alpha-beta pruning α-β剪枝[ ] Anomaly detection 异常检测[ ] Approximation 近似[ ] Area Under ROC Curve／AUC Roc 曲线下面积[ ] Artificial General Intelligence/AGI 通用人工智能[ ] Artificial Intelligence/AI 人工智能[ ] Association analysis 关联分析[ ] Attention mechanism 注意力机制[ ] Attribute conditional independence assumption 属性条件独立性假设[ ] Attribute space 属性空间[ ] Attribute value 属性值[ ] Autoencoder 自编码器[ ] Automatic speech recognition 自动语音识别[ ] Automatic summarization 自动摘要[ ] Average gradient 平均梯度[ ] Average-Pooling 平均池化Letter B[ ] Backpropagation Through Time 通过时间的反向传播[ ] Backpropagation/BP 反向传播[ ] Base learner 基学习器[ ] Base learning algorithm 基学习算法[ ] Batch Normalization/BN 批量归一化[ ] Bayes decision rule 贝叶斯判定准则[250 ] Bayes Model Averaging／BMA 贝叶斯模型平均[ ] Bayes optimal classifier 贝叶斯最优分类器[ ] Bayesian decision theory 贝叶斯决策论[ ] Bayesian network 贝叶斯网络[ ] Between-class scatter matrix 类间散度矩阵[ ] Bias 偏置/ 偏差[ ] Bias-variance decomposition 偏差-方差分解[ ] Bias-Variance Dilemma 偏差–方差困境[ ] Bi-directional Long-Short Term Memory/Bi-LSTM 双向长短期记忆[ ] Binary classification 二分类[ ] Binomial test 二项检验[ ] Bi-partition 二分法[ ] Boltzmann machine 玻尔兹曼机[ ] Bootstrap sampling 自助采样法／可重复采样／有放回采样[ ] Bootstrapping 自助法[ ] Break-Event Point／BEP 平衡点Letter C[ ] Calibration 校准[ ] Cascade-Correlation 级联相关[ ] Categorical attribute 离散属性[ ] Class-conditional probability 类条件概率[ ] Classification and regression tree/CART 分类与回归树[ ] Classifier 分类器[ ] Class-imbalance 类别不平衡[ ] Closed -form 闭式[ ] Cluster 簇/类/集群[ ] Cluster analysis 聚类分析[ ] Clustering 聚类[ ] Clustering ensemble 聚类集成[ ] Co-adapting 共适应[ ] Coding matrix 编码矩阵[ ] COLT 国际学习理论会议[ ] Committee-based learning 基于委员会的学习[ ] Competitive learning 竞争型学习[ ] Component learner 组件学习器[ ] Comprehensibility 可解释性[ ] Computation Cost 计算成本[ ] Computational Linguistics 计算语言学[ ] Computer vision 计算机视觉[ ] Concept drift 概念漂移[ ] Concept Learning System /CLS 概念学习系统[ ] Conditional entropy 条件熵[ ] Conditional mutual information 条件互信息[ ] Conditional Probability Table／CPT 条件概率表[ ] Conditional random field/CRF 条件随机场[ ] Conditional risk 条件风险[ ] Confidence 置信度[ ] Confusion matrix 混淆矩阵[300 ] Connection weight 连接权[ ] Connectionism 连结主义[ ] Consistency 一致性／相合性[ ] Contingency table 列联表[ ] Continuous attribute 连续属性[ ] Convergence 收敛[ ] Conversational agent 会话智能体[ ] Convex quadratic programming 凸二次规划[ ] Convexity 凸性[ ] Convolutional neural network/CNN 卷积神经网络[ ] Co-occurrence 同现[ ] Correlation coefficient 相关系数[ ] Cosine similarity 余弦相似度[ ] Cost curve 成本曲线[ ] Cost Function 成本函数[ ] Cost matrix 成本矩阵[ ] Cost-sensitive 成本敏感[ ] Cross entropy 交叉熵[ ] Cross validation 交叉验证[ ] Crowdsourcing 众包[ ] Curse of dimensionality 维数灾难[ ] Cut point 截断点[ ] Cutting plane algorithm 割平面法Letter D[ ] Data mining 数据挖掘[ ] Data set 数据集[ ] Decision Boundary 决策边界[ ] Decision stump 决策树桩[ ] Decision tree 决策树／判定树[ ] Deduction 演绎[ ] Deep Belief Network 深度信念网络[ ] Deep Convolutional Generative Adversarial Network/DCGAN 深度卷积生成对抗网络[ ] Deep learning 深度学习[ ] Deep neural network/DNN 深度神经网络[ ] Deep Q-Learning 深度Q 学习[ ] Deep Q-Network 深度Q 网络[ ] Density estimation 密度估计[ ] Density-based clustering 密度聚类[ ] Differentiable neural computer 可微分神经计算机[ ] Dimensionality reduction algorithm 降维算法[ ] Directed edge 有向边[ ] Disagreement measure 不合度量[ ] Discriminative model 判别模型[ ] Discriminator 判别器[ ] Distance measure 距离度量[ ] Distance metric learning 距离度量学习[ ] Distribution 分布[ ] Divergence 散度[350 ] Diversity measure 多样性度量／差异性度量[ ] Domain adaption 领域自适应[ ] Downsampling 下采样[ ] D-separation （Directed separation）有向分离[ ] Dual problem 对偶问题[ ] Dummy node 哑结点[ ] Dynamic Fusion 动态融合[ ] Dynamic programming 动态规划Letter E[ ] Eigenvalue decomposition 特征值分解[ ] Embedding 嵌入[ ] Emotional analysis 情绪分析[ ] Empirical conditional entropy 经验条件熵[ ] Empirical entropy 经验熵[ ] Empirical error 经验误差[ ] Empirical risk 经验风险[ ] End-to-End 端到端[ ] Energy-based model 基于能量的模型[ ] Ensemble learning 集成学习[ ] Ensemble pruning 集成修剪[ ] Error Correcting Output Codes／ECOC 纠错输出码[ ] Error rate 错误率[ ] Error-ambiguity decomposition 误差-分歧分解[ ] Euclidean distance 欧氏距离[ ] Evolutionary computation 演化计算[ ] Expectation-Maximization 期望最大化[ ] Expected loss 期望损失[ ] Exploding Gradient Problem 梯度爆炸问题[ ] Exponential loss function 指数损失函数[ ] Extreme Learning Machine/ELM 超限学习机Letter F[ ] Factorization 因子分解[ ] False negative 假负类[ ] False positive 假正类[ ] False Positive Rate/FPR 假正例率[ ] Feature engineering 特征工程[ ] Feature selection 特征选择[ ] Feature vector 特征向量[ ] Featured Learning 特征学习[ ] Feedforward Neural Networks/FNN 前馈神经网络[ ] Fine-tuning 微调[ ] Flipping output 翻转法[ ] Fluctuation 震荡[ ] Forward stagewise algorithm 前向分步算法[ ] Frequentist 频率主义学派[ ] Full-rank matrix 满秩矩阵[400 ] Functional neuron 功能神经元Letter G[ ] Gain ratio 增益率[ ] Game theory 博弈论[ ] Gaussian kernel function 高斯核函数[ ] Gaussian Mixture Model 高斯混合模型[ ] General Problem Solving 通用问题求解[ ] Generalization 泛化[ ] Generalization error 泛化误差[ ] Generalization error bound 泛化误差上界[ ] Generalized Lagrange function 广义拉格朗日函数[ ] Generalized linear model 广义线性模型[ ] Generalized Rayleigh quotient 广义瑞利商[ ] Generative Adversarial Networks/GAN 生成对抗网络[ ] Generative Model 生成模型[ ] Generator 生成器[ ] Genetic Algorithm/GA 遗传算法[ ] Gibbs sampling 吉布斯采样[ ] Gini index 基尼指数[ ] Global minimum 全局最小[ ] Global Optimization 全局优化[ ] Gradient boosting 梯度提升[ ] Gradient Descent 梯度下降[ ] Graph theory 图论[ ] Ground-truth 真相／真实Letter H[ ] Hard margin 硬间隔[ ] Hard voting 硬投票[ ] Harmonic mean 调和平均[ ] Hesse matrix 海塞矩阵[ ] Hidden dynamic model 隐动态模型[ ] Hidden layer 隐藏层[ ] Hidden Markov Model/HMM 隐马尔可夫模型[ ] Hierarchical clustering 层次聚类[ ] Hilbert space 希尔伯特空间[ ] Hinge loss function 合页损失函数[ ] Hold-out 留出法[ ] Homogeneous 同质[ ] Hybrid computing 混合计算[ ] Hyperparameter 超参数[ ] Hypothesis 假设[ ] Hypothesis test 假设验证Letter I[ ] ICML 国际机器学习会议[450 ] Improved iterative scaling/IIS 改进的迭代尺度法[ ] Incremental learning 增量学习[ ] Independent and identically distributed/i.i.d. 独立同分布[ ] Independent Component Analysis/ICA 独立成分分析[ ] Indicator function 指示函数[ ] Individual learner 个体学习器[ ] Induction 归纳[ ] Inductive bias 归纳偏好[ ] Inductive learning 归纳学习[ ] Inductive Logic Programming／ILP 归纳逻辑程序设计[ ] Information entropy 信息熵[ ] Information gain 信息增益[ ] Input layer 输入层[ ] Insensitive loss 不敏感损失[ ] Inter-cluster similarity 簇间相似度[ ] International Conference for Machine Learning/ICML 国际机器学习大会[ ] Intra-cluster similarity 簇内相似度[ ] Intrinsic value 固有值[ ] Isometric Mapping/Isomap 等度量映射[ ] Isotonic regression 等分回归[ ] Iterative Dichotomiser 迭代二分器Letter K[ ] Kernel method 核方法[ ] Kernel trick 核技巧[ ] Kernelized Linear Discriminant Analysis／KLDA 核线性判别分析[ ] K-fold cross validation k 折交叉验证／k 倍交叉验证[ ] K-Means Clustering K –均值聚类[ ] K-Nearest Neighbours Algorithm/KNN K近邻算法[ ] Knowledge base 知识库[ ] Knowledge Representation 知识表征Letter L[ ] Label space 标记空间[ ] Lagrange duality 拉格朗日对偶性[ ] Lagrange multiplier 拉格朗日乘子[ ] Laplace smoothing 拉普拉斯平滑[ ] Laplacian correction 拉普拉斯修正[ ] Latent Dirichlet Allocation 隐狄利克雷分布[ ] Latent semantic analysis 潜在语义分析[ ] Latent variable 隐变量[ ] Lazy learning 懒惰学习[ ] Learner 学习器[ ] Learning by analogy 类比学习[ ] Learning rate 学习率[ ] Learning Vector Quantization/LVQ 学习向量量化[ ] Least squares regression tree 最小二乘回归树[ ] Leave-One-Out/LOO 留一法[500 ] linear chain conditional random field 线性链条件随机场[ ] Linear Discriminant Analysis／LDA 线性判别分析[ ] Linear model 线性模型[ ] Linear Regression 线性回归[ ] Link function 联系函数[ ] Local Markov property 局部马尔可夫性[ ] Local minimum 局部最小[ ] Log likelihood 对数似然[ ] Log odds／logit 对数几率[ ] Logistic Regression Logistic 回归[ ] Log-likelihood 对数似然[ ] Log-linear regression 对数线性回归[ ] Long-Short Term Memory/LSTM 长短期记忆[ ] Loss function 损失函数Letter M[ ] Machine translation/MT 机器翻译[ ] Macron-P 宏查准率[ ] Macron-R 宏查全率[ ] Majority voting 绝对多数投票法[ ] Manifold assumption 流形假设[ ] Manifold learning 流形学习[ ] Margin theory 间隔理论[ ] Marginal distribution 边际分布[ ] Marginal independence 边际独立性[ ] Marginalization 边际化[ ] Markov Chain Monte Carlo/MCMC 马尔可夫链蒙特卡罗方法[ ] Markov Random Field 马尔可夫随机场[ ] Maximal clique 最大团[ ] Maximum Likelihood Estimation/MLE 极大似然估计／极大似然法[ ] Maximum margin 最大间隔[ ] Maximum weighted spanning tree 最大带权生成树[ ] Max-Pooling 最大池化[ ] Mean squared error 均方误差[ ] Meta-learner 元学习器[ ] Metric learning 度量学习[ ] Micro-P 微查准率[ ] Micro-R 微查全率[ ] Minimal Description Length/MDL 最小描述长度[ ] Minimax game 极小极大博弈[ ] Misclassification cost 误分类成本[ ] Mixture of experts 混合专家[ ] Momentum 动量[ ] Moral graph 道德图／端正图[ ] Multi-class classification 多分类[ ] Multi-document summarization 多文档摘要[ ] Multi-layer feedforward neural networks 多层前馈神经网络[ ] Multilayer Perceptron/MLP 多层感知器[ ] Multimodal learning 多模态学习[550 ] Multiple Dimensional Scaling 多维缩放[ ] Multiple linear regression 多元线性回归[ ] Multi-response Linear Regression ／MLR 多响应线性回归[ ] Mutual information 互信息Letter N[ ] Naive bayes 朴素贝叶斯[ ] Naive Bayes Classifier 朴素贝叶斯分类器[ ] Named entity recognition 命名实体识别[ ] Nash equilibrium 纳什均衡[ ] Natural language generation/NLG 自然语言生成[ ] Natural language processing 自然语言处理[ ] Negative class 负类[ ] Negative correlation 负相关法[ ] Negative Log Likelihood 负对数似然[ ] Neighbourhood Component Analysis/NCA 近邻成分分析[ ] Neural Machine Translation 神经机器翻译[ ] Neural Turing Machine 神经图灵机[ ] Newton method 牛顿法[ ] NIPS 国际神经信息处理系统会议[ ] No Free Lunch Theorem／NFL 没有免费的午餐定理[ ] Noise-contrastive estimation 噪音对比估计[ ] Nominal attribute 列名属性[ ] Non-convex optimization 非凸优化[ ] Nonlinear model 非线性模型[ ] Non-metric distance 非度量距离[ ] Non-negative matrix factorization 非负矩阵分解[ ] Non-ordinal attribute 无序属性[ ] Non-Saturating Game 非饱和博弈[ ] Norm 范数[ ] Normalization 归一化[ ] Nuclear norm 核范数[ ] Numerical attribute 数值属性Letter O[ ] Objective function 目标函数[ ] Oblique decision tree 斜决策树[ ] Occam’s razor 奥卡姆剃刀[ ] Odds 几率[ ] Off-Policy 离策略[ ] One shot learning 一次性学习[ ] One-Dependent Estimator／ODE 独依赖估计[ ] On-Policy 在策略[ ] Ordinal attribute 有序属性[ ] Out-of-bag estimate 包外估计[ ] Output layer 输出层[ ] Output smearing 输出调制法[ ] Overfitting 过拟合／过配[600 ] Oversampling 过采样Letter P[ ] Paired t-test 成对t 检验[ ] Pairwise 成对型[ ] Pairwise Markov property 成对马尔可夫性[ ] Parameter 参数[ ] Parameter estimation 参数估计[ ] Parameter tuning 调参[ ] Parse tree 解析树[ ] Particle Swarm Optimization/PSO 粒子群优化算法[ ] Part-of-speech tagging 词性标注[ ] Perceptron 感知机[ ] Performance measure 性能度量[ ] Plug and Play Generative Network 即插即用生成网络[ ] Plurality voting 相对多数投票法[ ] Polarity detection 极性检测[ ] Polynomial kernel function 多项式核函数[ ] Pooling 池化[ ] Positive class 正类[ ] Positive definite matrix 正定矩阵[ ] Post-hoc test 后续检验[ ] Post-pruning 后剪枝[ ] potential function 势函数[ ] Precision 查准率／准确率[ ] Prepruning 预剪枝[ ] Principal component analysis/PCA 主成分分析[ ] Principle of multiple explanations 多释原则[ ] Prior 先验[ ] Probability Graphical Model 概率图模型[ ] Proximal Gradient Descent/PGD 近端梯度下降[ ] Pruning 剪枝[ ] Pseudo-label 伪标记[ ] Letter Q[ ] Quantized Neural Network 量子化神经网络[ ] Quantum computer 量子计算机[ ] Quantum Computing 量子计算[ ] Quasi Newton method 拟牛顿法Letter R[ ] Radial Basis Function／RBF 径向基函数[ ] Random Forest Algorithm 随机森林算法[ ] Random walk 随机漫步[ ] Recall 查全率／召回率[ ] Receiver Operating Characteristic/ROC 受试者工作特征[ ] Rectified Linear Unit/ReLU 线性修正单元[650 ] Recurrent Neural Network 循环神经网络[ ] Recursive neural network 递归神经网络[ ] Reference model 参考模型[ ] Regression 回归[ ] Regularization 正则化[ ] Reinforcement learning/RL 强化学习[ ] Representation learning 表征学习[ ] Representer theorem 表示定理[ ] reproducing kernel Hilbert space/RKHS 再生核希尔伯特空间[ ] Re-sampling 重采样法[ ] Rescaling 再缩放[ ] Residual Mapping 残差映射[ ] Residual Network 残差网络[ ] Restricted Boltzmann Machine/RBM 受限玻尔兹曼机[ ] Restricted Isometry Property/RIP 限定等距性[ ] Re-weighting 重赋权法[ ] Robustness 稳健性/鲁棒性[ ] Root node 根结点[ ] Rule Engine 规则引擎[ ] Rule learning 规则学习Letter S[ ] Saddle point 鞍点[ ] Sample space 样本空间[ ] Sampling 采样[ ] Score function 评分函数[ ] Self-Driving 自动驾驶[ ] Self-Organizing Map／SOM 自组织映射[ ] Semi-naive Bayes classifiers 半朴素贝叶斯分类器[ ] Semi-Supervised Learning 半监督学习[ ] semi-Supervised Support Vector Machine 半监督支持向量机[ ] Sentiment analysis 情感分析[ ] Separating hyperplane 分离超平面[ ] Sigmoid function Sigmoid 函数[ ] Similarity measure 相似度度量[ ] Simulated annealing 模拟退火[ ] Simultaneous localization and mapping 同步定位与地图构建[ ] Singular Value Decomposition 奇异值分解[ ] Slack variables 松弛变量[ ] Smoothing 平滑[ ] Soft margin 软间隔[ ] Soft margin maximization 软间隔最大化[ ] Soft voting 软投票[ ] Sparse representation 稀疏表征[ ] Sparsity 稀疏性[ ] Specialization 特化[ ] Spectral Clustering 谱聚类[ ] Speech Recognition 语音识别[ ] Splitting variable 切分变量[700 ] Squashing function 挤压函数[ ] Stability-plasticity dilemma 可塑性-稳定性困境[ ] Statistical learning 统计学习[ ] Status feature function 状态特征函[ ] Stochastic gradient descent 随机梯度下降[ ] Stratified sampling 分层采样[ ] Structural risk 结构风险[ ] Structural risk minimization/SRM 结构风险最小化[ ] Subspace 子空间[ ] Supervised learning 监督学习／有导师学习[ ] support vector expansion 支持向量展式[ ] Support Vector Machine/SVM 支持向量机[ ] Surrogat loss 替代损失[ ] Surrogate function 替代函数[ ] Symbolic learning 符号学习[ ] Symbolism 符号主义[ ] Synset 同义词集Letter T[ ] T-Distribution Stochastic Neighbour Embedding/t-SNE T –分布随机近邻嵌入[ ] Tensor 张量[ ] Tensor Processing Units/TPU 张量处理单元[ ] The least square method 最小二乘法[ ] Threshold 阈值[ ] Threshold logic unit 阈值逻辑单元[ ] Threshold-moving 阈值移动[ ] Time Step 时间步骤[ ] Tokenization 标记化[ ] Training error 训练误差[ ] Training instance 训练示例／训练例[ ] Transductive learning 直推学习[ ] Transfer learning 迁移学习[ ] Treebank 树库[ ] Tria-by-error 试错法[ ] True negative 真负类[ ] True positive 真正类[ ] True Positive Rate/TPR 真正例率[ ] Turing Machine 图灵机[ ] Twice-learning 二次学习Letter U[ ] Underfitting 欠拟合／欠配[ ] Undersampling 欠采样[ ] Understandability 可理解性[ ] Unequal cost 非均等代价[ ] Unit-step function 单位阶跃函数[ ] Univariate decision tree 单变量决策树[ ] Unsupervised learning 无监督学习／无导师学习[ ] Unsupervised layer-wise training 无监督逐层训练[ ] Upsampling 上采样Letter V[ ] Vanishing Gradient Problem 梯度消失问题[ ] Variational inference 变分推断[ ] VC Theory VC维理论[ ] Version space 版本空间[ ] Viterbi algorithm 维特比算法[760 ] Von Neumann architecture 冯· 诺伊曼架构Letter W[ ] Wasserstein GAN/WGAN Wasserstein生成对抗网络[ ] Weak learner 弱学习器[ ] Weight 权重[ ] Weight sharing 权共享[ ] Weighted voting 加权投票法[ ] Within-class scatter matrix 类内散度矩阵[ ] Word embedding 词嵌入[ ] Word sense disambiguation 词义消歧Letter Z[ ] Zero-data learning 零数据学习[ ] Zero-shot learning 零次学习第三部分A[ ] approximations近似值[ ] arbitrary随意的[ ] affine仿射的[ ] arbitrary任意的[ ] amino acid氨基酸[ ] amenable经得起检验的[ ] axiom公理，原则[ ] abstract提取[ ] architecture架构，体系结构；建造业[ ] absolute绝对的[ ] arsenal军火库[ ] assignment分配[ ] algebra线性代数[ ] asymptotically无症状的[ ] appropriate恰当的B[ ] bias偏差[ ] brevity简短，简洁；短暂[800 ] broader广泛[ ] briefly简短的[ ] batch批量C[ ] convergence 收敛，集中到一点[ ] convex凸的[ ] contours轮廓[ ] constraint约束[ ] constant常理[ ] commercial商务的[ ] complementarity补充[ ] coordinate ascent同等级上升[ ] clipping剪下物；剪报；修剪[ ] component分量；部件[ ] continuous连续的[ ] covariance协方差[ ] canonical正规的，正则的[ ] concave非凸的[ ] corresponds相符合；相当；通信[ ] corollary推论[ ] concrete具体的事物，实在的东西[ ] cross validation交叉验证[ ] correlation相互关系[ ] convention约定[ ] cluster一簇[ ] centroids 质心，形心[ ] converge收敛[ ] computationally计算(机)的[ ] calculus计算D[ ] derive获得，取得[ ] dual二元的[ ] duality二元性；二象性；对偶性[ ] derivation求导；得到；起源[ ] denote预示，表示，是…的标志；意味着，[逻]指称[ ] divergence 散度；发散性[ ] dimension尺度，规格；维数[ ] dot小圆点[ ] distortion变形[ ] density概率密度函数[ ] discrete离散的[ ] discriminative有识别能力的[ ] diagonal对角[ ] dispersion分散，散开[ ] determinant决定因素[849 ] disjoint不相交的E[ ] encounter遇到[ ] ellipses椭圆[ ] equality等式[ ] extra额外的[ ] empirical经验；观察[ ] ennmerate例举，计数[ ] exceed超过，越出[ ] expectation期望[ ] efficient生效的[ ] endow赋予[ ] explicitly清楚的[ ] exponential family指数家族[ ] equivalently等价的F[ ] feasible可行的[ ] forary初次尝试[ ] finite有限的，限定的[ ] forgo摒弃，放弃[ ] fliter过滤[ ] frequentist最常发生的[ ] forward search前向式搜索[ ] formalize使定形G[ ] generalized归纳的[ ] generalization概括，归纳；普遍化；判断（根据不足）[ ] guarantee保证；抵押品[ ] generate形成，产生[ ] geometric margins几何边界[ ] gap裂口[ ] generative生产的；有生产力的H[ ] heuristic启发式的；启发法；启发程序[ ] hone怀恋；磨[ ] hyperplane超平面L[ ] initial最初的[ ] implement执行[ ] intuitive凭直觉获知的[ ] incremental增加的[900 ] intercept截距[ ] intuitious直觉[ ] instantiation例子[ ] indicator指示物，指示器[ ] interative重复的，迭代的[ ] integral积分[ ] identical相等的；完全相同的[ ] indicate表示，指出[ ] invariance不变性，恒定性[ ] impose把…强加于[ ] intermediate中间的[ ] interpretation解释，翻译J[ ] joint distribution联合概率L[ ] lieu替代[ ] logarithmic对数的，用对数表示的[ ] latent潜在的[ ] Leave-one-out cross validation留一法交叉验证M[ ] magnitude巨大[ ] mapping绘图，制图；映射[ ] matrix矩阵[ ] mutual相互的，共同的[ ] monotonically单调的[ ] minor较小的，次要的[ ] multinomial多项的[ ] multi-class classification二分类问题N[ ] nasty讨厌的[ ] notation标志，注释[ ] naïve朴素的O[ ] obtain得到[ ] oscillate摆动[ ] optimization problem最优化问题[ ] objective function目标函数[ ] optimal最理想的[ ] orthogonal(矢量，矩阵等)正交的[ ] orientation方向[ ] ordinary普通的[ ] occasionally偶然的P[ ] partial derivative偏导数[ ] property性质[ ] proportional成比例的[ ] primal原始的，最初的[ ] permit允许[ ] pseudocode伪代码[ ] permissible可允许的[ ] polynomial多项式[ ] preliminary预备[ ] precision精度[ ] perturbation 不安，扰乱[ ] poist假定，设想[ ] positive semi-definite半正定的[ ] parentheses圆括号[ ] posterior probability后验概率[ ] plementarity补充[ ] pictorially图像的[ ] parameterize确定…的参数[ ] poisson distribution柏松分布[ ] pertinent相关的Q[ ] quadratic二次的[ ] quantity量，数量；分量[ ] query疑问的R[ ] regularization使系统化；调整[ ] reoptimize重新优化[ ] restrict限制；限定；约束[ ] reminiscent回忆往事的；提醒的；使人联想…的（of）[ ] remark注意[ ] random variable随机变量[ ] respect考虑[ ] respectively各自的；分别的[ ] redundant过多的；冗余的S[ ] susceptible敏感的[ ] stochastic可能的；随机的[ ] symmetric对称的[ ] sophisticated复杂的[ ] spurious假的；伪造的[ ] subtract减去；减法器[ ] simultaneously同时发生地；同步地[ ] suffice满足[ ] scarce稀有的，难得的[ ] split分解，分离[ ] subset子集[ ] statistic统计量[ ] successive iteratious连续的迭代[ ] scale标度[ ] sort of有几分的[ ] squares平方T[ ] trajectory轨迹[ ] temporarily暂时的[ ] terminology专用名词[ ] tolerance容忍；公差[ ] thumb翻阅[ ] threshold阈，临界[ ] theorem定理[ ] tangent正弦U[ ] unit-length vector单位向量V[ ] valid有效的，正确的[ ] variance方差[ ] variable变量；变元[ ] vocabulary词汇[ ] valued经估价的；宝贵的[ ] W [1038 ] wrapper包装。
WeMix 4.0.3 混合效应模型使用多层次伪最大似然估计说明书
Package‘WeMix’November3,2023Version4.0.3Date2023-11-02Title Weighted Mixed-Effects Models Using Multilevel Pseudo MaximumLikelihood EstimationMaintainer Paul Bailey<***************>Depends lme4,R(>=3.5.0)Imports numDeriv,Matrix(>=1.5-4.1),methods,minqa,matrixStatsSuggests testthat,knitr,rmarkdown,withr,tidyr,EdSurvey(>=4.0.0),glmmTMBDescription Run mixed-effects models that include weights at every level.The WeMix pack-agefits a weighted mixed model,also known as a multilevel,mixed,or hierarchical lin-ear model(HLM).The weights could be inverse selection probabilities,such as those devel-oped for an education survey where schools are sampled probabilistically,and then students in-side of those schools are sampled probabilistically.Although mixed-effects models are al-ready available in R,WeMix is unique in implementing methods for mixed models us-ing weights at multiple levels.Both linear and logit models are supported.Mod-els may have up to three levels.Random effects are estimated using the PIRLS algo-rithm from'lme4pureR'(Walker and Bates(2013)<https:///lme4/lme4pureR>). License GPL-2VignetteBuilder knitrByteCompile trueNote This publication was prepared for NCES under Contract No.ED-IES-12-D-0002with American Institutes for Research.Mentionof trade names,commercial products,or organizations does notimply endorsement by the ernment.RoxygenNote7.2.3URL https://american-institutes-for-research.github.io/WeMix/BugReports https:///American-Institutes-for-Research/WeMix/issues Encoding UTF-8NeedsCompilation no12WeMix-package Author Emmanuel Sikali[pdr],Paul Bailey[aut,cre],Blue Webb[aut],Claire Kelley[aut],Trang Nguyen[aut],Huade Huo[aut],Steve Walker[cph](lme4pureR PIRLS function),Doug Bates[cph](lme4pureR PIRLS function),Eric Buehler[ctb],Christian Christrup Kjeldsen[ctb]Repository CRANDate/Publication2023-11-0305:30:02UTCR topics documented:WeMix-package (2)mix (3)waldTest (7)Index9 WeMix-package Estimate Weighted Mixed-Effects ModelsDescriptionThe WeMix package estimates mixed-effects models(also called multilevel models,mixed models, or HLMs)with survey weights.DetailsThis package is unique in allowing users to analyze data that may have unequal selection prob-ability at both the individual and group levels.For linear models,the model is evaluated with a weighted version of the estimating equations used by Bates,Maechler,Bolker,and Walker(2015) in lme4.In the non-linear case,WeMix uses numerical integration(Gauss-Hermite and adaptive Gauss-Hermite quadrature)to estimate mixed-effects models with survey weights at all levels of the model.Note that lme4is the preferred way to estimate such models when there are no survey weights or weights only at the lowest level,and our estimation starts with parameters estimated in lme4.WeMix is intended for use in cases where there are weights at all levels and is only for use with fully nested data.To start using WeMix,see the vignettes covering the mathematical background of mixed-effects model estimation and use the mix function to estimate e browseVignettes(package="WeMix")to see the vignettes.mix3ReferencesBates,D.,Maechler,M.,Bolker,B.,&Walker,S.(2015).Fitting Linear Mixed-Effects ModelsUsing lme4.Journal of Statistical Software,67(1),1-48.doi:10.18637/jss.v067.i01Rabe-Hesketh,S.,&Skrondal,A.(2006)Multilevel Modelling of Complex Survey Data.Journal ofthe Royal Statistical Society:Series A(Statistics in Society),169,805-827.https:///10.1111/j.1467-985X.2006.00426.xBates,D.&Pinheiro,J.C.(1998).Computational Methods for Multilevel Modelling.Bell labsworking paper.mix Survey Weighted Mixed-Effects ModelsDescriptionImplements a survey weighted mixed-effects model using the provided formula.Usagemix(formula,data,weights,cWeights=FALSE,center_group=NULL,center_grand=NULL,max_iteration=10,nQuad=13L,run=TRUE,verbose=FALSE,acc0=120,keepAdapting=FALSE,start=NULL,fast=FALSE,family=NULL)Argumentsformula a formula object in the style of lme4that creates the model.data a data frame containing the raw data for the model.weights a character vector of names of weight variables found in the data frame startswith units(level1)and increasing(larger groups).cWeights logical,set to TRUE to use conditional weights.Otherwise,mix expects uncon-ditional weights.4mix center_group a list where the name of each element is the name of the aggregation level, and the element is a formula of variable names to be group mean centered;for example to group mean center gender and age within the group student:list("student"=~gender+age),default value of NULL does not perform anygroup mean centering.center_grand a formula of variable names to be grand mean centered,for example to center the variable education by overall mean of education:~education.Default isNULL which does no centering.max_iteration a optional integer,for non-linear modelsfit by adaptive quadrature which lim-its number of iterations allowed before quitting.Defaults to10.This is usedbecause if the likelihood surface isflat,models may run for a very long timewithout converging.nQuad an optional integer number of quadrature points to evaluate models solved by adaptive quadrature.Only non-linear models are evaluated with adaptive quadra-ture.See notes for additional guidelines.run logical;TRUE runs the model while FALSE provides partial output for debugging or testing.Only applies to non-linear models evaluated by adaptive quadrature.verbose logical,default FALSE;set to TRUE to print results of intermediate steps of adap-tive quadrature.Only applies to non-linear models.acc0deprecated;ignored.keepAdapting logical,set to TRUE when the adaptive quadrature should adapt after every New-ton step.Defaults to FALSE.FALSE should be used for faster(but less accurate)results.Only applies to non-linear models.start optional numeric vector representing the point at which the model should start optimization;takes the shape of c(coef,vars)from results(see help).fast logical;deprecatedfamily the family;optionally used to specify generalized linear mixed models.Cur-rently only binomial()and poisson()are supported.DetailsLinear models are solved using a modification of the analytic solution developed by Bates and Pinheiro(1998).Non-linear models are solved using adaptive quadrature following the methods in STATA’s GLAMMM(Rabe-Hesketh&Skrondal,2006)and Pineiro and Chao(2006).The posterior modes used in adaptive quadrature are determined following the method in lme4pureR(Walker& Bates,2015).For additional details,see the vignettes Weighted Mixed Models:Adaptive Quadra-ture and Weighted Mixed Models:Analytical Solution which provide extensive examples as well as a description of the mathematical basis of the estimation procedure and comparisons to model specifications in other common software.Notes:•Standard errors of random effect variances are robust;see vignette for details.•To see the function that is maximized in the estimation of this model,see the section on"Model Fitting"in the Introduction to Mixed Effect Models With WeMix vignette.•When all weights above the individual level are1,this is similar to a lmer and you should use lme4because it is much faster.mix5•If starting coefficients are not provided they are estimated using lme4.•For non-linear models,when the variance of a random effect is very low(<.1),WeMix doesn’t estimate it,because very low variances create problems with numerical evaluation.In these cases,consider estimating without that random effect.•The model is estimated by maximum likelihood estimation.•Non-linear models may have up to3nested levels.•To choose the number of quadrature points for non-linear model evaluation,a balance is needed between accuracy and speed;estimation time increases quadratically with the number of points chosen.In addition,an odd number of points is traditionally used.We recommend starting at13and increasing or decreasing as needed.Valueobject of class WeMixResults.This is a list with elements:lnlf function,the likelihood function.lnl numeric,the log-likelihood of the model.coef numeric vector,the estimated coefficients of the model.ranefs the group-level random effects.SE the cluste robust(CR-0)standard errors of thefixed effects.vars numeric vector,the random effect variances.theta the theta vector.call the original call used.levels integer,the number of levels in the model.ICC numeric,the intraclass correlation coefficient.CMODE the conditional mean of the random effects.invHessian inverse of the second derivative of the likelihood function.ICC the interclass correlation.is_adaptive logical,indicates if adaptive quadrature was used for estimation.sigma the sigma value.ngroups the number of observations in each group.varDF the variance data frame in the format of the variance data frame returned by lme4.varVC the variance-covariance matrix of the random effects.cov_mat the variance-covariance matrix of thefixed effects.var_theta the variance covariance matrix of the theta terms.wgtStats statistics regarding weights,by level.ranefMat list of matrixes;each list element is a matrix of random effects by level with IDs in the rows and random effects in the columns.Author(s)Paul Bailey,Blue Webb,Claire Kelley,and Trang Nguyen6mix Examples##Not run:library(lme4)data(sleepstudy)ss1<-sleepstudy#Create weightsss1$W1<-ifelse(ss1$Subject%in%c(308,309,310),2,1)ss1$W2<-1#Run random-intercept2-level modeltwo_level<-mix(Reaction~Days+(1|Subject),data=ss1,weights=c("W1","W2"))#Run random-intercept2-level model with group-mean centeringgrp_centered<-mix(Reaction~Days+(1|Subject),data=ss1,weights=c("W1","W2"),center_group=list("Subject"=~Days))#Run three level model with random slope and intercept.#add group variables for3level modelss1$Group<-3ss1$Group<-ifelse(as.numeric(ss1$Subject)%%10<7,2,ss1$Group)ss1$Group<-ifelse(as.numeric(ss1$Subject)%%10<4,1,ss1$Group)#level-3weightsss1$W3<-ifelse(ss1$Group==2,2,1)three_level<-mix(Reaction~Days+(1|Subject)+(1+Days|Group),data=ss1,weights=c("W1","W2","W3"))#Conditional Weights#use vignette examplelibrary(EdSurvey)#read in datadownloadPISA("~/",year=2012)cntl<-readPISA("~/PISA/2012",countries="USA")data<-getData(cntl,c("schoolid","pv1math","st29q03","sc14q02","st04q01","escs","w_fschwt","w_fstuwt"),omittedLevels=FALSE,addAttributes=FALSE)#Remove NA and omitted Levelsom<-c("Invalid","N/A","Missing","Miss",NA,"(Missing)")for(i in1:ncol(data)){data<-data[!data[,i]%in%om,]}#relevel factors for modeldata$st29q03<-relevel(data$st29q03,ref="Strongly agree")data$sc14q02<-relevel(data$sc14q02,ref="Not at all")#run with unconditional weightsm1u<-mix(pv1math~st29q03+sc14q02+st04q01+escs+(1|schoolid),data=data,weights=c("w_fstuwt","w_fschwt"))summary(m1u)#conditional weightsdata$pwt2<-data$w_fschwtdata$pwt1<-data$w_fstuwt/data$w_fschwt#run with conditional weightsm1c<-mix(pv1math~st29q03+sc14q02+st04q01+escs+(1|schoolid),data=data,weights=c("pwt1","pwt2"),cWeights=TRUE)summary(m1c)#the results are,up to rounding,the same in m1u and m1c,only the calls are different ##End(Not run)waldTest Mixed Model Wald TestsDescriptionThis function calculates the Wald test for eitherfixed effects or variance parameters.UsagewaldTest(fittedModel,type=c("beta","Lambda"),coefs=NA,hypothesis=NA)ArgumentsfittedModel a model of class WeMixResults that is the result of a call to mixtype a string,one of"beta"(to test thefixed effects)or"Lambda"(to test the variance-covariance parameters for the random effects)coefs a vector containing the names of the coefficients to test.For type="beta"these must be the variable names exactly as they appear in thefixed effects table of thesummary.For type="Lambda"these must be the names exactly as they appearin the theta element of thefitted model.hypothesis the hypothesized values of beta or Lambda.If NA(the default)0will be used.DetailsBy default this function tests against the null hypothesis that all coefficients are zero.To identify which coefficients to test use the name exactly as it appears in the summary of the object.ValueObject of class WeMixWaldTest.This is a list with the following elements:wald the value of the test statistic.p the p-value for the test statistic.Based on the probabilty of the test statistic under the chi-squared distribution.df degrees of freedom used to calculate p-value.H0The vector(for a test of beta)or matrix(for tests of Lambda)containing the null hypothesis for the test.HA The vector(for a test of beta)or matrix(for tests of Lambda)containing the alternative hypothesis for the test(i.e.the values calculated by thefitted modelbeing tested.)Examples##Not run:library(lme4)#to use the example datasleepstudyU<-sleepstudysleepstudyU$weight1L1<-1sleepstudyU$weight1L2<-1wm0<-mix(Reaction~Days+(1|Subject),data=sleepstudyU,weights=c("weight1L1","weight1L2"))wm1<-mix(Reaction~Days+(1+Days|Subject),data=sleepstudyU,weights=c("weight1L1","weight1L2"))waldTest(wm0,type="beta")#test all betas#test only beta for dayswaldTest(wm0,type="beta",coefs="Days")#test only beta for intercept against hypothesis that it is1waldTest(wm0,type="beta",coefs="(Intercept)",hypothesis=c(1))waldTest(wm1,type="Lambda")#test all values of Lambda#test only some Lambdas.The names are the same as names(wm1$theta)waldTest(wm1,type="Lambda",coefs="Subject.(Intercept)")#specify test valueswaldTest(wm1,type="Lambda",coefs="Subject.(Intercept)",hypothesis=c(1))##End(Not run)Indexmix,3,7waldTest,7WeMix-package,29。
深度多网络嵌入聚类
深度多网络嵌入聚类陈 锐1,2,3 唐永强2 张彩霞1,3 张文生2 郝志峰1摘 要 现有的深度无监督聚类方法通常局限于单网络结构设计,无法充分利用多种异构网络提取特征中蕴含的互补信息,制约深度聚类方法性能的进一步提升.为此,文中提出深度多网络嵌入聚类算法(DMNEC).首先,以端到端的方式预训练多个异构网络分支,获取各网络的初始化参数.在此基础上,定义多网络软分配,借助多网络辅助目标分布建立面向聚类的KL散度损失.与此同时,利用样本重建损失对预训练阶段的解码网络进行微调,保留数据的局部结构性质,避免特征空间发生扭曲.通过随机梯度下降与反向传播优化重建损失与聚类损失的加权和,联合学习多网络表征及其簇分配.在4个公开图像数据集上的实验验证文中算法的优越性.关键词 深度无监督聚类,数据表征,多网络分支,互补信息,局部结构保留引用格式 陈锐,唐永强,张彩霞,张文生,郝志峰.深度多网络嵌入聚类.模式识别与人工智能,2021,34(1):14-24.DOI 10.16451/ki.issn1003⁃6059.202101002 中图法分类号 TP391Deep Multi⁃network Embedded ClusteringCHEN Rui1,2,3,TANG Yongqiang2,ZHANG Caixia1,3,ZHANG Wensheng2,HAO Zhifeng1 ABSTRACT Existing deep unsupervised clustering methods cannot make full use of the complementary information between the extracted features of different network structures due to the single network structure in them,and thus the clustering performance is restricted.A deep multi⁃network embedded clustering(DMNEC)algorithm is proposed to solve this problem.Firstly,the initialization parameters of each network are obtained by pretraining multi⁃network branches in an end⁃to⁃end manner.On this basis, the multi⁃network soft assignment is defined,then the clustering⁃oriented Kullback⁃Leibler divergence loss is established with the help of the multi⁃network auxiliary target distribution.The decoding network in the pretraining stage is finetuned via reconstruction loss to preserve the local structure and avoid the distortion of feature space.The weighted sum of reconstruction loss and clustering loss is optimized by stochastic gradient descent(SGD)and back propagation(BP)to jointly learn multi⁃network representation and cluster assignment.Experiments on four public image datasets demonstrate the superiority of the proposed algorithm.收稿日期:2020-09-02;录用日期:2020-11-23 Manuscript received September2,2020; accepted November23,2020国家自然科学基金青年基金项目(No.61803087)㊁广东省教育厅特色创新项目(No.2019KTSCX192)㊁广东省基础与应用基础研究基金粤港澳应用数学中心项目(No.2020B1515310 003)㊁佛山核心技术攻关项目(No.1920001001367)资助Supported by Youth Program of National Natural Science Foun⁃dation of China(No.61803087),Feature Innovation Project of Guangdong Province Department of Education(No.2019KTSCX1 92),Guangdong⁃Hong Kong⁃Macao Applied Mathematics Center Project of Guangdong Basic and Applied Basic Research Fund (No.2020B1515310003),Foshan Core Technology Research Project(No.1920001001367)本文责任编委王士同Recommended by Associate Editor WANG Shitong1.佛山科学技术学院机电工程与自动化学院 佛山5282252.中国科学院自动化研究所精密感知与控制研究中心 北京1001903.广东省工程技术研究中心广东省智慧城市基础设施健康监测与评估工程技术研究中心 佛山5280001.School of Mechatronic Engineering and Automation,Foshan University,Foshan5282252.Research Center of Precision Sensing and Control,Institute of Automation,Chinese Academy of Sciences,Beijing1001903.Guangdong Province Smart City Infrastructure Health Monito⁃ring and Evaluation Engineering Technology Research Center, Guangdong Engineering Technology Research Center,Foshan 528000第34卷 第1期模式识别与人工智能Vol.34 No.1 2021年1月Pattern Recognition and Artificial Intelligence Jan. 2021Key Words Deep Unsupervised Clustering,Data Representation,Multi⁃network Branches,Comple⁃mentary Information,Local Structure PreservationCitation CHEN R,TANG Y Q,ZHANG C X,ZHANG W S,HAO Z F.Deep Multi⁃network Em⁃bedded Clustering.Pattern Recognition and Artificial Intelligence,2021,34(1):14-24. 无监督聚类[1]旨在对无标注数据的潜在分布结构进行分析,进而将相似样本划分至同一簇内,是数据科学和机器学习领域中的一个重要研究课题,已成功在图像分类[2-4]㊁数据可视化[5]等众多现实场景中得到广泛应用.无监督聚类方法的性能很大程度上取决于数据的表征,例如,对于传统聚类方法K⁃均值(K⁃means,KM)[6]或高斯混合模型(Gaussian Mixture Model,GMM)[7]而言,随着数据表征维度的升高,相似性度量不再可靠,致使聚类变得无效.针对这一问题,一种直观的解决方案是首先利用降维技术,如主成分分析(Principal Component Analysis, PCA)[8]㊁非负矩阵分解(Non⁃negative Matrix Factoriza⁃tion,NMF)[9]㊁多维缩放(Multiple Dimensional Sca⁃ling,MDS)[10]等,将数据从高维空间转至低维空间,再对降维后的数据进行聚类.然而,典型的PCA㊁NMF㊁MDS等降维方法本质上属于线性模型,难以深刻描述实际数据中蕴含的复杂分布结构.深度神经网络作为一种非线性关系建模的有力工具,可对输入的原始数据进行连续㊁非线性变换,从而获得高质量的数据表征.其中,自动编码器(Autoencoder,AE)[11]是深度神经网络的一种特殊形式,以完全无监督的方式学习数据表征.AE基本原理为:首先将原始数据嵌入低维表征空间,基于此空间重建原始数据.尽管AE在数据表征的非线性提取方面优势明显,但其学习到的表征往往难以与数据的聚类结构相适配.针对这一问题,近年来,学者们相继提出一系列深度无监督聚类方法,旨在利用深度神经网络同时学习原始数据的表征及其对应的簇分配.Yang 等[12]提出联合无监督学习(Joint Unsupervised Lear⁃ning,JULE),结合卷积神经网络(Convolutional Neural Network,CNN)[13]的表征学习与层次聚类,基于统一权重的三元组损失进行优化,取得较优的聚类表现,但计算复杂度较高.Xie等[14]提出深度嵌入聚类算法(Deep Embedded Clustering,DEC),预训练自动编码器,学习原始数据的低维表征,在自学习辅助目标分布的帮助下迭代优化基于KL散度的聚类损失.Guo等[15]提出改进的深度嵌入聚类算法(Improved DEC,IDEC),在DEC损失函数中加入重建项,用于保留特征空间属性.Li等[16]提出判别性提升聚类(Discriminatively Boosted Clustering,DBC),将DEC的预训练网络置换为CNN,提取包含像素空间信息的高质量特征,提升整体聚类性能.Yang 等[17]提出深度聚类网络(Deep Clustering Network,DCN),利用深度神经网络进行数据降维,学习一个与KM算法相适配的潜在表征空间,在此空间中交替优化网络参数㊁簇质心㊁簇分配.Fard等[18]提出深度K⁃均值(Deep K⁃means,DKM),对数据表征㊁簇质心及簇分配进行连续的端到端联合学习.Guo 等[19]提出自适应自步聚类(Adaptive Self⁃paced Clustering,ASPC),借鉴自步学习(Self⁃paced Lear⁃ning,SPL)思想,优先利用高置信度样本训练聚类网络,消除聚类边界样本的负面影响.Peng等[20]提出深度子空间聚类(Deep Subspace Clustering, DSC),计算样本的稀疏重构关系,保留样本的局部性子空间结构和全局性子空间结构.Chang等[21]提出深度自适应聚类(Deep Adaptive Clustering, DAC),假设成对图像为二进制关系,将聚类目标转化为二值成对分类问题.Bo等[22]提出结构化深度聚类网络(Structural Deep Clustering Network,SD⁃CN),将图卷积网络融入聚类网络中,旨在捕捉数据的结构化信息,获取更具判别性的数据表征,提升模型聚类性能.有关更多方法的介绍可参考文献[23]㊁文献[24].尽管上述深度方法显著提升聚类性能,但均运行于单网络结构环境下.DEC借助有效的辅助目标分布指导聚类,取得良好的性能.但是,基于单网络结构设计提取的表征质量不高,导致初始化表现不理想,经常出现数值不稳定情况,最终难以获得优越的聚类表现.众所周知,同个网络结构的不同层提取的特征存在互补性:低层包含较多细节信息,但是语义性较低;高层具有较强的语义信息,但是分辨率较低,对细节感知能力较差.受此启发,本文提出深度多网络嵌入聚类算法(Deep Multi⁃network Embedded Clus⁃tering,DMNEC),旨在将DEC从单网络结构扩展至多网络,捕获包含多种异构网络互补信息的高质量表征,解决由DEC基于单网络结构设计引起的聚类性能不佳问题.同时,为了避免特征空间扭曲,进一步引入局部结构保留(Local Structure Preservation,51第1期 陈 锐 等:深度多网络嵌入聚类LSP)机制.通过优化多网络表征与相应簇质心,达成聚类目的.在MNIST [25]㊁USPS [26]㊁FMNIST [27]㊁COIL20[28]基准图像数据集上的实验验证本文算法的有效性和优越性.1 相关工作1.1 深度嵌入聚类深度嵌入聚类(DEC)[14]框图如图1所示.图1 DEC 框图Fig.1 Framework of DECDEC 包含两个阶段:参数初始化阶段与联合学习阶段.在参数初始化阶段,DEC 首先使用3个去噪自动编码器(Denoising Autoencoder,DAE)进行逐层贪婪训练(Greedy Layer⁃Wise Training),将编码层按顺序连接,解码层按逆序连接,形成一个堆栈式自动编码器(Stacked Autoencoder,SAE).然后,以SAE作为基础模型,将原始数据x i ∈R D映射至潜在特征空间,用于学习低维表征z i ∈R d ,再基于表征Z ={z 1,z 2, ,z n }∈R d ×n执行KM 算法,获取初始化簇质心μj .在联合学习阶段,DEC 移除SAE 的解码网络g θ′(㊃),仅保留编码网络f θ(㊃),其中θ表示编码网络的参数集.在t 分布随机邻域嵌入(t⁃Distributed Stochastic Neighbour Embedding,t ⁃SNE)[5]的启发下,DEC 采用学生t 分布(Student′s t ⁃Distribution)作为软分配,度量低维表征z i =f θ(x i )与簇质心μj 之间的相似性:q ij æèçç=1+z i -μj2öø÷÷α-α+12∑æèççj′1+z i -μj′2öø÷÷α-α+12,其中,α表示学生t 分布的自由度,通常取值为1.q ij 被称为软分配,是因为它可解释为模型将第i 个样本分配给第j 个簇的概率.由于无监督任务中原始数据是未标注的,所以DEC 借助辅助目标分布p ij ,通过提高软分配的高置信度以指导聚类.辅助目标分布的定义为p ij =q 2ij∑iq æèççij ∑æèççj′q 2ij′∑iq öø÷÷öø÷÷ij′-1.利用上述软分配q ij 和辅助目标分布p ij ,DEC 优化如下基于KL 散度的聚类目标:L (z i ,μj )=∑i ∑j p ij æèççln p ij q öø÷÷ij .采用随机梯度下降(Stochastic Gradient Descent,SGD)与反向传播(Back Propagation,BP)迭代更新低维表征z i 和簇质心μj :z i =z i -λ∂L ∂z i ,μj =μj -λ∂L ∂μj,其中λ表示学习率.网络训练结束后,未标注数据的簇分配为s i =arg max jq ij .1.2 基于局部结构保留的深度嵌入聚类相比DEC,改进的深度嵌入聚类算法(IDEC)[15]保留数据的局部结构,框图如图2所示.图2 IDEC 框图Fig.2 Framework of IDEC为了实现这个目的,IDEC 保留解码网络,目标函数为L (z i ,μj )= ∑ni =1x i -g θ′(f θ(x i ))22+γ∑i ∑j p ij æèççln p ij q öø÷÷ij ,其中γ≥0用于权衡重建损失与聚类损失的重要性.将重建损失加入目标函数中可避免嵌入空间出现大范围的扭曲,较好地保留数据局部结构与特征属性.2 深度多网络嵌入聚类为了解决DEC 基于单网络结构设计引起的聚类性能不佳问题,本文提出深度多网络嵌入聚类算法(DMNEC),旨在将DEC 扩展为多网络结构设计,提升聚类性能.与DEC 相似,DMNEC 也包含特征提61模式识别与人工智能(PR&AI) 第34卷取阶段和网络微调阶段.具体而言,在特征提取阶段,首先以不同结构的自动编码器作为多网络分支,预训练多网络分支,提取每个网络分支的潜在表示.再将潜在表示进行拼接融合,得到包含互补信息的完备融合表示.基于融合表示执行KM算法,得到初始化簇质心.在网络微调阶段,引入多网络软分配及其辅助目标分布,保留多网络分支的解码网络.基于聚类损失和多网络分支重建损失微调网络,实现多网络分支特征和簇质心的联合学习.DMNEC框图如图3所示.图3 DMNEC框图Fig.3 Framework of the proposed DMNEC2.1 特征提取给定原始数据集X={x1,x2, ,x n}∈R D×n,DMNEC使用多个非线性编码映射建模x i∈R D与其潜在表示z(v)i∈R d×v之间的关系,再使用同等数量的非线性解码映射建模z(v)i与其重建数据x′i∈R D之间的关系:z(v)i=f(v)θ(x i),x′i=g(v)θ′(z(v)i),其中,f(v)θ(㊃)表示多网络编码映射,g(v)θ′(㊃)表示解码映射,v表示多网络索引,θ表示编码参数集,θ′表示解码参数集.由于不同网络结构f(v)→g(v)提取的特征具有不同特性,为了捕获这种异构互补信息,DMNEC通过最小化如下重建损失提取每个网络分支的低维特征:L(v)(r)=∑ni=1xi-g(v)θ′(f(v)θ(x i))22.(1)2.2 网络微调特征提取工作完成,将多个低维特征z(v)i进行拼接融合,此种融合机制可最大限度地保留每种特征的独有属性.通过执行KM算法获取初始化簇质心μ(v)j,以学生t分布衡量z(v)i与μ(v)j的相似度,引出多网络软分配:q ij=∑æèççv1+z(v)i-μ(v)j2öø÷÷α-α+12∑j′∑æèççv′1+z(v′)i-μ(v′)j2öø÷÷α-α+12,其中α=1表示学生t分布的自由度.由q ij可推导对应辅助目标分布:p ij=q2ij∑i qæèççij∑æèççj′q2ij′∑i qöø÷÷öø÷÷ij′-1.(2)基于上述多网络软分配Q和辅助目标分布P,以KL(P‖Q)作为聚类约束:L c=∑i∑j p ijæèççln p ij qöø÷÷ij.受IDEC[11]启发,进一步保留各个分支对应的解码网络,保留数据特征属性.因此,DMNEC的损失函数如下:L(z(v)i,μ(v)j)=L r+γL c,其中,γ≥0用于平衡多网络分支重建损失与聚类损失.基于上述损失微调网络,可最大限度地避免扭曲特征空间,最终实现对多网络分支特征和簇质心的联合学习.2.3 模型优化通过随机梯度下降和反向传播优化L(z(v)i,μ(v)j),有3种参数需要优化:簇质心μ(v)j㊁编码网络参数θ㊁解码网络参数θ′.由于α=1,为了简化符号,在此定义:d(v)ij=z(v)i-μ(v)j2,U=∑j′∑v′(1+d(v′)ij)-1.因此,聚类损失L c关于多网络分支特征z(v)i㊁簇质心μ(v)j的梯度如下:71第1期 陈 锐 等:深度多网络嵌入聚类∂L c ∂z (v )i =2∑j ∂L c ∂d (v )ij (z (v )i -μ(v )j ),∂L c ∂μ(v )j =-2∑j ∂L c ∂d (v )ij (z (v )i -μ(v )j ),推导可得∂L c∂d (v )ij=-∑t p it ∂ln qit ∂d (v )ij=-∑t p it ∂(ln q it U -ln U )∂d (v )ij=-∑t p æèççit 1q it U ∂q it U ∂d (v )ij -1U ∂U ∂d (v )öø÷÷ij =-∑t p æèççççit 1q it æèçç∂∑v′(1+d (v′)ij′)-öø÷÷1∂d (v )ij -1U æèçç∂∑j′∑v′(1+d (v′)ij′)-öø÷÷1∂d (v )öø÷÷÷÷ij=p ij 1q ij U (1+d (v )ij )-2-1U (1+d (v )ij )-2=(1+d (v )ij )-2q ij U(p ij -q ij ). 在学习率λ下,簇质心μ(v )j ㊁编码参数θ㊁解码参数θ′更新如下: μ(v )j =μ(v )j-λ∂L c∂μ(v )j,(3)θ=θ-æèççλ∂L r ∂θ+γ∂L c∂öø÷÷θ,(4) θ′=θ′-λ∂L r∂θ′.(5)待所有参数优化完毕,无标签样本的预测标签为s i =arg max jq ij .(6)DMNEC 步骤如算法1所示.算法1 DMNEC 输入 数据集X ,簇数量K ,平衡系数γ,收敛阈值δ,最大迭代次数T 输出 簇分配S//多网络分支预训练for v ={1,2, ,n }do 根据式(1)初始化θ㊁θ′,获取低维表征Z (v )=f (v )θ(X )end for//质心初始化基于Z (v )执行KM 算法以获取簇质心M (v )//网络微调for t ={1,2, ,T }do 根据式(2)更新辅助目标分布P 根据式(6)更新簇分配S 根据式(3)~式(5)更新簇质心μ(v )j㊁编码参数θ㊁解码参数θ′ if 1-1n ∑i ,j s t ij s t -1ij <δthen满足收敛判别准则,停止迭代 end ifend for3 实验及结果分析3.1 实验环境本文实验环境如下:操作系统为Linux.硬件平台为Intel(R)Xeon(R)E5⁃2640v4@2.40GHz CPU,120GB 内存,11GB 高速缓存,NVIDIA GeForceGTX 1080Ti GPU.编程环境为Python 3.7.深度学习框架为Tensorflow 2.0.0⁃beta0.在MNIST [25]㊁USPS [26]㊁FMNIST [27]㊁COIL20[28]图像数据集上评估DMNEC.MNIST 数据集为经典手写数字识别库,包含70000个样本,类别总数为10类,图像大小为28×28,每幅图像中的数字都是居中状态,已标准化处理.其中训练集包含60000个样本,测试集包含10000个样本.USPS 数据集包含9298幅来自10个类别的灰度手写数字图像,图像大小为16×16.FMNIST 数据集涵盖70000幅来自10种类别的时尚产品正面图像,图像大小㊁格式㊁训练/测试划分比例与MNIST 数据集完全一致.COIL20数据集包含1440幅来自20个类别的灰度实体图像,图像大小为128×128,实验中将尺寸重置为32×32.上述图像数据集的属性描述如表1所示.特别说明,对于已被划分为训练集和测试集的数据集,合并后再进行实验.另外,所有数据集的图像像素值都被缩放至数值区间[-1,1],以便神经网络更好地训练.实验选用的对比算法如下:1)传统聚类算法:KM [6]㊁GMM [7]㊁谱聚类(Spectral Clustering,SC)[34].2)基于表征的聚类算法:SAE +KM㊁变分自动81模式识别与人工智能(PR&AI) 第34卷编码器(Variational Autoencoder,VAE)+KM㊁卷积自动编码器(Convolutional Autoencoder,CAE)+KM.3)深度聚类算法:DEC [14]㊁IDEC [15]㊁DCN [17]㊁DKM [18]㊁ASPC [19]㊁SDCN [22]㊁深度散度聚类(DeepDivergence⁃Based Clustering,DDC)[35]㊁深度张量核聚类(Deep Tensor Kernel Clustering,DTKC)[36]㊁深度堆栈式稀疏嵌入聚类(Deep Stacked Sparse Embedded Clustering,DSSEC)[37].表1 实验数据集Table 1 Experimental datasets名称样本数类别数尺寸维度通道数MNIST 700001028×287841USPS92981016×162561FMNIST 700001028×287841COIL2014002032×32102413.2 评价指标为了衡量算法的聚类性能,采用如下3个聚类评价指标:聚类精度(Clustering Accuracy,ACC)[29]㊁归一化互信息(Normalized Mutual Information,NMI)[30]和调整兰德指数(Adjusted Rand Index,ARI)[31].ACC 计算如下:ACC =max m 1n ∑ni =11{l i =map (c i )},其中,n 为样本数量,l i 为真实标签,c i 为模型产生的预测标签,map (c i )为映射函数,包含预测标签与真实标签之间所有可能的一对一映射.匈牙利算法(Hungarian Algorithm)[32]可有效计算最佳映射.NMI 是衡量2个聚类之间共享信息量的信息论度量,较可靠地评价不平衡数据集聚类效果.NMI 计算如下:NMI =I (l ;c )max{H (l ),H (c )},其中,I (l ;c )表示l 和c 之间的互信息,H (l )表示的熵值,H (c )表示c 的熵值.ARI 是兰德指数(Rand Index,RI)[33]的修正版本,计算如下:ARI =RI -E (RI )max(RI )-E (RI ),其中E (RI )表示RI 的数学期望.总体而言,上述3种指标是评价聚类性能较常用的度量,各有利弊,将它们综合起来可更客观地说明聚类算法的有效性.ACC㊁NMI 在[0,1]内取值,数值越大表示聚类性能越优;ARI 在[-1,1]内取值,1表示最优的聚类表现,-1表示最差的聚类表现.3.3 实验设置DMNEC 设置3个多网络分支,分别为堆栈式自动编码器(SAE)㊁变分自动编码器(VAE)和卷积自动编码器(CAE).对于第1个网络分支SAE,编码网络结构为配备全连接层(Fully Connected Layer)的多层感知机(Multi⁃layer Perceptron,MLP),前向网络维度变化为D →500→500→2000→10,其中D 表示输入数据的原始维度.对于第2个网络分支VAE,编码网络结构为conv 26→conv 320→conv 360→fc 256→fc 10.其中:conv k n 表示配置n 个过滤器㊁过滤器尺寸为k ×k ㊁卷积步长为2的卷积层;fcn 表示包含n 个结点的全连接层.对于第3个网络分支CAE,编码网络结构为conv 532→conv 564→conv 3128→fc 10.解码网络均为编码网络的镜像版本,将编码网络置于解码网络顶部,形成端到端连接的3个异构深度神经网络,除了输入层㊁瓶颈层和输出层之外,其它层均使用修正线性单元(Rectified Linear Unit,ReLU)进行非线性数值转换.对上述3个多网络分支分别进行端到端的预训练,次数分别为200㊁400㊁600,采用自适应矩估计(Adaptive Moment Estimation,Adam)优化器(初始学习率为0.001)优化对应分支的网络参数,批量大小设置为256.在后续微调网络过程中,采用自适应梯度(Adaptive Gradient,Adagrad)优化器,初始学习率设置为0.0001,批量大小设置为256,平衡系数γ=0.1,最大迭代次数设置为20000.当满足收敛判别准则δ=0.001时,停止迭代.此外,为了公平起见,在4个图像数据集上对DMNEC 进行10次随机重启,求取各个指标的平均值,将其作为最终实验结果.3.4 方法对比各算法在4个数据集上的指标值对比如表2所示,其中,黑体数字表示最优结果,斜体数字表示次优结果,-表示没有结果.为了说明局部结构保留的重要性,表2中也给出DMNEC 在网络微调阶段的多分支解码网络移除后所得算法(简称为DMNEC w /o LSP)的结果.由表可知:DMNEC 在3个聚类评价指标上最优.特别地,在MNIST 数据集上,相比ASPC㊁DSS⁃EC,DMNEC 的ACC 值分别提升7.5%㊁5.7%,达到91第1期 陈 锐 等:深度多网络嵌入聚类93.4%,这表明DMNEC 的优越性.在USPS 数据集上,相比SDCN,DMNEC 的ACC 值㊁NMI 值㊁ARI 值分别提升0.6%㊁3.4%㊁3.3%,达到78.7%㊁82.9%㊁75.1%,表明DMNEC 性能较优.另外,在小型数据集COIL20上,相比ASPC,DMNEC 的NMI 值分别提升5.3%,达到79.6%,这表明DMNEC 具备良好的泛化性能.由表2可看出,DMNEC w /o LSP 在4个数据集上均取得较优的聚类表现,表明DMNEC 在预训练阶段使用多网络分支,可有效挖掘多种网络结构特征之间的互补信息,学习更高质量的嵌入特征,更好地衔接后续的聚类任务.此外,在大多数数据集上,DMNEC 性能优于DMNEC w /o LSP,表明DMNEC 在网络微调阶段保留的解码网络可一定程度上避免特征空间扭曲,最大限度保留数据局部结构,提升最终聚类性能.表2 各算法在4个图像数据集上的指标值对比Table 2 Comparison of metric values of different algorithms on 4image datasets算法MNIST ACCNMIARI USPS ACCNMIARI FMNIST ACCNMIARI COIL20ACC NMIARI KM0.5340.5000.3660.6720.6140.5360.4750.5120.3480.6070.487-GMM 0.4330.366-0.5510.530-0.5560.557----SC 0.6560.731-0.6490.794-0.5080.575-0.6280.523-SAE 0.8460.7830.7450.7190.7100.6100.5050.5430.3790.5930.7420.545VAE 0.8780.8150.7890.7380.7320.6570.5810.6170.4580.6560.7780.597CAE 0.8960.8290.8130.7440.7390.6590.5820.6170.4530.6490.7710.584DEC 0.8710.8260.7980.7600.7710.6970.5500.5870.4420.6140.7780.582IDEC 0.8930.8760.8460.7780.8070.7270.5670.6240.4780.6190.7770.589DCN 0.8110.7570.7020.7300.7190.6340.5010.558----DKM 0.8400.7960.7500.7570.7760.6850.5390.563-0.6320.502-ASPC 0.8590.8420.8050.7530.7660.6680.5830.6200.4650.5690.7430.518DDC 0.7700.730-0.6900.700-0.5500.490----DTKC 0.7700.740-0.7000.730-0.5600.500----SDCN ---0.7810.7950.718------DSSEC 0.8770.8570.8230.7840.8110.736------DMNEC w /o LSP 0.9250.9030.8870.7850.8230.7430.5880.6370.4720.6960.8090.643DMNEC0.9340.9060.8930.7870.8290.7510.5980.6520.4860.6860.7960.629 图4为DMNEC㊁DEC 在MNIST 数据集上的部分聚类结果,随机筛选每簇中的10个图像样本进行可视化,每行对应一个簇. (a)DMNEC (b)DEC 图4 各算法在MNIST 数据集上的部分聚类结果Fig.4 Some clustering results of different algorithms on MNISTdataset由图4可清晰地观察到,DEC 经常混淆数字4㊁9,说明DEC 倾向于将手写数字集合聚为9类,与实际类别数(10类)矛盾.而这一现象在图4(a)中未出现,说明DMNEC 可准确地将手写数字集合聚为10类,反映DMNEC 在聚类任务中表现更出色.3.5 消融实验由于本文算法包含多个异构网络分支,因此探究每个网络分支对最终聚类结果的影响.DMNEC 配备3个网络分支:Net 1(SAE)㊁Net 2(VAE)㊁Net 3(CAE).图5为在USPS 数据集上算法只考虑单个网络与同时考虑3个网络的ACC㊁ARI 指标随迭代次数的变化情况.由图5可观察到,在迭代过程的各个阶段,多网络模型的聚类性能明显优于任何单网络模型,表明预训练阶段使用多网络结构,可获取包含互补信息的高质量特征,进而更好地衔接后续的聚类任务.02模式识别与人工智能(PR&AI) 第34卷0.800.780.760.740.720.70A C C0.700.680.760.740.720.620.660.640.60A R I (a)ACC (b)ARI图5 网络数量不同时指标值随迭代次数的变化情况Fig.5 Metric values variation with iteration times with different numbers of networks 为了更直观的理解,在此将预训练阶段使用单网络提取的特征和使用多网络提取的特征进行可视化,如图6所示.由图可看出,相比使用单网络提取的特征,使用多网络提取的特征表现更佳的团簇结构,说明多网络模型可捕获不同网络结构特征之间的互补信息,充分反映数据潜在的聚类结构.在FMNIST㊁COIL20数据集上的实验结果如表3所示,这也验证上述结论. (a)Net 1 (b)Net 2 (c)Net 3 (d)DMNEC图6 基于MNIST 子集的异构网络特征鲁棒性可视化结果Fig.6 Visualization results of robustness of heterogeneous network features based on a subset of MNIST表3 DMNEC 在2个数据集上的消融实验结果Table 3 Results of ablation experiment of DMNEC on 2datasets聚类阶段对比方法FMNIST ACCNMIARICOIL20ACCNMIARI初始化表现Net 1+KM Net 2+KM Net 3+KM DMNEC+KM 0.50500.58100.58240.58750.54310.61690.61660.62340.37890.45750.45340.46290.59280.65630.64890.67940.74210.77830.77120.78240.54480.59720.58420.6058最终聚类表现DEC-Net 1DEC-Net 2DEC-Net 3DMNEC w /o LSPDMNEC0.55000.58550.58400.58830.59760.58730.63560.63300.63660.65150.44210.47010.46760.47200.48580.61380.67290.68010.69580.68610.77760.79660.79480.80880.79550.58220.61360.62390.64310.62923.6 收敛性分析本节分析DMNEC 的收敛情况.首先使用t ⁃SNE [5]对DMNEC 在MNIST 子集(包含1000个样本)上的聚类过程进行可视化,完整的聚类过程如图7所示.由图7可看出,原始数据点分布高度重叠,这意味着聚类任务的艰巨.簇质心初始化后,相比原始数据点,预训练多网络分支提取的融合特征点更容易被分离,但仍存在许多边缘样本点.随着微调网络的进行,如在第140次迭代时,同个簇中的大多数数据12第1期 陈 锐 等:深度多网络嵌入聚类点都聚集在一起,只有少数未被较好地分离.迭代过程继续进行,当满足收敛判定准则时,训练进程终止,此时数据点分布已达到稳定状态,较好地分离数据点,簇内元素高度集中,簇间间隔尤其明显. (a)原始状态 (b)初始化状态 (c)第140次迭代状态 (d)最终状态 (a)Original image (b)Initial image (c)Results after140iterations (d)Final results图7 DMNEC在MNIST子集上不同阶段的可视化Fig.7 Visualization of DMNEC on a subset of MNIST at different phases 图8为DMNEC在MNIST㊁USPS数据集上的聚类指标随迭代次数的变化情况.由图8可看出,指标数值在最初的几轮迭代不断升高,最后趋于稳定.综上所述,DMNEC在通常情况下都可在一个较理想的局部极小值处收敛. (a)MNIST (b)USPS图8 DMNEC在2个数据集上的指标值随迭代次数的变化情况Fig.8 Variation of metric values of DMNEC with iteration times on2datasets3.7 复杂度分析考虑到对深度模型的复杂度理论分析较困难,在此采纳模型在某个数据集上的训练时长,用于评价模型的复杂度.表4为不同聚类算法在USPS数据集上的耗时与性能情况,由表可看出,KM算法效率较高但性能较差.DEC㊁IDEC由于只涉及单个网络的预训练,效率可观,性能良好.特别地,DMNEC耗时为DEC和IDEC的8倍多,这也反映DMNEC虽然性能优越,但是多网络分支的预训练过程及解码网络的微调过程较耗时,导致效率并不理想.在今后的研究工作中,将致力于改进模型的训练效率.表4 各算法在USPS数据集上的耗时与指标值对比Table4 Comparison of time consumption and metric values ofdifferent algorithms on USPS dataset算法耗时/s ACC/%NMI/%KM667.261.4DEC5576.077.1IDEC5977.880.7DMNEC48278.782.922模式识别与人工智能(PR&AI) 第34卷4 结束语本文提出深度多网络嵌入聚类算法(DMNEC),可联合学习包含互补信息的多网络特征及其簇分配.DMNEC包含2个阶段:第1阶段通过端到端地预训练多网络分支,获取完备的鲁棒低维表征;第2阶段定义多网络软分配,借助多网络辅助目标分布建立面向聚类的KL散度损失.同时,保留编码器的解码网络以保留数据局部结构,最大程度地避免特征空间扭曲.最后基于多网络分支重建损失和聚类损失微调网络.在4个公开的图像数据集上的实验表明,DMNEC具有较优的聚类性能与良好的泛化性能.今后将会探究更有效的特征融合机制,用于挖掘多网络特征之间更深层次的互补信息,尝试在大型三通道场景数据集上进行实验,探索更先进的深度多网络聚类算法.参考文献[1]孙吉贵,刘杰,赵连宇.聚类算法研究.软件学报,2008,19(1): 48-61. (SUN J G,LIU J,ZHAO L Y.Clustering Algorithms Research. Journal of Software,2008,19(1):48-61.)[2]SIMONYAN K,ZISSERMAN A.Very Deep Convolutional Networks for Large⁃Scale Image Recognition[C/OL].[2020-08-24].https:// /pdf/1409.1556.pdf.[3]SZEGEDY C,LIU W,JIA Y Q,et al.Going Deeper with Convolu⁃tions//Proc of the IEEE Conference on Computer Vision and Pa⁃ttern Recognition.Washington,USA:IEEE,2015.DOI:10. 1109/CVPR.2015.7298594.[4]HE K M,ZHANG X Y,REN S Q,et al.Deep Residual Learning for Image Recognition//Proc of the IEEE Conference on Computer Vision and Pattern Recognition.Washington,USA:IEEE,2016: 770-778.[5]VAN DER MAATEN L,HINTON G.Visualizing Data Using t⁃SNE.Journal of Machine Learning Research,2008,9:2579-2605.[6]MACQUEEN J.Some Methods for Classification and Analysis of Multivariate Observations//Proc of the5th Berkeley Symposium on Mathematical Statistics and Probability.Berkeley,USA:University of California Press,1967:281-297.[7]BISHOP C.Pattern Recognition and Machine Learning.Berlin,Ger⁃many:Springer,2006.[8]WOLD S,ESBENSEN K,GELADI P.Principal Component Ana⁃lysis.Chemometrics and Intelligent Laboratory Systems,1987,2:37-52.[9]XU W,LIU X,GONG Y H.Document Clustering Based on Non⁃negative Matrix Factorization//Proc of the26th Annual Internatio⁃nal ACM SIGIR Conference on Research and Development in Infor⁃mation Retrieval.New York,USA:ACM,2003:267-273.[10]COX M A A,COX T F.Multidimensional Scaling//CHEN C H,HÄRDLE W,UNWIN A,eds.Hand Book of Data Visualization.Berlin,Germany:Springer,2008:315-347.[11]贾文娟,张煜东.自编码器理论与方法综述.计算机系统应用,2018,27(5):1-9.(JIA W J,ZHANG Y D.Survey on Theories and Methods of Au⁃puter Systems and Applications,2018,27(5):1-9.)[12]YANG J W,PARIKH D,BATRA D.Joint Unsupervised Learningof Deep Representations and Image Clusters//Proc of the IEEE Conference on Computer Vision and Pattern Recognition.Washing⁃ton,USA:IEEE,2016:5147-5156.[13]周飞燕,金林鹏,董军.卷积神经网络研究综述.计算机学报,2017,40(6):1229-1251.(ZHOU F Y,JIN L P,DONG J.Review of Convolutional Neural Network.Chinese Journal of Computers,2017,40(6):1229-1251.)[14]XIE J Y,GIRSHICK R,FARHADI A.Unsupervised Deep Em⁃bedding for Clustering Analysis//Proc of the33rd International Conference on Machine Learning.New York,USA:ACM,2016: 478-487.[15]GUO X F,GAO L,LIU X W,et al.Improved Deep EmbeddedClustering with Local Structure Preservation//Proc of the26th In⁃ternational Joint Conference on Artificial Intelligence.San Francis⁃co,USA:Morgan Kaufmann,2017:1753-1759. 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[20]PENG X,XIAO S J,FENG J S,et al.Deep Subspace Clusteringwith Sparsity Prior//Proc of the25th International Joint Confe⁃rence on Artificial Intelligence.San Francisco,USA:Morgan Kaufmann,2016:1925-1931.[21]CHANG J L,WANG L F,MENG G F,et al.Deep Adaptive Im⁃age Clustering//Proc of the IEEE International Conference on Computer Vision.Washington,USA:IEEE,2017:5880-5888.[22]BO D Y,WANG X,SHI C,et al.Structural Deep Clustering Net⁃work//Proc of the International World Wide Web Conference.New York,USA:ACM,2020:1400-1410.[23]ALJALBOUT E,GOLKOV V,SIDDIQUI Y,et al.Clustering withDeep Learning:Taxonomy and New Methods[C/OL].[2020-08-24].https:///pdf/1801.07648.pdf.[24]MIN E X,GUO X F,LIU Q,et al.A Survey of Clustering withDeep Learning:From the Perspective of Network Architecture.32第1期 陈 锐 等:深度多网络嵌入聚类。
众包中关于DS模型及其扩展设定总结
众包中关于DS模型及其扩展设定总结2019-01-25最近对众包领域的⽂章有了新的认识，之前写的太乱了，下⾯来重新整理⼀下。
Error Rate Bounds and Iterative Weighted Majority Voting for Crowdsourcing（Arxiv14）这篇⽂章对众包中的 Dawid-Skene model 有着⾮常好的总结和概括。
我个⼈认为这篇⽂章挂在 Arxiv 上，最终没发表出来的原因，在于其提出的加权投票法中的两种权重设置（w=2p−1, w=log(p1−p) ），已经被前⼈研究出来过，并且它们都有更加简单和浅显的证明和分析，在这篇⽂章中⽤更加复杂的理论重新发明了“轮⼦“，有些可惜。
下⾯来注记⼀下其提供的 DS model 的总结：General DS model：最初的DS model 是针对的 “多分类问题”，设有 L 个类别，每个⼯⼈有⼀个⼤⼩为L×L的 confusion matrix。
每个⼯⼈由L2个参数决定。
其有两种特殊情形：1. class-conditional DS model: 这⾥假定⼯⼈错误选择任何不正确的类别标记的概率都相同。
即假定 confusion matrix 同⼀⾏的⾮对⾓元都相等。
每个⼯⼈（每个矩阵）只需其对⾓线的 L 个参数刻画。
2. Homogenous DS model（one coin model）：不仅假定confusion matrix 的同⼀⾏的对⾓元相等，还假定矩阵的对⾓元相同。
每个⼯⼈（每个矩阵）只需⼀个参数刻画当类别数 L = 2 时， General DS model 与 Class-conditional DS model 是相同的，通常称为 two-coin model。
（每个⼯⼈只需两个参数刻画）在信号处理中，one-coin model 通常也被称为 random classification noise model.另外众包中 DS model 还有两种模式的扩展:TrueLabel + confusions: A spectrum of probabilistic models in analyzing multiple ratings (ICML12)主要内容： This paper generalizes the well-known D-S model to a spectrum of probabilistic models under the same " TrueLabel + Confusion " paradigm.The original D-S model has a large number of parameters---each worker has her own confusion matrix, which may lead to overfitting. So it proposes a model called SingleConfusion --- all workers share the same confusion matrix. But SingleConfusion is too rigid for real-world data and it may result to underfitting. As a tradeoff of the two model, the paper further proposes a hierarchical Bayesian model called HybridConfusion whith allows each worker to have her own confusion matrix, but at the same time regularizes these matrices through Bayesian shrinkage.注：这是⼀篇⾮常有意思的⼯作! 作者claim 原始的 D-S model 中混淆矩阵参数过多，导致模型过于复杂，易于过拟合，作者在这篇⽂章中考虑了减少混淆矩阵中的参数个数: 多个⼯⼈在某种程度上共⽤⼀个混淆矩阵。
模型跟踪
Dynamic surface
backstepping control
模型跟踪的主要思想是让飞控系统的信号和参考
模型的信号实时比较, 将信号误差反馈给控制器以调节
系统的性能, 使之在故障情况下依然与参考模型保持一
致。文献[ 10 ]基于伪逆思想设计了模型跟踪重构方法,
In this paper the rigorous proof of fault diagnosis and self-repairing control comprehensive study on the repair capacity of various faults, this method ensures that the repair time is short, good quality repair process control, repair, and other aspects of the higher capacity needs. The simulation results also support the conclusion.
ence , S an Francisco , US A , 2005 ; 1 - 30.
[ 29 ] Napolitano M R , An Y, Seanor B A. A fault tolerant flight
cont rol system for sensor and act uator failures using neural net2
出一种渐近调节的主动容错控制方案, 在维持系统性能的
同时有效克服了由于故障检测和诊断的延时[ tF , tR ]对系统
基于自适应权重的多重稀疏表示分类算法_段刚龙_魏龙_李妮
网络出版时间：2012-08-16 10:45网络出版地址：/kcms/detail/11.2127.TP.20120816.1045.019.htmlComputer Engineering and Applications计算机工程与应用基于自适应权重的多重稀疏表示分类算法段刚龙, 魏龙, 李妮DUAN Ganglong, WEI Long, LI Ni西安理工大学信息管理系, 陕西西安 710048Department of Information Management, Xi’an University of Technology, Xi’an 710048, ChinaAdaptive weighted multiple sparse representation classification approach Abstract：An adaptive weighted multiple sparse representation classification method is proposed in this paper. To address the weak discriminative power of the conventional SRC (sparse representation classifier) method which uses a single feature representation, we propose using multiple features to represent each sample and construct multiple feature sub-dictionaries for classification. To reflect the different importance and discriminative power of each feature, we present an adaptive weighted method to linearly combine different feature representations for classification. Experimental results demonstrate the effectiveness of our proposed method and better classification accuracy can be obtained than the conventional SRC method.Key words：adaptive weight; multiple sparse representation; SRC摘要：提出了一种基于多特征字典的稀疏表示算法。
网络术语2
1、DARPA—分组交换2、POP（Point of Presence）--呈现点3、NAP(Network Aceess Point)网络交换中心4、AS(Autonomous System )—自治系统5、CE（Custmer Equipment）--边缘路由器6、PE(Provider Equipment)—运营商路由器7、QoS(Quality of Service)8、EOS(Experience of Service)9、RTT(Round-Trip Time)收发来回时间10、IANA(互联网编号分配机构)11、RIRs(Regional Internet Registries)12、ICANN(互联网名称与数字地址分配结构)13、OC(Optical Carrier)14、SDH(Synchronous Digital Hierarchy)15、STS(Synchronous Transport Signal)16、PAM(Pulse Amplitude Modulation)17、PCM(Pulse Code Modulation)18、ASK(Amplitude Shift Keying)19、FSK(Frequency Shift Keying)20、PSK(Phase Shift Keying)21、QAM(Quadrature Amplitude Modulation)22、DDCMP(Digital Data Communication Message Protcol23、SDLC(Synchronous Data Link Control Protocol)24、TMD(Time Division Multiplexing)时分复用25、FDM(Frequency Division Multiplexing)26、WDM(Wave Division Multiplexing)27、CDM(Code Division Multiplexing)28、DWDM(Dense Wavelength Division Multiplexing Access)29、PC(Parity Checking)30、CRC(Cyclic Redundancy Check)循环冗余校验31、SCTP流控制传输协议32、RP(Rendezvous Point)汇聚点33、RPT(Rendezvous Point Tree)34、SPT(Shortest Path Tree)最短路径树35、DR(Designated Router)指定路由器36、RPB37、MPB38、BSR,IGMP,MBGP,MSDP,PIM-SM,PIM-DM,RP,RPT,SPT,DR ppt第一章倒数第3页。
软件工程外文文献—软件稳定性模型SSM
外文原文Due to the instability of software systems produced over a period of time unlike other systems, it has become essential to research upon and ascertain the Stabilrty of software systems which determines other factors such as reliability, trustworthiness etc. Though theoretically there is no deterioration expected for a software product, it does owing to changes in software which involves re-engineering of the changed code. The re-engineering of the software product is not essential for smafl changes that would have been made in the code of the software modules.The idea behind this research work is to bring out the basic techniques used in Pattern identification of Real Time Computing Systems by using the Software Stability Model (SSM).A case study has been built for illustrating the application of SSM to real time computing systems that use Adaptive ReconfigurabIe controls. The "Control Software" that is being used in the real time computing system makes use of the properties of Adaptive Control [8]. Adaptive Reconfigurable Control finds applications in areas including real time systems such as Air Traffic Control Systems, Networked Multimedia Systems, Command Control Systems, Medical Critical Care systems, Real Time Operating Systems (RTOS) etc. In essence the n Control Software** is modeled as a "System" and hence the concepts of stability of a physical system (as defined in Control Engineering) are applied to that of the software used in real- time systems.Software failure happens in many real time systems such as transportation systems, medical systems, defense systems, etc. A software which is dynamically controlling the buffering functions of a database management system, or a software that uses the concept of caching for OS memory management are typical examples of software using algorithms with embedded control and adaptation. We have considered a Real Time Computing System that uses Adaptive Control Algorithms. The intuitive use of the stability concepts available in Control Engineering in Real Time Computing systems with the support of the Software Stabilrty Model(SSM) is the theme of this research work.For the real time system shown in fig I, using Re- configurable control, the control laws are stored in the Controller Database. The required n Control Law" would be chosen as required. The highlight of reconfigurable control is that the controller could be redesigned at runtime.The code level implementation of the control law as shown in [9], could be used in reconfigurable control, in order to produce stability and performance checks on the "control software** used. Adaptive components are included in Real r∏me Systems in order to cope up With changing environments .Fig I. Btock Diagram of a Real Time System with Adaptive Reconfigurab Ie Control In [3] the stability criteria for software has been stated as follows :" A system is said to be stable when little disturbances applied to the system have negligible effects on the system In case of model driven software system this implies the very small changes in the input model do not radically change the behavior of the system". This concept when extended to defining the term "controllability" in software engineering is to establish the fact that software systems will perform as per the g iven specifications when the inputs are changed. In a simikιr fashion the "observability*1 criteria for software systems could also be given. A software system is said to be "observable" if it becomes possible to obtain information about the state of the system at any point of time.M.E Fayad discusses the Software Stability Model (SSM) in [4] using EBT∕B0∕10. Enduring Business Themes (EBTs) remain constant for a given system. EBTs are so chosen that the objects will remain stable in order to make up the core of software systems. Business Objects (BOs) also remain stable, but the internal processes might exchange on a need basis. Therefore externally BOs remain as stable as EBls. Industrial Objects (IOs) are the objects that one designs in a classical object model An Industrial Object represents a physical entity.As defined by Fayad in SSM, The EB r Is are determined by answering the question :"What is this system for?'*, the BOs are deteπnined by answering the question :" Howdo the intangible conceptual themes map into more concrete objects?" The IOs are determined by answering the question :" What is the physical representation of the BOs? "[ 10].It is difficult for Software Engineers to identify the objects of Stabilrty in Real Time Domain Applications, who are not so much exposed to stability concepts. It is the control engineer who should be able to advice the software engineers in the identification of EBTs, BOs and IOs. The domain knowledge of the application is very essential to identify all the three objects clearly. Stability over time, Adaptability, Essentiality, Intuition, Explicitness, Commonality to the domain, Tangibility etc. are the identification criteria M.E. Fayad has suggested to identify the EBT/80/1O [5,7].As a software system is controlled by the control software programs running, it is important to analysis the reliability of such systems while code change happens. It is also inportant to identify the range over which the software systems would behave stable during such code changes. This in line with the principles involved in defining the Controllability and Observability criteria for systems that would serve as a strong methodology to support the stability of Software systems.As in any other physical system, stability is defined over the Control Gain Factor Kin the Loop Transfer Function of the system, there are ranges over which the control parameters of the Software systems would also behave stable. The core idea of this research is to do an in-depth analysis of the behavior of Software systems on code changes and determining the cond⅛ions under which the control parameters would make the Software System stable. This in turn suggests the design of appropriate controllers using software programs in order to keep the software system within a stable region.Computing System from the external entities. Ideally the Real Time Computing system is a MIMO (Mult⅛>le I叩Ul Multiple Output) system. The inputs thus received are being processed by the Conputing System based on the parameter settings made in the Real Time Computing System. The Algorrthms used in the control software of theReal Time Computing System will process the inputs (signals) received. Appropriate Computation using real-time data meeting the required conditions as defined by the control parameters of the real time applications are being handled by the Conputing System. The Output thus obtained is fed into the Transaction Processing System which mon⅛ors for example - the database operations that take place in the backend database server.The control signals coming out of the TP system are fed into the Adaptive Control Server that has the master control system The signals received from the TP system which refers to the Model Estimator and Controller Designer Database chooses the apt control values as defined by the control parameters of the particular Real Time Application. The reconfigurable control used in the Adaptive Control Server gives the advantage that the controller is being redesigned at runtime since both the Model Estimator and Controller Designer refer to their respective Databases and hence adaptive nature of the server helps the server act appropriately.The various EBTs, BOs and IOs have been identified for the Real Tune TP system as shown in Fig 3. Based on the concepts of software stability, the categorization of the objects viz., EBT, BO and IO has been done based on the degree of stability [6,10]. Computing, Monitoring and Controlling represent the EBls of the system. The main objective of the TP System is to perform the computation of the control parameters based on the sensor values inputted and algorithms implemented using the control software. The other objective of the TP system is to track the Transactions triggered and compare the actual values computed with the real time system parameter limits pre- defined.Based on the comparison, the Adaptive Control system in turn controls the TP system and the output is thus controlled by the values chosen from the Controller Database dynamically at run-time ." Computing" is an enduring theme since it remains stable extremely and internally as long as this system lasts .n Monrtoring" is an enduring theme that represents the process of conparing the actual values conputedwith the real time system parameter limits pre- defined, which also renns stable both externally and internally."Controlling" is an enduring theme that provides Adaptive control to the TP system at run-time which also remains stable both externally and internally. All the three EBls identified here, define the concept of the system since these are the main aims of TP SystemReal Time Control Parameters, Real-time system parameter limits and Adaptive Control parameters represent the BOs. Every BO identified here are externally stable and highly adaptable in ternally. For exaπple, Real time control parameters are the ones which are always the key control elements that are stable for a TP system, yet they can depend on the sensors, control Algorithms, process controllers etc.Fig 3 shows a stable model of a TP system. We now identify a domain pattern for the TP system based on the SSM, by extracting the EBTs and BOs of the stable model of TP system. We see that the chosen EBTs, BOs etc. based on the SSM is owing to the domain of the problem. Hence software stable models for other applications in the TP domain will have these objects as their EBTs and BOs. Fig 6 shows a domain pattern for the TP system. As defined in [10], the various elements of the stability model for the TP System has been discussed in this section.Intent: This pattern suggests the basic structure of any Transaction Processing (TP) System Context: There are many Online Transaction Processing Systems I Software that require TP function.Problem: Arrive at the stable objects which represent the basic structure of the TP System Forces: The pattern identified should depict the basic structure of the TP System. It has to be generic in nature so that it could be applied to any kind of TP systems. It is quite challenging to arrive at a pattern which will handle different types/ functions of TP systems.How far a real time (Transaction Processing) system is dependent on the input parameters defines the controllability of the TP system. How far the outputs are dependent on the varying system parameters determines the Observability of the TP System. The determining control parameters of the TP System uħimately determines the EBTζ80s and 10s. Therefore decision on the control parameters decides whether the TP systems is Controllable as well Observable. Since the Controllability and Observability are the key elements of stability, we thereby ensure determination of EB r Is,80s and K)s as well depend on the control parameters governing the Control Software being used in Adaptive Re-ConfigurabIe Control based Transaction Processing System. The TP System Pattern thus arrived gives a reliable system which is more stable.中文翻译由于与其他系统不同，在一段时间内产生的软件系统不稳定，因此研究和确定软件系统的稳定性变得至关重要，这些系统决定了其他因素，如可靠性，可信度等。
S t e r e o M a t c h i n g 文 献 笔 记
立体匹配综述阅读心得之Classification and evaluation of cost aggregation methods for stereo correspondence学习笔记之基于代价聚合算法的分类，主要针对cost aggregration 分类，20081.?Introduction经典的全局算法有：本文主要内容有：从精度的角度对比各个算法，主要基于文献【23】给出的评估方法，同时也在计算复杂度上进行了比较，最后综合这两方面提出一个trade-off的比较。
2?Classification?of?cost?aggregation?strategies?主要分为两种：1)The?former?generalizes?the?concept?of?variable?support?by? allowing?the?support?to?have?any?shape?instead?of?being?built?u pon?rectangular?windows?only.2)The?latter?assigns?adaptive?-?rather?than?fixed?-?weights?to?th e?points?belonging?to?the?support.大部分的代价聚合都是采用symmetric方案，也就是综合两幅图的信息。
（实际上在后面的博客中也可以发现，不一定要采用symmetric的形式，而可以采用asymmetric+TAC的形式，效果反而更好）。
采用的匹配函数为（matching?(or?error)?function?）：Lp distance between two vectors包括SAD、Truncated SAD [30,25]、SSD、M-estimator [12]、similarity?function?based?on?point?distinctiveness[32] 最后要指出的是，本文基于平行平面（fronto-parallel）support。
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INTERNATIONAL JOURNAL OF ADAPTIVE CONTROL AND SIGNAL PROCESSINGInt.J.Adapt.Control Signal Process.(2012)Published online in Wiley Online Library().DOI:10.1002/acs.2328Stable weighted multiple model adaptive control:discrete-timestochastic plantWeicun Zhang*,†School of Automation Science and Electrical Engineering,University of Science and Technology Beijing,Beijing100083,ChinaSUMMARYA stable weighted multiple model adaptive control system for uncertain linear,discrete-time stochastic plant is presented in the paper.First,a new scheme for calculating controller weights is proposed with assured convergence,that is,the controller weight corresponding to the model closest to the true plant converges to 1,and others converge to0;second,on the basis of virtual equivalent system concept and methodology,the stability of the overall closed-loop control system is proved under a unified framework which is independent of specific‘local’control strategy.Copyright©2012John Wiley&Sons,Ltd.Received2August2011;Revised27June2012;Accepted10July2012KEY WORDS:stable;weighted multiple model adaptive control;virtual equivalent system1.INTRODUCTIONThe research on weighted multiple model adaptive estimation and control appeared around1960’s to1970’s,where multiple Kalmanfilter-based models were studied to improve the accuracy of the state estimate in estimation and control problems[1–3].This was followed in later years by several practical applications[4–7].This kind of multiple model adaptive control is always produced as the probability-weighted average of elemental controller outputs.In recent years,a new type of weighted multiple model adaptive control(WMMAC),that is,robust multiple model adaptive control(RMMAC)architecture,was put forward with convincing experiment results[8–10].As theoretical progress of WMMAC,some convergence results on the probabilistic weighting algo-rithm have been obtained under suitable assumptions[11–14].Specifically,as Fekri,Athans,and Pascoal pointed out in[9]that under certain ergodicity and stationarity assumptions,one of the pos-terior probabilities will converge almost surely to unity and will‘identify’the model closest to the true plant,that is,the one with smallest Baram proximity measure.In spite of decades of theoretical and experimental research,it is widely accepted that the stability of RMMAC/WMMAC system is difficult to prove[9,15,16].Actually,to the best of the authors’knowledge,reference[16]seems to be thefirst attempt to deal with the stability of RMMAC/WMMAC,in which the weighting structure was modified to switching structure.In this paper,we made efforts from two directions to address the stability issue of WMMAC. First,a new scheme for calculating controller weights is proposed with assured convergence under smooth assumptions.Second,virtual equivalent system(VES)concept and methodology is adopted to give a positive answer to the stability of the closed-loop WMMAC system.VES is an artificial system that is equivalent to the original adaptive control system in the input–output sense.It was*Correspondence to:Weicun Zhang,School of Automation Science and Electrical Engineering,University of Science and Technology Beijing,Beijing100083,China.†E-mail:weicunzhang@;weicunzhang@W.ZHANGoriginated from[17]and gradually adapted later in[18–20].VES has been successful in under-standing and judgment of the stability and convergence of a general self-tuning control system, which consists of arbitrary control strategy,arbitrary parameter estimation algorithm,and a deter-ministic/stochastic minimum/nonminimum phase linear time-invariant(LTI)plant.For more details, the reader is referred to[20].It is worth noting that the proposed analysis method is independent of specific‘local’control strategy and weighting algorithm;instead,it requires only the properties of the‘local’control strategy(stabilizing and tracking)and weighting algorithm(convergence).Besides,this paper is focused on the discussion of WMMAC for discrete-time systems because most practical systems are controlled by computers that are discrete in nature.As Narendra pointed out in[21],the pres-ence of random noise can be dealt with more easily in the case of discrete-time systems.Because most practical systems have to operate in the presence of noise,the stability and performance of MMAC systems in such contexts have to be well understood,if the theory is tofind wide application in practice.To avoid ambiguity,we emphasize that the stability of WMMAC means the boundedness of its input–output signals and the convergence of its performance index to that of‘local’nonadaptive control systems.In addition,we need to point out that all the limit operations in this paper are in the sense of probability one.The rest of the paper is organized as follows.Section2gives the description of WMMAC. Section3introduces two kinds of VESs of a general WMMAC system in two different situations. The main results are then developed in Section4.The simulation results are presented in Section5. Finally,some conclusions and future works are drawn in Section6.2.DESCIPTION OF WEIGHTED MULTIPLE MODEL ADAPTIVE CONTROL Consider the following discrete-time stochastic plant P with single input and single output:Aq 1y.k/D q d Bq 1u.k/C!.k/(2.1)whereAq 1D1C a1q 1C C a n q nBq 1D b0C b1q 1C C b m q my.k/,u.k/,and!.k/are the output,input,and the exogenous disturbance/measurement noise of the system,respectively,and y.k/D0,u.k/D0,!.k/D0for k<0.Further,we suppose that !.k/is a zero-mean white noise with constant variance0<R<1,that is,lim k!11kkXi D1!2.i/D R(2.2)The plant P can be stable or nonstable and minimum phase or nonminimum phase.The plant output y.k/can be rewritten asy.k/D T.k d/ÂC!.k/(2.3) whereT.k d/DŒy.k 1/,:::,y.k n/,u.k d/,:::,u.k d m/ (2.4)ÂDŒ a1,:::, a n,b0,b1,:::,b m (2.5) M D f M i,i D1,2,:::,N g is the model set that may include the true model of the unknown plant P.STABLE WEIGHTED MULTIPLE MODEL ADAPTIVE CONTROLFor each model M i2M,its output is given byy mi.k/D T.k d/Âi(2.6) whereÂi is the parameter vector of model M i.Further,define the output error of each model M i, that is,e i.k/D y.k/ y mi.k/D y.k/ T.k d/Âi D T.k d/ T.k d/Âi C!.k/(2.7) As we will see later,e i.k/is used to calculate the weight for a‘local’controller C i,which may be designed according to any possible control strategies,if only C i stabilizes model M i2M and the resulting closed-loop system tracks the reference input0<y r.k/<1.C D f C i,i D1,2,:::,N g is the controller set corresponding to the model set M D f M i,i D1,2,:::,N g.We use a concise block diagram as shown in Figure1to represent a general WMMAC system of discrete-time plant, in which the details of design strategy of‘local’controllers and algorithm for calculating controllers’weights p i.k/are omitted.In Figure1,each‘local’controller C i outputs u i.k/,and the global control u.k/is obtained byu.k/DNXi D1p i.k/u i.k/(2.8)Typically,controller weights are calculated through a bank of Kalmanfilters and the so-called posterior probability evaluator;for details,the reader is referred to[9].But in this paper,we propose a new algorithm to calculate p i.k/,that is,l i.0/D 1N,p i.0/D l i.0/(2.9)for all k>0l0i.k/D1C 1kkXr D1e2i.r/(2.10)l0min.k/D mini ˚l0i.k/«(2.11)l i.k/D l0min.k/l0i.k/l i.k 1/(2.12)p i.k/Dl i.k/P Nr D1l r.k/(2.13)In contrast to other existing WMMAC schemes,such as,RMMAC and classical WMMAC, the aforementioned algorithm is simpler in calculation.We have the following result regarding its convergence character.Figure1.Simplified block diagram of a general weighted multiple model adaptive control system.W.ZHANGTheorem2.1Suppose M j is closest in the model set M D f M i,i D1,2,:::,N g to the true plant in the following sense with probability one:1 kkXr D1e2j.r/<1kkXr D1e2i.r/,8k>k ,i¤j(2.14)lim k!11kkXr D1e2j.r/D R j I limk!11kkXr D1e2i.r/D R i,R j<R i,i¤j(2.15)where k is an unknown limited time instant,R j is a constant,and R i may be constant or infinity. Then,we havelim k!1p j.k/D1I limk!1p i.k/D0,i¤jProofIt is not difficult to see that algorithms(2.9)–(2.13)together with(2.14)guarantee with probability one that8ˆˆˆˆˆ<ˆˆˆˆˆ:l0min.k/D l0j.k/l0min.k/l0j.k/D1l0min.k/l0i.k/<18k>k ,i¤j(2.16)Further,considering(2.15),we havelim k!1l0min.k/l0i.k/D1C R j1C R i<1,i¤j(2.17)Putting(2.16),(2.17),and(2.12)together,we obtainlim k!1l j.k/D l j.k />0I limk!1l i.k/D0,i¤j(2.18)Then from(2.13),we havelim k!1p j.k/D1I limk!1p i.k/D0,i¤j(2.19)That completes the proof of Theorem2.1 Next,we discuss the relationship between the convergence conditions in Theorem2.1and the signal-to-noise ratio.Considering(2.7)and that!.k/is a white noise,we know that e i.k/consists of two independent components,the noise!.k/and the determinant output error between the plant and the i th model, that is, y i.k/D T.k d/ T.k d/Âi.Then,(2.7)can be rewritten ase i.k/D y i.k/C!.k/(2.20) Consequently,it is not difficult to imagine that the convergence conditions of weighting algorithms (2.9)–(2.13)depend on the noise power,as well as the signal power of y i.k/.In other words,index (2.10)should be discriminable under the disturbance of noise.To be specific,let usfirst consider a simple situation that the true model of plant,M j,is included in the model set,that is,M j2M.Then from(2.7),we havee j.k/D!.k/(2.21)STABLE WEIGHTED MULTIPLE MODEL ADAPTIVE CONTROLl0min.k/D l0j.k/D1C 1kkXr D1e2j.r/(2.22)lim k!1"1C1kkXr D1e2j.r/#D1C R(2.23)To ensure the convergence(rate)of weighting algorithms(2.9)–(2.13),we need,with probability one,thatl0min.k/l0 i .k/61K,K>1,k>k (2.24)that is,l0i.k/>K l0j.k/,K>1,k>k ,i¤j(2.25) This together with(2.10)and(2.20)yieldslim k!1"1C1kkXr D1e2i.r/#>K limk!1"1C1kkXr D1e2j.r/#,i¤j(2.26)Further,considering that y i.k/and!.k/are independent,we have1C R C limk!11kkXr D1Œ y i.r/ 2>K .1C R/(2.27)Denote P yi D lim k!11kP kr D1Œ y i.r/ 2,and then we obtainP yi1C R>K 1(2.28)Equation(2.28)implies that if we want sharper convergence rate,then we need higher signal-to-noise ratio,that is,P yi =.1C R/,which,considering R is a constant,depends on the differencebetween the true model of plant and each of the other models.Actually,(2.28)represents an upper bound for K,that is,K61C P y i1C R ,whereas a lower boundfor K could be more useful,that is,K>1C˛(2.29) where˛should be decided by word length and rounding(truncating)rules of thefloating-point system to avoid that1=K is approximately1.Similarly,for the situation that the true model of plant is not included in the model set but M j2M is the closest one to the true model of plant,we have the following limitations on K:1C R C P yi1C R C P yj>K>1C˛,i¤j(2.30)where P yj D lim k!11kP kr D1Œ y j.r/ 2and˛is the same as in(2.29).3.VIRTUAL EQUIV ALENT SYSTEMThis section describes two types of VESs of WMMAC under the condition that lim k!1p j.k/D1; lim k!1p i.k/D0,i¤j,where j indicates the closest model M j2M to the true plant.For the first type of VES,M j is the true model of plant;for the second type of VES,M j is not the true model of plant.W.ZHANGFigure2.Virtual equivalent system I of a weighted multiple model adaptive control system.3.1.Type I of virtual equivalent systemSupposelim k!1p j.k/D1I limk!1p i.k/D0,i D1,:::N,i¤j(3.1)M j is the true model of the plant P.Then,we have a VES of WMMAC based on C D C j and P D M j,as shown in Figure2,whereu.k/DNXi D1p i.k/ u i.k/(3.2)u i.k/is the output of‘local’controller C i,i D1,:::,j,:::,N,and u j.k/is the controller output difference between u.k/and u j.k/,that is,u j.k/D u.k/ u j.k/DNXi D1p i.k/ u i.k/ u j.k/DŒ.p j.k/ 1 u j.k/CNXi D1,i¤jp i.k/ u i.k/(3.3)Without loss of generality,we denoteu i.k/D T c.k/Âci(3.4) whereT c.k/DŒy.k/,y.k 1/,:::,y.k s1/,u.k 1/,:::,u.k s2/,y r.k/,:::,y r.k s3/(3.5)is the regression vector of control signal u i.k/.The numbers of the elements of T c.k/,that is,s1, s2,and s3,are limited integers and depend on specific design strategy;Âci is the parameter vector of‘local’controller C i.Putting(3.3)and(3.4)together,we haveu j.k/ k c.k/k DŒp j.k/ 1T c.k/Âcjk c.k/kCNXi D1,i¤jp i.k/T c.k/Âcik c.k/k(3.6)Considering(3.1)and thatÂci,i D1,:::,j,:::,N,are constant vectors,it is not difficult to see thatlim k!1 u j.k/k c.k/kD0(3.7)that is,u j.k/D o.k c.k/k/(3.8)STABLE WEIGHTED MULTIPLE MODEL ADAPTIVECONTROLFigure3.Virtual equivalent system II of a weighted multiple model adaptive control system.The Little-Oh operator is defined in the Appendix.As we will see in the next section,the property of u j.k/together with the‘local’control strategy is the key factor to the stability of the WMMAC system.3.2.Type II of virtual equivalent systemSupposelim k!1p j.k/D1I limk!1p i.k/D0,i D1,:::N,i¤j(3.9)M j is not the true model of the plant but the closest to the true model of plant P.Then,we have a VES of WMMAC based on C j and M j,as shown in Figure3,where u.k/,u j.k/, T c.k/,and T.k d/are the same as defined in Section3.1for VES I and e0j .k/isdefined as follows:e0j.k/D y.k/ T.k d/Âj !.k/D e j.k/ !.k/(3.10)As we will see in the next section,the properties of u j.k/and e0j .k/together with the‘local’control strategy are the key factors to the stability of the WMMAC system.4.MAIN RESULTOn the basis of two types of VESs,this section gives the stability proof of the WMMAC system,in which the‘local’controller may be designed according to any stabilizing strategy.4.1.Stability of virtual equivalent system ITheorem4.1If a WMMAC system has the following properties:(1)The true model of plant,say M j,is included in the model set M;(2)Model M j generates with probability one the minimum output error in the sense that8ˆˆˆˆˆ<ˆˆˆˆˆ:kXr D1e2j.r/<kXr D1e2i.r/,8k>k ,i¤jlimk!11kkXr D1e2j.r/D R j I limk!11kkXr D1e2i.r/D R i,R j<R i,i¤jwhere k is an unknown limited time instant,R j is a constant,R i may be constant or infinity;(3)Each‘local’controller is well defined such that C i is stabilizing M i,i D1,:::,j,:::N,andthe output of the resulting closed-loop system f C i,M i g,say y d.k/,is tracking the reference signal y r.k/in the sense thatlim k!11kkXi D1Œy d.i/ y r.i/ 2D R0,R6R0<1then it is stable.W.ZHANGRemark1R0may achieve its minimum value if the plant is minimum phase and the‘local’controller is designed according to minimum variance principle.Remark2y d.k/generally refers to the output of each closed-loop system f C i,M i g,which exists only in design.ProofFirst,according to Theorem2.1,Condition(2)guarantees thatlim k!1p j.k/D1I limk!1p i.k/D0,i D1,:::N,i¤j(4.1)where j indexes the true model of plant P.Then,we know that the WMMAC system in this situation is equivalent to VES I in the input–output sense.Next,we decompose VES I of Figure2into two subsystems,see Figures4and5.Because VES I is an LTI system in structure,we havey.k/D y0.k/C y00.k/(4.2)u.k/D u0.k/C u00.k/(4.3) where y0.k/D0,u0.k/D0,y00.k/D0,and u00.k/D0for k<0.To facilitate the proof,we need to define a new vector e .k/,whose elements are the union of that of .k d/and c.k/.Without loss of generality,we assume s1<n,s2<m,and then e .k/takes the form ofe .k/DŒy.k/,:::,y.k n/,u.k 1/,:::,u.k d m/,y r.k/,:::,y r.k s3/(4.4)Similarly,define its counterparts e 1.k/in subsystem1(Figure4),and e 2.k/in subsystem2 (Figure5),respectively,that is,e 1.k/DŒy0.k/,:::,y0.k n/,u0.k 1/,:::,u0.k d m/,y r.k/,:::,y r.k s3/(4.5)e 2.k/DŒy00.k/,:::,y00.k n/,u00.k 1/,:::,u00.k d m/,0,:::,0(4.6)Figure4.Subsystem1of virtual equivalent system I.Figure5.Subsystem2of virtual equivalent system I.STABLE WEIGHTED MULTIPLE MODEL ADAPTIVE CONTROLThen,we havee .k/D e 1.k/C e 2.k/(4.7)k .k d/k D Ok e .k/k(4.8)k c.k/k D Ok e .k/k(4.9)The Big-Oh operator is defined in the Appendix.Obviously,subsystem1(Figure4)is a time-invariant stochastic system,and Condition(3) guarantees that the closed-loop system is stable and tracking.That meanslim k!11kkXi D1k e 1.i/k2<1(4.10)lim k!11kkXi D1Œy0.i/ y r.i/ 2D R0(4.11)Subsystem2(Figure5)is a stable deterministic system with input signal given by(3.8).Considering(4.9),we obtain by Theorem14at page111in[22],j y00.k/j D O.j u j.k/j/D o.j c.k/k/D ok e .k/k(4.12)j u00.k/j D O.j u j.k/j/D o.k c.k/k/D ok e .k/k(4.13)Further,we have1 kkXi D1Œy00.i/ 2D o1kkXi D1k e .i/k2!(4.14)1 kkXi D1Œu00.i/ 2D o1kkXi D1k e .i/k2!(4.15)Equations(4.14)and(4.15)imply that1 kkXi D1k e 2.i/k2D o1kkXi D1k e .i/k2!(4.16)Then,we conclude by Lemma1thatlim k!11kkXi D1k e .i/k2<1(4.17)That means the boundedness of the input–output signals of the WMMAC system. Next,we turn to the tracking performance of the WMMAC system. Considering(4.14)and(4.17),it is obvious that1 kkXi D1Œy00.i/ 2D o.1/(4.18)Further,by Lemma2,we havelim k!11kkXi D1Œy.i/ y r.i/ 2D limk!11kkXi D1Œy0.i/ y r.i/C y00.i/ 2D limk!11kkXi D1Œy0.i/ y r.i/ 2(4.19)W.ZHANG that is,lim k!11kkXi D1Œy.i/ y r.i/ 2D R0(4.20)That completes the proof of Theorem4.1.4.2.Stability of virtual equivalent system IITheorem4.2If a WMMAC system has the following properties:(1)M j2M is the model closest to the true plant in the following sense with probability one8ˆˆˆˆˆ<ˆˆˆˆˆ:kXr D1e2j.r/<kXr D1e2i.r/,8k>k ,i¤jlimk!11kkXr D1e2j.r/D R j I limk!11kkXr D1e2i.r/D R i,R j<R i,i¤jwhere k is an unknown limited time instant,R j is a constant,and R i may be constant or infinity;(2)Each‘local’controller is well defined such that C i is stabilizing M i,i D1,:::,j,:::N,andthe output of the resulting closed-loop system f C i,M i g,say y d.k/,is tracking the reference signal y r.k/in the sense thatlim k!11kkXi D1Œy d.i/ y r.i/ 2D R0,R6R0<1(3)For the closest model M j,we havej e0j.k/j D j e j.k/ !.k/j D o.k .k d/k/ then the WMMAC system is stable.ProofFirst,according to Theorem2.1,Condition(1)guarantees thatlim k!1p j.k/D1I limk!1p i.k/D0,i D1,:::N,i¤j(4.21)where j indexes the model closest to the true plant P,that is,M j.Then,we know that the WMMAC system in this situation is equivalent to VES II in the input–output sense.Next,we decompose VES II(Figure3)into three subsystems,as shown in Figure6–8,respectively.Figure6.Subsystem1of virtual equivalent system II.Figure7.Subsystem2of virtual equivalent system II.Figure8.Subsystem3of virtual equivalent system II.By superposition principle,we havey.k/D y0.k/C y00.k/C y000.k/(4.22)u.k/D u0.k/C u00.k/C u000.k/(4.23) Similar to the proof of Theorem4.1,we define e .k/,e 1.k/,e 2.k/,and e 3.k/.In detail,e .k/, e 1.k/,and e 2.k/are the same as(4.4),(4.5),and(4.1),respectively,ande 3.k/DŒy000.k/,:::,y000.k n/,u000.k 1/,:::,u000.k d m/,0,:::,0(4.24) Then,we havee .k/D e 1.k/C e 2.k/C e 3.k/(4.25)k c.k/k D Ok e .k/k(4.26)k .k d/k D Ok e .k/k(4.27)First,by Condition(2),we know that subsystem1(Figure6)is a stable stochastic LTI system,which means thatlim k!11kkXi D1k e 1.i/k2<1(4.28)lim k!11kkXi D1Œy0.i/ y r.i/ 2D R0(4.29)Second,subsystem2(Figure7)is a stable deterministic system with input signal given by(3.8). Thus,we havej y00.k/j D O.j u j.k/j/D o.k c.k/k/D ok e .k/k(4.30)j u00.k/j D O.j u j.k/j/D o.k c.k/k/D ok e .k/k(4.31)Further,we obtain1 kkXi D1Œy00.i/ 2D o1kkXi D1k e .i/k2!(4.32)1 kkXi D1Œu00.i/ 2D o1kkXi D1k e .i/k2!(4.33)1 kkXi D1k e 2.i/k2D o1kkXi D1k e .i/k2!(4.34)Finally,let us consider subsystem3(Figure8),which is also a stable deterministic system. According to Condition(3),the input signal of subsystem3has the following property:1 kkXi D1Œe0j.i/ 2D o1kkXi D1k .i d/k2!D o1kkXi D1k e .i/k2!(4.35)By the fact that subsystem3is stable,we havej y000.k/j D O.j e0j.k/j/(4.36)k u000.k/k D O.j e0j.k/j/(4.37) Further,we obtain1 kkXi D1Œy000.i/ 2D o1kkXi D1k e .i/k2!(4.38)1 kkXi D1Œu000.i/ 2D o1kkXi D1k e .i/k2!(4.39)1 kkXi D1k e 3.i/k2D o1kkXi D1k e .i/k2!(4.40)Then by Lemma1,regarding e 2.k/and e 3.k/as one variate,we obtainlim k!11kkXi D1k e .i/k2<1(4.41)That means the boundedness of the input–output signals of the WMMAC system. Further by Lemma2,we obtain the tracking performance of VES II,that is,lim k!11kkXi D1Œy.i/ y r.i/ 2D limk!11kkXi D1Œy0.i/ y r.i/ 2D R0(4.42)That completes the proof of Theorem4.2. Similar to the proof of Theorem4.2(so the details are omitted),we have the following corollary for a general WMMAC system.Corollary 4.1If a WMMAC system has the following properties:(1)M j 2M is the model closest to the true plant in the following sense with probability one8ˆˆˆˆˆ<ˆˆˆˆˆ:k X r D 1e 2j .r/<k X r D 1e 2i .r/,8k >k ,i ¤j lim k !11k k X r D 1e 2j .r/D R j I lim k !11k k X r D 1e 2i .r/D R i ,R j <R i ,i ¤j where k is an unknown limited time instant,R j is a constant,and R i may be constantor infinity;(2)Each ‘local’controller is well defined such that C i is stabilizing M i ,i D 1,:::,j ,:::N ,andthe output of the resulting closed-loop system f C i ,M i g ,say y d .k/,is tracking the reference signal y r .k/in the sense thatlim k !11kk X i D 1Œy d .i/ y r .i/ 2D R 0,R 6R 0<1(3)For the closest model M j ,we have1k k X i D 1e 0j .i/ 2D 1k k X i D 1Œe j .i/ !.i/ 2D o 1kk X i D 1k .i d /k 2!then it is stable.Remark 3Although we only considered single input and single output system,it is straightforward to develop the same results for multi-input multi-output system,because we adopted norm operation to draw the theorems and the corollary.5.SIMULATION RESULTSConsider an uncertain discrete-time plant1C a 1q 1C a 2q 2 y.k/D q 1 b 0C b 1q 1u.k/C !.k/(5.1)where !.k/is a zero-mean white noise sequence that was created with the Matlab randn function.The deterministic part of (5.1)is obtained by converting the following continuous-time LTI model to a discrete-time model with sample time t s D 0.5s and the zero order hold.ks 2 3s C 2(5.2)The uncertainty of (5.1)originates from k in (5.2).For simplicity,we suppose there are only four possible situations as the uncertainty of k ,that is,k D 0.7,k D 0.8,k D 1,and k D 0.9.That means in (5.1),a 1and a 2are constants,that is,a 1D 4.3670,a 2D 4.4817,and b 0and b 1depend on k .Four ‘local’controllers were designed by pole assignment strategy.Each controller stabilizes a possible model by formulating an expected closed-loop characteristic polynomial,say A m q 1 ,and track the reference signal y r .k/.In detail,controller 1is designed according to Model 1(k D 0.7),that is,1 4.3670q 1C 4.4817q2 y.k/D q 1 0.1473C 0.2428q 1u.k/C !.k/(5.3)Controller 2is designed according to Model 2(k D 0.8),that is,1 4.3670q 1C 4.4817q2 y.k/D q 1 0.1683C 0.2775q 1u.k/C !.k/(5.4)Controller 3is designed according to Model 3(k D 1),that is,1 4.3670q 1C 4.4817q2 y.k/D q 1 0.2104C 0.3469q 1u.k/C !.k/(5.5)Controller 4is designed according to Model 4(k D 0.9),that is,1 4.3670q 1C 4.4817q2 y.k/D q 1 0.1894C 0.3122q 1u.k/C !.k/(5.6)The expected closed-loop characteristic polynomial is chosen to beA m q 1D 1 1.3205q 1C 0.4966q 2(5.7)which corresponds to the characteristic polynomial of the following continuous-time second-order system!n 2s 2C 2 !n s C !n 2(5.8)with D 0.707,!n D 1,and sample time t s D 0.5s.Case 1The true model of plant is included in the model set,say Model 2(k D 0.8);the variance of !.k/is chosen to be D 0.1.The simulation results,that is,the four weights signals,the closed-loop output y.k/against reference signal y r .k/,and the control signal u.k/are shown in Figures 9and 10.5010015020000.10.20.30.4kp 1(k )0501001502000.20.40.60.81kp 2(k )5010015020000.050.10.150.20.25k p 3(k )0501001502000.10.20.30.4kp 4(k )Figure 9.Controller weight signals of Case 1.050100150200250300350400−20−1001020ky r (k )/y (k )y r(k)y(k)50100150200250300350400−100−50050ku (k )u(k)Figure 10.Output,reference,and control signals of Case 1.Case 2The true model of plant is not included in the model set,which corresponds to k D 1.03in (5.2),that is,1 4.3670q 1C 4.4817q2 y.k/D q 1 0.2167C 0.3573q 1u.k/C !.k/(5.9)Model 3is the closest in the model set to model (5.9);the variance of !.k/is chosen to be D 0.1.The simulation results are shown in Figures 11and 12.In summary,the four weights p i .k/,i D 1,2,3,4converge correctly in each case,and consequently,the closed-loop control system is stable.501001502000.10.20.30.4kp 1(k )5010015020000.10.20.30.4kp 2(k )501001502000.20.40.60.81k p 3(k )0501001502000.10.20.30.4kp 4(k )Figure 11.Controller weight signals of Case 2.050100150200250300350400−20−10010ky r (k )/y (k )ry(k)050100150200250300350400−5050ku (k )u(k)Figure 12.Output,reference,and control signals of Case 2.However,as shown in case 3,if the noise level is high enough,while the difference between the true model of plant and each of the other models is not significant,then the WMMAC sys-tem exhibits ‘model-identification confusion’,that is,controller weights cannot converge correctly.Consequently,the system performance will be drastically degraded because related theoretical assumptions,that is,(2.14)and (2.15),were severely violated.Case 3Suppose there are four possible situations as the uncertainty of k in (5.2),that is,k D 0.97,k D 0.98,k D 1,and k D 0.99.The true model of plant is not included in the modelset,which corresponds to k D 1.01in (5.2).The variance of !.k/is D 10.The simulation results are shown in Figures 13and 14.501001502000.20.40.60.81kp 1(k )0501001502000.10.20.30.40.5kp 2(k )5010015020000.050.10.150.20.25k p 3(k )5010015020000.050.10.150.20.25kp 4(k )Figure 13.Controller weight signals of Case 3.。