案例-聚类分析

PAGEPAGE8我国各地区城镇居民消费性支出的聚类分析刘肖A31114042一、问题的背景下表列出了1999年全国31个省、直辖市和自治区（港、澳、台不在其中）的城镇居民家庭平均每人全年消费性支出的八个主要变量数据。这八个变量是：食品：交通和通讯：衣着：娱乐教育文化服务：家庭设备用品及服务：居住：医疗保健：杂项商品和服务 消费性支出数据 单位：元地区北京2959.19730.79749.41513.34467.871141.82478.42457.64天津2459.77495.47697.33302.87284.19735.97570.84305.08河北1495.63515.90362.37285.32272.95540.58364.91188.63山西1406.33477.77290.15208.57201.50414.72281.84212.10内蒙古1303.97524.29254.83192.17249.81463.09287.87192.96辽宁1730.84553.90246.91279.81239.18445.20330.24163.86吉林1561.86492.42200.49218.36220.69459.62360.48147.76黑龙江1410.11510.71211.88277.11224.65376.82317.61152.85上海3712.31550.74893.37346.93527.001034.98720.33462.03江苏2207.58449.37572.40211.92302.09585.23429.77252.54浙江2629.16557.32689.73435.69514.66795.87575.76323.36安徽1844.78430.29271.28126.33250.56513.18314.00151.39福建2709.46428.11334.12160.77405.14461.67535.13232.29江西1563.78303.65233.81107.90209.70393.99509.39160.12山东1675.75613.32550.71219.79272.59599.43371.62211.84河南1427.65431.79288.55208.14217.00337.76421.31165.32湖北1783.43511.88282.84201.01237.60617.74523.52182.52湖南1942.23512.27401.39206.06321.29697.22492.60226.45广东3055.17353.23564.56356.27811.88873.061082.82420.81广西2033.87300.82338.65157.78329.06621.74587.02218.27海南2057.86186.44202.72171.79329.65477.17312.93279.19重庆2303.29589.99516.21236.55403.92730.05438.41225.80四川1974.28507.76344.79203.21240.24575.10430.36223.46贵州1673.82437.75461.61153.32254.66445.59346.11191.48云南2194.25537.01369.07249.54290.84561.91407.70330.95西藏2646.61839.70204.44209.11379.30371.04269.59389.33陕西1472.95390.89447.95259.51230.61490.90469.10191.34甘肃1525.57472.98328.90219.86206.65449.69249.66228.19青海1654.69437.77258.78303.00244.93479.53288.56236.51宁夏1375.46480.89273.84317.32251.08424.75228.73195.93新疆1608.82536.05432.46235.82250.28541.30344.85214.40资料来源：2000年《中国统计年鉴》我们希望根据上述八个指标对各地区进行聚类。通过SPSS软件进行聚类分析得：描述统计量N极小值极大值均值标准差X1311303.97003712.31001980.660323586.8861630X231186.4400839.7000489.073226120.4565793X331200.4900893.3700395.985484179.9287151X431107.9000513.3400244.36032386.3531009X531201.5000811.8800311.018387128.1287843X631337.76001141.8200569.571613189.5094636X731228.73001082.8200430.370323168.1435201X831147.7600462.0300243.04516188.0562187有效的N（列表状态）31对变量进行描述性统计的上图。案例处理汇总a,b案例有效缺失总计N百分比N百分比N百分比31100.00.031100.0a.平方Euclidean距离已使用b.单个联结观测量的概述表。聚类表阶群集组合系数首次出现阶群集下一阶群集1群集2群集1群集21428.212002245.510108368.6300074331.677001051723.800001162930.814009767.817308846.94827994291.0258612103151.04140121117181.058501312341.12010913133171.130121114143161.144130161512241.6770017163221.87714017173121.931161518183271.95717019193101.98418020203252.17519021213142.995200232213203.630002423233.63502124242134.026232225252215.21824026262116.0942502727129.43502628281910.567270292912610.570280303011917.8342900聚类进度表，上图显示了变量的聚类过程。在步骤一，将观测量4与观测量28进行聚类距离测量系数为0.212，这一类的下次聚类合并是在步骤二。在首次出现阶群集中，0表示非类聚类，1表示同类聚类。上图为树状图。从以上图中可得分为两类或三类最为合适。以下用matlab软件进行聚类分析1：数据的读取与标准化首先将数据保存至excel文件中[data,textdata]=xlsread(‘book1.xls’);data=zscore(data)2:一步聚类直接利用clusterdata函数进行一步聚类，其命令与结果如下obslabel=textdata(2:end,1);Taverage=clusterdata(data,'linkage','average','maxclust',3);obslabel(Taverage==1)obslabel(Taverage==2)obslabel(Taverage==3)从上面可知，我们可以利用函数直接对样本进行聚类3：分步聚类利用pdist函数计算距离，利用linkage函数创建系统聚类树，最后做出聚类树形图，命令与结果如下y=pdist(data);Z=linkage(y,'average')obslabel=textdata(2:end,1);H=dendrogram(Z,0,'orientation','right','labels',obslabel);set(H,'Linewidth',2,'color','k');4：确定分类