聚类分析
Detailed data attached at the end
Detailed code see github.com
A hclustering example
1.缩放数据
Province.data.sd=scale(Province.data)2.计算距离
Province=dist(Province.data.sd, method = "euclidean", diag=TRUE)
#method:"euclidean" euclide距离
# "maximum" Chebyshev距离
# "manhattan" 绝对值距离
# "canberra" Lance距离
# "binary" 定性变量的距离
# "minkowski" minkowski距离, p是阶数3.选择聚类算法
hc1=hclust(Province, "single") #最短距离法
hc2=hclust(Province, "complete") #最长距离法
hc3=hclust(Province, "median") #中间距离法
hc4=hclust(Province, "average") #类平均法
hc5=hclust(Province, "centroid") #重心法
hc6=hclust(Province, "mcquitty") #相似分析法
hc7=hclust(Province, "ward.D") #离差平方和
hc8=hclust(Province, "ward.D2")4.结果可视化
根据地区标注不同的color
myplclust(hc7, lab.col = unclass(region))
legend("topright", pch=17, col=unique(unclass(region)),
legend=unique(region))
K-Means Clustering: an example
km=kmeans(Arrest.data.sd, 3, nstart=100)
print(km)## K-means clustering with 3 clusters of sizes 19, 17, 14
##
## Cluster means:
## Murder Assault Rape
## 1 1.0431796 1.062614 0.8523875
## 2 -0.2754591 -0.299928 -0.1233698
## 3 -1.0812577 -1.077921 -1.0070054
##
## Clustering vector:
## 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
## 1 1 1 2 1 1 3 2 1 1 3 3 1 2 3 2 2 1 3 1 2 1 3 1 2
## 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50
## 2 3 1 3 2 1 1 1 3 2 2 2 2 3 1 3 1 1 2 3 2 2 3 3 2
##
## Within cluster sum of squares by cluster:
## [1] 26.305392 9.205038 5.645542
## (between_SS / total_SS = 72.0 %)
##
## Available components:
##
## [1] "cluster" "centers" "totss" "withinss"
## [5] "tot.withinss" "betweenss" "size" "iter"
## [9] "ifault"sort(km$cluster)## 1 2 3 5 6 9 10 13 18 20 22 24 28 31 32 33 40 42 43 4 8 14 16 17 21
## 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 2 2 2 2 2 2
## 25 26 30 35 36 37 38 44 46 47 50 7 11 12 15 19 23 27 29 34 39 41 45 48 49
## 2 2 2 2 2 2 2 2 2 2 2 3 3 3 3 3 3 3 3 3 3 3 3 3 3clusplot(Arrest.data.sd, km$cluster, labels = 2)
Appendix: datasets
| City | x1 | x2 | x3 | x4 | x5 | x6 | x7 | x8 | region |
|---|---|---|---|---|---|---|---|---|---|
| Beijing | 8091.1 | 2651.3 | 11252.0 | 2272.7 | 4860.4 | 4027.6 | 2369.5 | 1117.4 | huabei |
| Tianjing | 8447.7 | 2144.4 | 5667.2 | 1593.0 | 3403.0 | 2282.6 | 1888.1 | 803.4 | huabei |
| Hebei | 4581.1 | 1544.2 | 4111.6 | 1178.7 | 2386.4 | 1870.8 | 1500.6 | 413.1 | huabei |
| Shanxi1 | 3981.0 | 1705.1 | 3019.5 | 947.9 | 2148.1 | 2207.9 | 1394.1 | 414.9 | huabei |
| Neimenggu | 6210.3 | 2474.0 | 3710.3 | 1430.2 | 3231.3 | 2504.7 | 1575.7 | 739.9 | huabei |
| Liaoning | 6092.5 | 2065.6 | 4416.1 | 1359.5 | 2768.9 | 2418.7 | 1761.9 | 673.6 | dongbei |
| Jilin | 4640.6 | 1812.9 | 3532.3 | 1026.7 | 2322.5 | 2161.8 | 1924.2 | 551.7 | dongbei |
| Heilongjiang | 4749.7 | 1773.5 | 3416.4 | 908.1 | 2058.9 | 1846.7 | 1924.3 | 474.5 | dongbei |
| Shanghai | 9690.7 | 1711.6 | 12137.0 | 1573.1 | 4457.2 | 4046.0 | 2361.7 | 968.9 | huadong |
| Jiangsu | 7003.8 | 1781.4 | 5644.7 | 1516.6 | 3619.8 | 3058.4 | 1594.3 | 747.2 | huadong |
| Zhejiang | 8092.0 | 2041.3 | 7230.5 | 1360.5 | 4753.2 | 2962.8 | 1539.0 | 682.0 | huadong |
| Anhui | 5802.1 | 1403.3 | 3460.0 | 926.4 | 2265.7 | 1913.3 | 1073.3 | 389.5 | huadong |
| Fujian | 7759.1 | 1489.8 | 5811.4 | 1336.9 | 3021.5 | 2314.0 | 1165.3 | 622.1 | huadong |
| Jiangxi | 5407.8 | 1478.3 | 3619.9 | 1007.5 | 2083.7 | 1874.4 | 841.4 | 418.8 | huazhong |
| Shandong | 5527.4 | 1943.0 | 4058.4 | 1476.5 | 2747.7 | 2141.1 | 1416.1 | 543.5 | huadong |
| Henan | 4818.7 | 1797.6 | 3391.1 | 1382.2 | 1874.1 | 1991.9 | 1365.5 | 533.1 | huazhong |
| Hubei | 5828.6 | 1523.1 | 3742.7 | 1099.3 | 2155.4 | 1972.2 | 1482.0 | 389.0 | huazhong |
| Hunan | 6075.5 | 1638.1 | 3519.6 | 1202.6 | 2430.2 | 2934.1 | 1174.6 | 526.6 | huazhong |
| Guangdong | 8533.4 | 1453.7 | 5715.3 | 1526.3 | 3905.0 | 2671.5 | 1096.4 | 771.4 | huanan |
| Guangxi | 5610.2 | 845.8 | 3629.3 | 952.0 | 2249.5 | 1845.0 | 866.2 | 323.1 | huanan |
| Hainan | 7051.8 | 828.6 | 3679.8 | 964.3 | 2643.4 | 1617.8 | 1307.1 | 355.6 | huanan |
| Chongqing | 6627.6 | 1931.7 | 3679.6 | 1370.6 | 2383.2 | 1951.3 | 1394.1 | 404.2 | xinan |
| Sichuan | 6783.1 | 1703.8 | 3335.5 | 1251.4 | 2414.4 | 1863.0 | 1369.3 | 556.4 | xinan |
| Guizhou | 5282.7 | 1346.7 | 3468.4 | 1078.5 | 2248.4 | 2312.7 | 872.2 | 304.5 | xinan |
| Yunnan | 5346.4 | 1138.2 | 3612.4 | 1061.4 | 2664.0 | 2079.0 | 1351.9 | 421.6 | xinan |
| Xizang | 7237.5 | 1611.6 | 3588.9 | 739.5 | 2037.5 | 757.9 | 534.4 | 514.6 | xinan |
| Shanxi3 | 5146.4 | 1500.5 | 3823.4 | 1297.9 | 2308.4 | 2201.1 | 1783.6 | 402.6 | xibei |
| Gansu | 5345.9 | 1758.5 | 3539.9 | 1124.9 | 1850.5 | 2044.9 | 1390.8 | 395.5 | xibei |
| Qinhai | 5502.6 | 1902.5 | 3340.1 | 1179.9 | 3354.8 | 2022.5 | 1459.3 | 439.0 | xibei |
| Ningxia | 4883.4 | 1787.0 | 3608.3 | 1185.4 | 2509.6 | 2389.8 | 2016.0 | 604.5 | xibei |
| Xinjiang | 5954.9 | 2013.1 | 3166.9 | 1286.3 | 2869.4 | 2105.4 | 1517.1 | 501.6 | xibei |
| Murder | Assault | UrbanPop | Rape | |
|---|---|---|---|---|
| Alabama | 13.2 | 236 | 58 | 21.2 |
| Alaska | 10.0 | 263 | 48 | 44.5 |
| Arizona | 8.1 | 294 | 80 | 31.0 |
| Arkansas | 8.8 | 190 | 50 | 19.5 |
| California | 9.0 | 276 | 91 | 40.6 |
| Colorado | 7.9 | 204 | 78 | 38.7 |
| Connecticut | 3.3 | 110 | 77 | 11.1 |
| Delaware | 5.9 | 238 | 72 | 15.8 |
| Florida | 15.4 | 335 | 80 | 31.9 |
| Georgia | 17.4 | 211 | 60 | 25.8 |
| Hawaii | 5.3 | 46 | 83 | 20.2 |
| Idaho | 2.6 | 120 | 54 | 14.2 |
| Illinois | 10.4 | 249 | 83 | 24.0 |
| Indiana | 7.2 | 113 | 65 | 21.0 |
| Iowa | 2.2 | 56 | 57 | 11.3 |
| Kansas | 6.0 | 115 | 66 | 18.0 |
| Kentucky | 9.7 | 109 | 52 | 16.3 |
| Louisiana | 15.4 | 249 | 66 | 22.2 |
| Maine | 2.1 | 83 | 51 | 7.8 |
| Maryland | 11.3 | 300 | 67 | 27.8 |
| Massachusetts | 4.4 | 149 | 85 | 16.3 |
| Michigan | 12.1 | 255 | 74 | 35.1 |
| Minnesota | 2.7 | 72 | 66 | 14.9 |
| Mississippi | 16.1 | 259 | 44 | 17.1 |
| Missouri | 9.0 | 178 | 70 | 28.2 |
| Montana | 6.0 | 109 | 53 | 16.4 |
| Nebraska | 4.3 | 102 | 62 | 16.5 |
| Nevada | 12.2 | 252 | 81 | 46.0 |
| New Hampshire | 2.1 | 57 | 56 | 9.5 |
| New Jersey | 7.4 | 159 | 89 | 18.8 |
| New Mexico | 11.4 | 285 | 70 | 32.1 |
| New York | 11.1 | 254 | 86 | 26.1 |
| North Carolina | 13.0 | 337 | 45 | 16.1 |
| North Dakota | 0.8 | 45 | 44 | 7.3 |
| Ohio | 7.3 | 120 | 75 | 21.4 |
| Oklahoma | 6.6 | 151 | 68 | 20.0 |
| Oregon | 4.9 | 159 | 67 | 29.3 |
| Pennsylvania | 6.3 | 106 | 72 | 14.9 |
| Rhode Island | 3.4 | 174 | 87 | 8.3 |
| South Carolina | 14.4 | 279 | 48 | 22.5 |
| South Dakota | 3.8 | 86 | 45 | 12.8 |
| Tennessee | 13.2 | 188 | 59 | 26.9 |
| Texas | 12.7 | 201 | 80 | 25.5 |
| Utah | 3.2 | 120 | 80 | 22.9 |
| Vermont | 2.2 | 48 | 32 | 11.2 |
| Virginia | 8.5 | 156 | 63 | 20.7 |
| Washington | 4.0 | 145 | 73 | 26.2 |
| West Virginia | 5.7 | 81 | 39 | 9.3 |
| Wisconsin | 2.6 | 53 | 66 | 10.8 |
| Wyoming | 6.8 | 161 | 60 | 15.6 |