R软件应用多元分析.ppt

Click to edit Master title style,Click to edit Master text styles,Second level,Third level,Fourth level,Fifth level,*,*,Click to edit Master title style,Click to edit Master text styles,Second level,Third level,Fourth level,Fifth level,*,*,R,软件应用多元分析,8.1 判别法则(分类),已知有多少类，并且在训练样本的前提下，利用训练样本得到判别,函,数，对待测样本进行分类；,距离判别,判别问题，就是将,p,维欧几里得空间,R,p,划分成,k,个互不相交的区域,R,1,R,2,R,k,。,若,xR,i,i=1,2,k,则判定,x,属于总体,X,i,i=1,2,k.,Mahalanobis,距离的概念：,定义,8.1,设,x,y,是从均值为,协方差矩阵为,的总体,X,中抽取的两个样本,则总体,X,内两点,x,y,的,Mahalanobis,距离定义为,样本,x,与总体,X,的,Mahalanobis,距离为：,例如：,=1.66,1.66,2.34,从欧氏距离看,A,到,1,的距离比到,2,的距离要近，,但从概率分布的角度看,说明,A,到,2,的,距离,比到,1,的距离要近,.,标准化,Mahalanobis,距离符合概率分布内涵,.,2.判别准则与判别函数,2.1,两个总体的距离判定,.,总体,X,1,X,2,的均值向量分别为,1,2,协方差分别为,1,2,给定样本,x,，判断,x,来自哪一个总体,.,1.,1,2,1,=,2,判断准则,:,判断准则,:,总体的均值与协方差未知时：,设 是来自总体,X1,的,n1,个样本,是来自总体,X2,的,n2,个样本,则样本的均值与协方差阵为,判断准则,:,1.,1,2,1,2,判断函数,:,总体的均值与协方差未知时：,总体的均值与协方差已知时：,Mahalanobis Distance,Returns the squared Mahalanobis distance of all rows in x and the vector,mu,=center with respect to,Sigma,=cov.This is(for vector x)defined as,D2=(x-)-1(x-),Usage:mahalanobis(x,center,cov,inverted=FALSE,.),X:vector or matrix of data with,say,p,columns.,Center:mean vector of the distribution or second data vector of length,p,.,Cov:covariance matrix(,p x p,)of the distribution.,R程序,discriminiant.distance-function (,TrnX1,TrnX2,TstX=NULL,var,.equ,al,=,FALSE,),if(is.null(TstX)=TRUE)TstX-rbind(TrnX1,TrnX2),if(is.vector(TstX)=TRUE)TstX-t(as.matrix(TstX),else if(is.matrix(TstX)!=TRUE),TstX-as.matrix(TstX),if(is.matrix(TrnX1)!=TRUE)TrnX1-as.matrix(TrnX1),if(is.matrix(TrnX2)!=TRUE)TrnX2-as.matrix(TrnX2),nx-nrow(TstX),#,测定待测样本的个数,blong-,matrix(rep(0,nx),nrow=1,byrow=TRUE,dimnames=list(,“,blong,”,1:nx)#,产生一个行矩阵,，,共,nx,个数,mu1-colMeans(TrnX1);mu2-colMeans(TrnX2),if(var.equal=TRUE|var.equal=T),S-var(rbind(TrnX1,TrnX2),w-mahalanobis(TstX,mu2,S)-mahalanobis(TstX,mu1,S),else,S1-var(TrnX1);S2-var(TrnX2),w0)blongi-1,else blongi-2 ,blong,#X1,，,X2,类的训练样本,#,TstX=NULL,待测样本,为,2,个训练样本之和,#,数据全部转化成矩阵,行表示样本个数，列表,示样本维数,n,#,根据第,i,个样本的,w,i,值,返回样本类别结果,理论中的样本按列排列,X=(X1,X2,Xn),，每列是一个样本，,n,列表示,n,个样本，这里样本按行排,X=(X1,X2,Xn)T,4.判别实例,例8.1 在研究砂基液化问题中，选了7个因子，今从已液化和未液化的地层中分别抽了12个和23个样本，数据列在表中，其中I类表示已液化类，II类表示未液化类。试建立距离判别的判别准则，并按判别准则对原35个样本进行回代(即按判别准则进行分类)，分析误判情况。,编号,类别,x1,x2,x3,x4,x5,x6,x7,1,I,6.6,39,1,6,6,0.12,20,2,I,6.6,39,1,6,12,0.12,20,3,I,6.1,47,1,6,6,0.08,12,4,I,6.1,47,1,6,12,0.08,12,5,I,8.4,32,2,7.5,19,0.35,75,6,I,7.2,6,1,7,28,0.3,30,7,I,8.4,113,3.5,6,18,0.15,75,8,I,7.5,52,1,6,12,0.16,40,9,I,7.5,52,3.5,7.5,6,0.16,40,10,I,8.3,113,0,7.5,35,0.12,180,11,I,7.8,172,1,3.5,14,0.21,45,12,I,7.8,172,1.5,3,15,0.21,45,13,II,8.4,32,1,5,4,0.35,75,14,II,8.4,32,2,9,10,0.35,75,15,II,8.4,32,2.5,4,10,0.35,75,16,II,6.3,11,4.5,7.5,3,0.2,15,17,II,7,8,4.5,4.5,9,0.25,30,18,II,7,8,6,7.5,4,0.25,30,19,II,7,8,1.5,6,1,0.25,30,20,II,8.3,161,1.5,4,4,0.08,70,21,II,8.3,161,0.5,2.5,1,0.08,70,22,II,7.2,6,3.5,4,12,0.3,30,23,II,7.2,6,1,3,3,0.3,30,24,II,7.2,6,1,6,5,0.3,30,25,II,5.5,6,2.5,3,7,0.18,18,26,II,8.4,113,3.5,4.5,6,0.15,75,27,II,8.4,113,3.5,4.5,8,0.15,75,28,II,7.5,52,1,6,6,0.16,40,29,II,7.5,52,1,7.5,8,0.16,40,30,II,8.3,97,0,6,5,0.15,180,31,II,8.3,97,2.5,6,5,0.15,180,32,II,8.3,89,0,6,10,0.16,180,33,II,8.3,56,1.5,6,13,0.25,180,34,II,7.8,172,1,3.5,6,0.21,45,35,II,7.8,283,1,4.5,6,0.18,45,#R,里的数据就是这样排,样本均值是对每个指标按列求均值,然后组成样本均值,R实现：,classx1=read.table(dataexample801x1.txt),classx2=read.table(dataexample801x2.txt),discriminiant.distance(classx1,classx2,var.equal=T),1 2 3 4 5 6 7 8,9,10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26,1 1 1 1 1 1 1 1,2,1 1 1 2 2 2 2 2 2 2 2 2 2 2 2 2 2,27,28 29,30 31 32 33 34 35,blong 2,1 1,2 2 2 2 2 2,blong,#,在认为两个总体协方差相同的情况下，有,3,个点判错,discriminiant.distance(classx1,classx2),1 2 3 4 5 6 7 8,9,10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26,1 1 1 1 1 1 1 1,2,1 1 1 2 2 2 2 2 2 2 2 2 2 2 2 2 2,27 28 29 30 31 32 33 34 35,blong 2 2 2 2 2 2 2 2 2,blong,#,在认为两个总体协方差不同的情况下，有,1,个点判错,5.多分类问题的距离判别,1,2,k,1=,2,=,k,相应的判别准则：,distinguish.distance-function,(TrnX,TrnG,TstX=NULL,var.equal=FALSE),if(is.factor(TrnG)=FALSE),mx-nrow(TrnX);mg-nrow(TrnG)TrnX-rbind(TrnX,TrnG),TrnG-factor(rep(1:2,c(mx,mg),if(is.null(TstX)=TRUE)TstX-TrnX,#,如果待测样本为空,则将训练样本视为待测样本,if(is.vector(TstX)=TRUE)TstX-t(as.matrix(TstX),else if(is.matrix(TstX)!=TRUE),#,待测样本是多样本,但不是矩阵形式时,TstX-as.matrix(TstX,),#,转成矩阵,(,如,data.frame,类型转成矩阵,),if(is.matrix(TrnX)!=TRUE)TrnX-as.matrix(TrnX)nx-nrow(TstX),blong-matrix(rep(0,nx),nrow=1,dimnames=list(,“,blong,”,1:nx),#,本页语句都是准备工作,#,如果,TrnG,从主函数未接收到,因子,数据,#,待测样本,TstX,是单样本时候,是向量,vector,此时将其转为矩阵,(,是列矩阵,),然后再转成行矩阵,#,则是,2,分类问题,而非多分类,可省略,#,行名称为,”,blong,”,列名称为数字,1,到,nx,#,产生类别矩阵,blong,初始值全为,0,Continue:,g-length(levels(TrnG),mu-matrix(0,nrow=g,ncol=ncol(TrnX),for(i in 1:g),mui,-colMeans(TrnXTrnG=i,),D-matrix(0,nrow=g,ncol=nx),#ncol,个样本因子按列排,g,个类别按行排,#,对属于第,i,个类的样本求他们因子的均值,结果存到,mu,的第,i,行,#,产生,0,阵,行数为类别数,g,列数为样本数,nx,#,得到多分类的类别,共,g,个,:1 2,1,2,3,4,5,6,7,1,0 0 0 0 0 0 0,2,0 0 0 0 0 0 0,1 ,2 ,3 ,4 ,5 ,6 ,7,1,7.358333 73.66667 1.458333 6.00000 15.250000 0.1716667 49.50000,2,7.686957 69.60870 2.043478 5.23913 6.347826 0.2156522 70.34783,1,2,3,4,5,6,7,8,9,10,11,12,13,1,0 0 0 0 0 0 0 0 0 0 0 0 0,2,0 0 0 0 0 0 0 0 0 0 0 0 0,26,27,28,29,30,31,32,33,34,35,1,0 0 0 0 0 0 0 0 0 0,2,0 0 0 0 0 0 0 0 0 0,Continue:,if(var.equal=TRUE|var.equal=T),for(i in 1:g),Di,-mahalanobis(TstX,mui,var(TrnX),else for(i in 1:g),Di,-mahalanobis(TstX,mui,var(TrnXTrnG=i,),for(j in 1:nx)dmin-Inf,for(i in 1:g),if(Di,jdmin),dmin-Di,j;,blongj-i,blong,#,待测样本到第,i,类的马氏距离,1 ,2 ,3 ,4 ,5 ,6 ,7 ,8,1,181.3889 182.5306 162.9359 164.1592 233.7561 205.8525 238.8812 214.1178,2,181.3889 182.5306 162.9359 164.1592 233.7561 205.8525 238.8812 214.1178,9 ,10 ,11 ,12 ,13 ,14 ,15 ,16,1,219.4913 201.6875 185.8174 184.6754 222.2703 241.7303 218.1065 169.8246,2,219.4913 201.6875 185.8174 184.6754 222.2703 241.7303 218.1065 169.8246,17 ,18 ,19 ,20 ,21 ,22 ,23 ,24,1,182.1071 197.3248 186.0215 224.1768 221.5524 185.4759 183.1583 192.0052,2,182.1071 197.3248 186.0215 224.1768 221.5524 185.4759 183.1583 192.0052,25 ,26 ,27 ,28 ,29 ,30 ,31 ,32,1,114.8461 229.1703 229.5824 213.1659 220.9516 181.5381 180.7470 181.3109,2,114.8461 229.1703 229.5824 213.1659 220.9516 181.5381 180.7470 181.3109,33 ,34 ,35,1,175.8290 184.0261 181.7853,2,175.8290 184.0261 181.7853,#,对第,j,个样本,纵向求,min,，如果该,最小值位于第,i,行，,则第,j,个样本就是属于第,i,类,方差未知,方差已知,判别,1.误判概率与误判损失,x,被判为,X2,x,实际来自,X1,来自,X2,但被判为,x1,的概率,:,来自,X1,但被判为,x2,的概率,:,来自,X1,但被判为,x1,的概率,:,来自,X2,但被判为,x2,的概率,:,总体,X1,的先验概率,平均误判损失,ECM:,ECM(R1,R2)=L(2|1)P(2|1)p,1,+L(1|2)P(1|2)p,2,来自,X1,被判为,X2,引起的损失,来自,X2,被判为,X1,引起的损失,2.两个总体的Bayes判别,ECM(R1,R2)=L(2|1)P(2|1)p1+L(1|2)P(1|2)p2,0,ECM=min,划分区域,R1,和,R2:,作为,Bayes,判别准则,须计算,正态分布的情况,:X,i,N(,i,i,)(i=1,2),1.,1,=,2,类似地,2.,1,2,3.R程序与例子,R,程序略；,例,8.3,下表是某气象站预报有无春旱的实际资料，,x1,与,x2,是综合预报因子，有春旱的是,6,个年份的资料，无春旱的是,8,个年份的资料，它们的先验概率分别用,6/14,和,8/14,来估计，并假设误判损失相等，试用,Bayes,估计对数据进行分析。,序号,春旱,无春旱,1,24.8,-2,22.1,-0.7,2,24.1,-2.4,21.6,-1.4,3,26.6,-3,22,-0.8,4,23.5,-1.9,22.8,-1.6,5,25.5,-2.1,22.7,-1.5,6,27.4,-3.1,21.5,-1,7,22.1,-1.2,8,21.4,-1.3,R实现,x1=scan(dataexample803x1.txt),x2=scan(dataexample803x2.txt),dim(x1)=c(2,6),1,2,3,4,5,6,1,24.8 24.1 26.6 23.5 25.5 27.4,2,-2.0-2.4-3.0-1.9-2.1-3.1,dim(x2)=c(2,8),x1=t(x1),x2=t(x2),discriminiant.bayes(x1,x2,rate=8/6,var.equal=T),1 ,2,1,24.8 23.5,2,-2.0-1.9,3,24.1 25.5,4,-2.4-2.1,5,26.6 27.4,6,-3.0-3.1,1 2 3,4,5 6 7 8 9 10 11 12 13 14,blong 1 1 1,2,1 1 2 2 2 2 2 2 2 2,#4,号样本被错判,discriminiant.bayes(x1,x2,rate=8/6),1 2 3 4 5 6 7 8 9 10 11 12 13 14,blong 1 1 1 1 1 1 2 2 2 2 2 2 2 2,#,无错判,.多分类问题的Bayes判别,样本共分,k,类,:X,1,X,2,X,k,相应的先验概率为,p,1,p,2,p,k,假定所有的错判损失相同,则判别准则为,:,1.,1,=,k,=,2.,1,k,R程序,if(var.equal=TRUE|var.equal=T),for(i in 1:g),d2-mahalanobis(TstX,mui,var(TrnX),Di,-d2-2*log(pi),else,for(i in 1:g),S-var(TrnXTrnG=i,),d2-mahalanobis(TstX,mui,S),Di,-d2-2*log(pi)-log(det(S),for(j in 1:nx),dmin-Inf,for(i in 1:g),if(Di,jdmin),dmin-Di,j;blongj-i ,blong,例8.4,用Bayes判别对Fisher Iris数据进行分析.假设先验概率相同,均为1.考虑总体协方差阵不同的情况.,x=iris,1:4,g=gl(3,50),distinguish.bayes(x,g),1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27,blong 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1,28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51,blong 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 2,52 53 54 55 56 57 58 59 60 61 62 63 64 65 66 67 68,69,70,71,72,73,74 75,blong 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2,3,2,3,2,3,2 2,76 77,78,79 80 81 82 83,84,85 86 87 88 89 90 91 92 93 94 95 96 97 98 99,blong 2 2,3,2 2 2 2 2,3,2 2 2 2 2 2 2 2 2 2 2 2 2 2 2,100 101 102 103 104 105 106 107 108 109 110 111 112 113 114 115 116 117,blong 2 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3,118 119 120 121 122 123 124 125 126 127 128 129 130 131 132 133 134 135,blong 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3,136 137 138 139 140 141 142 143 144 145 146 147 148 149 150,blong 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3,#,误判概率为,1-145/150=3.33%,判别,按,类内方差,尽量小,类间方差,尽量大的准则求判别函数,.(,以,2,个总体为例,),判别准则,总体,X1,X2,的均值与协方差阵分别为,1,2,和,1,2,对于样本,x,考虑其判别函数,:,判别准则为,:,U(x)=?,2.线性判别函数中系数的确定u(x)为线性函数,设总体,X1,X2,的样本容量为,n,1,n,2,;,则,u,1,u,2,和,1,2,的估计,:,确定判别函数,若 ：,进一步：,判别准则为,:,4.R程序与例子,例,8.5,用,Fisher,判别解例,8.1,classx1=read.table(dataexample801x1.txt),classx2=read.table(dataexample801x2.txt),discriminiant.fisher(classx1,classx2),结果：,1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26,blong,1 1 1 1 1 1 1 1 1 1 1 1 2 2 2 2 2 2 2 2 2 2 2 2 2 2,27,28,29,30 31 32 33 34 35,blong 2,1 1,2 2 2 2 2 2,#28,，,29,号样本为误判样本,R,程序,mu1-colMeans(TrnX1);mu2-colMeans(TrnX2),S-(n1-1)*var(TrnX1)+(n2-1)*var(TrnX2),mu-n1/(n1+n2)*mu1+n2/(n1+n2)*mu2,wr,x1 x2 x3 x4,1 1 1 1,center,x1 x2 x3 x4,1-0.5-0.5-0.5-0.5,2 0.5 0.5 0.5 0.5,x_star,x1 x2 x3 x4,1-0.5-0.5-0.5-0.5,2 0.5 0.5 0.5 0.5,x_star,x1 x2 x3 x4,1-0.7071068-0.7071068-0.7071068-0.7071068,2 0.7071068 0.7071068 0.7071068 0.7071068,#,普通标准化,continue,(2)极差正规化变换.,x=data.frame(x1=c(1,2),x2=c(1,2),x3=c(1,2),x4=c(1,2),x1 x2 x3 x4,1 1 1 1 1,2 2 2 2 2,ap=apply(x,2,min),x1 x2 x3 x4,1 1 1 1,center=sweep(x,2,ap),r=apply(x,2,max)-apply(x,2,min),x_star=sweep(center,2,r,/),r,x1 x2 x3 x4,1 1 1 1,center,x1 x2 x3 x4,1 0 0 0 0,2 1 1 1 1,x_star,x1 x2 x3 x4,1 0 0 0 0,2 1 1 1 1,3.相似系数,相似系数用于对变量进行分类。,夹角余弦,X,i,与,X,j,的夹角余弦称为两向量的相似系数,x=data.frame(x1=c(1,2),x2=c(1,2),x3=c(1,2),x4=c(1,2),y=scale(x,center=F,scale=T)/sqrt(nrow(x)-1),x1 x2 x3 x4,1,0.4472136 0.4472136 0.4472136 0.4472136,2,0.8944272 0.8944272 0.8944272 0.8944272,c=t(y)%*%y,将样本列,(,变量,),标准化,相关系数,中心化,样本,(,变量,),的相关矩阵,R,实现：,cor(x),系统聚类法,记号：,d,ij,:,第,i,个样本与第,j,个样本的距离,.,G,1,G,2,:,表示类,.,D,KL,:G,K,与,G,L,的,(,类,),距离,.,最短距离法,类与类之间的距离为两类最近样本间的距离,:,当某步骤类,GK,和,GL,合并为,GM,后,按最短距离法计算新类,GM,与其他类,GJ,的类间距离,:,最长距离法,递推公式,中间距离法,推广：,类平均法,可变类平均法,:,类,G,K,的样本个数,Mcquitty,相似分析,递推公式,类与类之间的距离定义为他们重心,(,均值,),之间的,Euclid,距离,.,设,G,K,和,G,L,的重心分别为 和,.,重心法,递推公式,离差平方和法,(ward,方法,),递推公式,GK,和,GL,的平方距离也可定义为：,与重心法相差一个系数，表明表明大样本类不易合并，这更符合实际。,7.R相关函数及其用法,Usage,hclust(d,method=complete,members=NULL),Description,Hierarchical cluster analysis on a set of dissimilarities and methods for analyzing it.,d:a dissimilarity structure as produced by dist.,method:ward,single,complete,average,mcquitty,median or centroid.,例,8.6,设有,5,个样本,每个样本只有一个指标,分别是,1,2,6,8,11,样本间的距离选用,Euclid,距离,试用最短距离法、最长距离法等方法进行聚类分析，并画出相应的谱系图,.,R,实现,:,x=c(1,2,6,8,11),dim(x)=c(5,1),d=dist(x),d,1 2 3 4,2,1,3,5 4,4,7 6 2,5,10 9 5 3,第一个样本到第,2,3,4,5,个样本的距离,例8.6(续),hc1=hclust(d,single),hc2=hclust(d,complete),hc3=hclust(d,median),hc4=hclust(d,mcquitty),hc5=hclust(d,average),hc6=hclust(d,centroid),hc7=hclust(d,ward),opar=par(mfrow=c(3,3),plot(hc1,hang=-1),plot(hc2,hang=-1),plot(hc3,hang=-1),plot(hc4,hang=-1),plot(hc5,hang=-1),plot(hc6,hang=-1),plot(hc7,hang=-1),例8.7,对,305,名女中学生测量,8,个体型指标,相应的相关矩阵如表，将相关系数看成相似系数,定义距离为,d,ij,=1-r,ij,用最长距离法做系统分析,.,身高,手臂长,上肢长,下肢长,体重,颈围,胸围,胸宽,x1,x2,x3,x4,x5,x6,x7,x8,x1,1,x2,0.846,1,x3,0.805,0.881,1,x4,0.859,0.826,0.801,1,x5,0.473,0.376,0.38,0.436,1,x6,0.398,0.326,0.319,0.329,0.762,1,x7,0.301,0.277,0.237,0.327,0.73,0.583,1,x8,0.382,0.277,0.345,0.365,0.629,0.577,0.539,1,R实现,x=scan(dataexample807.txt),r=as.matrix(x),dim(r)=c(8,8),d=as.dist(1-r),hc=hclust(d),plot(hc,hang=-1),d,1 2 3 4 5 6 7,2 0.154,3 0.195 0.119,4 0.141 0.174 0.199,5 0.527 0.624 0.620 0.564,6 0.602 0.674 0.681 0.671 0.238,7 0.699 0.723 0.763 0.673 0.270 0.417,8 0.618 0.723 0.655 0.635 0.371 0.423 0.461,8.类个数的确定,给定一个阈值,.,观测样本的散点图,.(,仅限于二维,三维样本,),试用统计量,.,根据谱系图确定分类个数的原则,:,A.,各类重心的距离必须很大,.,B.,确定的类中,各类所包含的元素都不要太多,.,C.,类的个数必须符合实用的目的,.,D.,若采用不同的聚类方法处理,则在各自的聚类图中应发现相同的类,.,Usage,rect.hclust(tree,k=NULL,which=NULL,x=NULL,h=NULL,border=2,cluster=NULL),Description,Draws rectangles around the branches of a dendrogram highlighting the corresponding clusters.,Tree,是由,hclust,生成的对象,;,K,是类的个数,;,H,是谱系图中的阈值,;,Rect.hclust()实例(8.7),9.实例,表中给出了1999年全国31个省,市,自治区的城镇居民家庭平均每人全年消费性支出的8个主要指标(变量)数据.这8个变量是:,x1:食品;x2:衣着;x3:家庭设备用品及服务;x4:医疗保障;x5:交通与通信;x6:娱乐教育文化服务;x7:居住;x8:杂项商品和服务;,分别使用最长距离法,类平均法,重心法和ward方法对各地区做聚类分析.,x1,x2,x3,x4,x5,x6,x7,x8,北京,2959.19,730.79,749.41,513.34,467.87,1141.82,478.42,457.64,天津,2459.77,495.47,697.33,302.87,284.19,735.97,570.84,305.08,河北,1495.63,515.9,362.37,285.32,272.95,540.58,364.91,188.63,山西,1046.33,477.77,290.15,208.57,201.5,414.72,281.84,212.1,内蒙,1303.97,524.29,254.83,192.17,249.81,463.09,287.87,192.96,辽宁,1730.84,553.9,246.91,279.81,239.18,445.2,330.24,163.86,吉林,1561.86,492.42,200.49,218.36,220.69,459.62,360.48,147.76,黑龙江,1410.11,510.71,211.88,277.11,224.65,376.82,317.61,152.85,上海,3712.31,550.74,893.37,346.93,527,1034.98,720.33,462.03,浙江,2629.16,557.32,689.73,435.69,514.66,795.87,575.76,323.36,安徽,1844.78,430.29,271.28,126.33,250.56,513.18,314,151.39,福建,2709.46,428.11,334.12,160.77,405.14,461.67,525.13,232.29,江西,1563.78,303.65,233.81,107.9,209.7,393.99,509.39,160.12,continue,山东,1675.75,613.32,550.71,219.79,272.59,599.43,371.62,211.84,河南,1427.65,431.79,288.55,208.14,217,337.76,421.31,165.32,湖北,1783.43,511.88,282.84,201.01,237.6,617.74,523.52,182.52,湖南,1942.23,512.27,401.39,206.06,321.29,697.22,492.6,226.45,广东,3055.17,353.23,564.56,356.27,811.88,873.06,1082.82,420.81,广西,2033.87,300.82,338.65,157.78,329.06,621.74,587.02,218.27,海南,2057.86,186.44,202.72,171.79,329.65,477.17,312.93,279.19,重庆,2303.29,589.99,516.21,236.55,403.92,730.05,438.41,225.8,四川,1974.28,507.76,344.79,203.21,240.24,575.1,430.36,223.46,贵州,1673.82,437.75,461.61,153.32,254.66,445.59,346.11,191.48,云南,2194.25,537.01,369.07,249.54,290.84,561.91,407.7,330.95,西藏,2646.61,839.7,204.44,209.11,379.3,371.04,269.59,389.33,陕西,1472.95,390.89,447.95,259.51,230.61,490.9,469.1,191.34,甘肃,1525.57,472.98,328.9,219.86,206.65,449.69,249.66,228.19,青海,1654.69,437.77,258.78,303,244.93,479.53,288.56,236.51,宁夏,1375.46,480.99,273.84,317.32,251.08,424.75,228.73,195.93,新疆,1608.82,536.05,432.46,235.82,250.28,541.3,344.85,214.4,R实现：,x=read.table(dataexample808.txt),y=c(,北京,天津,河北,山西,内蒙,辽宁,吉林,黑龙江,上海,浙江,安徽,福建,江西,山东,河南,湖北,湖南,广东,广西,海南,重庆,四川,贵州,云南,西藏,陕西,甘肃,青海,宁夏,新疆,),row.names(x)=y,d=dist(scale(x),hc1=hclust(d),hc2=hclust(d,average),hc3=hclust(d,centroid),hc4=hclust(d,ward),opar=par(mfrow=c(2,2),plot(hc1,hang=-1),re1=rect.hclust(hc1,k=5),plot(hc2,hang=-1),re2=rect.hclust(hc2,k=5),plot(hc3,hang=-1),re3=rect.hclust(hc3,k=5),plot(hc4,hang=-1),re4=rect.hclust(hc4,k=5),R实现:,通过作业分析学生关系(案例),我们实验课上经常出现同学们代