####聚类分析####
####计算各种距离#dist()函数
dist(x, method = "euclidean",
diag = FALSE, upper = FALSE, p = 2)
####数据中心化或标准化#scale（）函数
scale(x, center = TRUE, scale = TRUE)
####极差标准化变换#sweep（）函数
#变化过程
center <- sweep(x, 2, apply(x, 2, mean))
R <- apply(x, 2, max) - apply(x,2,min)
x_star <- sweep(center, 2, R, "/")
####相似系数-两向量夹角余弦
y <- scale(x, center = F, scale = T)/sqrt(nrow(x)-1)
C <- t(y) %*% y
####相关系数
C<-cor(x)
####系统聚类#hclust（）函数
hclust(d, method = "complete", members=NULL)
single——最短距离法
complete——最长距离法
median——中间距离法
mcquitty——相似法
average——类平均法
centroid——重心法
ward——类平均法
####谱系图#plot（）
plot(x, labels = NULL, hang = 0.1, #x为hclust（）生成的对象,hang表示所在位置
axes = TRUE, frame.plot = FALSE, ann = TRUE,
main = "Cluster Dendrogram",
sub = NULL, xlab = NULL, ylab = "Height", ...)
#plclust()函数
plclust(tree, hang=0.1, unit=FALSE, level=FALSE, hmin=0,
square=TRUE, labels=NULL, plot. = TRUE,
axes = TRUE, frame.plot = FALSE, ann = TRUE,
main = "", sub = NULL, xlab=NULL, ylab="Height")
#####例8.6
x<-c(1,2,6,8,11);dim<-c(5,1);d<-dist(x) #输入数据，生成距离结构
hc1<-hclust(d,"single");hc2<-hclust(d,"complete") #生成系统聚类
hc3<-hclust(d,"median");hc4<-hclust(d,"mcquitty")
opar<-par(mfrow=c(2,2)) #绘出所有树形结构图
plot(hc1,hang=-1);plot(hc2,hang=-1)
plot(hc3,hang=-1);plot(hc4,hang=-1)
par(opar)
##as.dendrogram()函数
#将系统聚类得到的对象强制为谱系图
as.dendrogram(object, hang = -1, ...)
#图8.4
dend1<-as.dendrogram(hc1)
opar <- par(mfrow = c(2, 2),mar = c(4,3,1,2))
plot(dend1)
plot(dend1, nodePar=list(pch = c(1,NA), cex=0.8, lab.cex=0.8),
type = "t", center=TRUE)
plot(dend1, edgePar=list(col = 1:2, lty = 2:3),
dLeaf=1, edge.root = TRUE)
plot(dend1, nodePar=list(pch = 2:1, cex=.4*2:1, col=2:3),
horiz=TRUE)
par(opar)
#例8.7
x<-c(1.000, 0.846, 0.805, 0.859, 0.473, 0.398, 0.301, 0.382,
0.846, 1.000, 0.881, 0.826, 0.376, 0.326, 0.277, 0.277,
0.805, 0.881, 1.000, 0.801, 0.380, 0.319, 0.237, 0.345,
0.859, 0.826, 0.801, 1.000, 0.436, 0.329, 0.327, 0.365,
0.473, 0.376, 0.380, 0.436, 1.000, 0.762, 0.730, 0.629,
0.398, 0.326, 0.319, 0.329, 0.762, 1.000, 0.583, 0.577,
0.301, 0.277, 0.237, 0.327, 0.730, 0.583, 1.000, 0.539,
0.382, 0.415, 0.345, 0.365, 0.629, 0.577, 0.539, 1.000)
names<-c("身高 x1", "手臂长 x2", "上肢长 x3", "下肢长 x4", "体重 x5",
"颈围 x6", "胸围 x7", "胸宽 x8")
r<-matrix(x, nrow=8, dimnames=list(names, names))
## 作系统聚类分析,
## as.dist()的作用是将普通矩阵转化为聚类分析用的距离结构.
d<-as.dist(1-r);hc<-hclust(d);dend<-as.dendrogram(hc)
## 写一段小程序, 其目的是在绘图命令中调用它, 使谱系图更好看.
nP<-list(col=3:2, cex=c(2.0, 0.75), pch= 21:22,
bg= c("light blue", "pink"),
lab.cex = 1.0, lab.col = "tomato")
addE <- function(n){
if(!is.leaf(n)) {
attr(n, "edgePar") <- list(p.col="plum")
attr(n, "edgetext") <- paste(attr(n,"members"),"members")
}
n
}
## 画出谱系图.
op<-par(mfrow=c(1,1), mar=c(4,3,0.5,0))
de <- dendrapply(dend, addE); plot(de, nodePar= nP)
par(op)
####类个数的确定#rect.hclust()函数
rect.hclust(tree, k = NULL, which = NULL, x = NULL, h = NULL,
border = 2, cluster = NULL)
#tree为hclust生成的结构；k为类的个数；h是谱系图的阀值；border表明数据框的颜色
plclust(hc,hang=-1);re<-rect.hclust(hc,k=3)
####例8.8
X<-data.frame(
x1=c(2959.19, 2459.77, 1495.63, 1046.33, 1303.97, 1730.84,
1561.86, 1410.11, 3712.31, 2207.58, 2629.16, 1844.78,
2709.46, 1563.78, 1675.75, 1427.65, 1783.43, 1942.23,
3055.17, 2033.87, 2057.86, 2303.29, 1974.28, 1673.82,
2194.25, 2646.61, 1472.95, 1525.57, 1654.69, 1375.46,
1608.82),
x2=c(730.79, 495.47, 515.90, 477.77, 524.29, 553.90, 492.42,
510.71, 550.74, 449.37, 557.32, 430.29, 428.11, 303.65,
613.32, 431.79, 511.88, 512.27, 353.23, 300.82, 186.44,
589.99, 507.76, 437.75, 537.01, 839.70, 390.89, 472.98,
437.77, 480.99, 536.05),
x3=c(749.41, 697.33, 362.37, 290.15, 254.83, 246.91, 200.49,
211.88, 893.37, 572.40, 689.73, 271.28, 334.12, 233.81,
550.71, 288.55, 282.84, 401.39, 564.56, 338.65, 202.72,
516.21, 344.79, 461.61, 369.07, 204.44, 447.95, 328.90,
258.78, 273.84, 432.46),
x4=c(513.34, 302.87, 285.32, 208.57, 192.17, 279.81, 218.36,
277.11, 346.93, 211.92, 435.69, 126.33, 160.77, 107.90,
219.79, 208.14, 201.01, 206.06, 356.27, 157.78, 171.79,
236.55, 203.21, 153.32, 249.54, 209.11, 259.51, 219.86,
303.00, 317.32, 235.82),
x5=c(467.87, 284.19, 272.95, 201.50, 249.81, 239.18, 220.69,
224.65, 527.00, 302.09, 514.66, 250.56, 405.14, 209.70,
272.59, 217.00, 237.60, 321.29, 811.88, 329.06, 329.65,
403.92, 240.24, 254.66, 290.84, 379.30, 230.61, 206.65,
244.93, 251.08, 250.28),
x6=c(1141.82, 735.97, 540.58, 414.72, 463.09, 445.20, 459.62,
376.82, 1034.98, 585.23, 795.87, 513.18, 461.67, 393.99,
599.43, 337.76, 617.74, 697.22, 873.06, 621.74, 477.17,
730.05, 575.10, 445.59, 561.91, 371.04, 490.90, 449.69,
479.53, 424.75, 541.30),
x7=c(478.42, 570.84, 364.91, 281.84, 287.87, 330.24, 360.48,
317.61, 720.33, 429.77, 575.76, 314.00, 535.13, 509.39,
371.62, 421.31, 523.52, 492.60, 1082.82, 587.02, 312.93,
438.41, 430.36, 346.11, 407.70, 269.59, 469.10, 249.66,
288.56, 228.73, 344.85),
x8=c(457.64, 305.08, 188.63, 212.10, 192.96, 163.86, 147.76,
152.85, 462.03, 252.54, 323.36, 151.39, 232.29, 160.12,
211.84, 165.32, 182.52, 226.45, 420.81, 218.27, 279.19,
225.80, 223.46, 191.48, 330.95, 389.33, 191.34, 228.19,
236.51, 195.93, 214.40),
row.names = c("北京", "天津", "河北", "山西", "内蒙古", "辽宁", "吉林",
"黑龙江", "上海", "江苏", "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")
)
##生成距离结构，做系统聚类
d<-dist(scale(X))
hc1<-hclust(d); hc2<-hclust(d, "average")
hc3<-hclust(d, "centroid");hc4<-hclust(d, "ward")
##绘出谱系图和聚类情况
opar<-par(mfrow=c(2,1),mar=c(5.2,4,0,0))
plclust(hc1,hang=-1);re1<-rect.hclust(hc1,k=5,border="red")
plclust(hc2,hang=-1);re2<-rect.hclust(hc2,k=5,border="red")
par(opar)
opar<-par(mfrow=c(2,1), mar=c(5.2,4,0,0))
plclust(hc3,hang=-1);re3<-rect.hclust(hc3,k=5,border="red")
plclust(hc4,hang=-1);re4<-rect.hclust(hc4,k=5,border="red")
par(opar)
#####动态聚类法#K均值
##kmeans()函数
kmeans(x, centers, iter.max = 10, nstart = 1,
algorithm = c("Hartigan-Wong", "Lloyd",
"Forgy", "MacQueen"))
##例8.9
km<-kmeans(scale(X),centers=5,nstart=20)
km
