聚类分析城市分类

江苏省 13 个城市分类表1-1江苏省各市要素信息城市 常住人口GDP（亿元）面积（平方第一产业第二产业第三产业（万人）公里）比重比重比重无锡 徐州 常州 苏州 南通 连云港 淮安 盐城 扬州 镇江 泰州 宿迁771.314230.2665823.05%45.64%51.31%619.574991.7247881.88%56.82%41.30%868.192390.161125810.46%52.26%37.29%445.182519.9343853.64%56.74%39.62%936.957740.2084881.85%58.75%39.41%713.372872.8080018.23%55.96%35.81%444.65941.13750016.41%46.29%37.30%481.491121.751007215.24%48.27%36.49%748.181917.001697217.24%48.19%34.58%449.551856.3966347.80%56.13%36.06%306.941672.0838474.49%58.20%37.32%466.611660.9257978.05%56.78%35.17%472.51826.85855519.30%46.30%34.39%注：数据来源为江苏统计局网站2009 年各市数据，常住人口是根据2009 年人口变动情况抽样调查数 据推算的。一 、史密斯法1.1 计算根据各市第二产业、第三产业所占GDP的比重，做出散点图。然后算出13个市第二、三产业比重的 平均数，分别向Y轴和X轴做辅助线。分类成果如图：*O00口厶山山帀帀帀巾111111山山 农迅州亞州钳州妣州汀 南南腐自菇:4:徐佃牌横1.2 分类 徐州、盐城、宿迁、连云港分为一类 扬州、南通、泰州、镇江分为一类 苏州、无锡、常州分为一类 南京为一类1.3 局限性 本方法过于机械，分类精度较粗，比如徐州和其他苏北城市有一定的差异，但是还被分在同一类 二、纳尔逊法2.1 计算 计算出江苏省 13 个城市三次产业的平均数和标准差。表 2 -1第一产业比重第二产业比重第三产业比重平均数0.09050.52790.3816标准差0.06190.05090.0445、.、八方差0.00380.00260.0020观测数1313132.2 分类 对每个城市分类，第一产业超过超过全省平均值一个标准差，为第一级，超出两个标准差，为第二级 以此类推。表 2-2城市第一产业等级第二产业等级第三产业等级南京0-12无锡-100徐州000常州000苏州-110南通000连云港1-10淮安100盐城100扬州000镇江010泰州000宿迁1-102.3 局限性 受到样本容量的限制，容易受到异常值的影响。三、聚类分析将南京、无锡、徐州、常州、苏州、南通、连云港、淮安、盐城、扬州、镇江、泰州、宿迁分别表示 为：Gl、G2、G3、G4、G5、G6、G7、G8、G9、Gl、0G11、G12、G13。第一步：将所有 6 项指标标准化。 结果如下：表 3-1人口标准化面积GDP标准化第一产业比重标准化第二产业比重标准化第三产业比重标准化G10.73710.20840.49230.06880.00001.0000G20.49620.07170.60240.00170.85280.4080G30.89090.56470.22610.49280.50500.1709G40.21940.04100.24490.10260.84670.3087G51.00000.35361.00000.00001.00000.2957G60.64510.31650.29590.36560.78720.0834G70.21860.27830.01650.83440.04960.1715G80.27710.47430.04270.76730.20060.1236G90.70041.00000.15770.88140.19450.0106G100.22640.21230.14890.34150.80020.0982G110.00000.00000.12230.15130.95800.1721G120.25340.14860.12060.35530.84970.0455G130.26280.35870.00001.00000.05030.0000第二步：求相应个点对应的距离，其中的距离为绝对值距离。G1G2G3G4G5G6G7G8G9G10G11G12G13G10G21.99950G32.53442.340G42.50430.87142.083700=(%)13*13=ij 13*13G52.68891.44462.20672.11720G62.39711.45441.06071.30011.88680G72.70792.94261.96572.1313.74922.03860G82.95122.88381.51382.18913.53981.80760.5470.0000G93.15943.51261.55353.25623.76022.05821.6971.29710G102.83281.56641.61320.77032.50490.72171.5231.46972.5030G113.1841.53892.35290.67972.54821.60922.1952.25293.3910.88740G123.00581.52061.76670.78482.58670.84561.6741.56652.5520.23510.8430G133.09853.33172.19282.60853.98762.17510.4790.67901.511.83822.6721.80第三步，采用最远距离法归类。可以看出G10和G12之间距离的值最小，将G10 （扬州）和G12 （泰 州）分为一类，并划去相应的行列，下表述中不在重复，新类别类别号为G14然后求出其中两个元素对应 的其它的距离，求其中的最大值。d =max（d d ） ，公式为： 1410, 12 然后依次照这种方法计算，最后归处类别。将G10和G12归类后图表如下：D=(dj)i2*12G1G2G3G4G5G6G7G8G9G11G13G14G10G21.99950G32.53442.340G42.50430.87142.08370G52.68891.44462.20672.11720G62.39711.45441.06071.30011.88680G72.70792.94261.96572.1313.74922.03860G82.95122.88381.51382.18913.53981.80760.5470.0000G93.15943.51261.55353.25623.76022.05821.6971.29710G113.1841.53892.35290.67972.54821.60922.1952.25293.3910G133.09853.33172.19282.60853.98762.17510.4790.67901.512.67230G143.00581.56641.76670.78482.58670.84561.6741.56652.5520.88741.8380重复上诉步骤，将G7（连云港）和G13 （宿迁）归并为一类G15，得表如下G1G10G21.9995G32.5344G42.5043D=(dij)ii*ii=G5G62.68892.3971G82.9512G93.1594G113.184G143.0058G153.0985G2G3G402.3400.87142.083701.44462.20672.11721.45441.06071.30012.88381.51382.18913.51261.55353.25621.53892.35290.67971.56641.76670.78483.33172.19282.6085G5G6G801.886803.53981.807603.76022.05821.29712.54821.60922.25292.58670.84561.56653.98762.17510.679G9G11G14G1503.390902.55160.88701.69742.6721.83820将G8 （淮安）和G15归并为G16，得图表如下:D=Vi0*i0G1G2G3G4G5G6G9G11G14G16G10G21.99950G32.53442.340G42.50430.87142.08370G52.68891.44462.20672.11720G62.39711.45441.06071.30011.88680G93.15943.51261.55353.25623.76022.05820G113.1841.53892.35290.67972.54821.60923.39090G143.00581.56641.76670.78482.58670.84562.55160.88740G163.09853.33172.19282.60853.98762.17511.69742.67231.8380将G4 （常州）和G11 （镇江）归并为G17，得图如下:G1G2G3G5G6G9G14G16G17G10G21.99950G32.53442.340D=(dij)9*9=G52.68891.44462.20670G62.39711.45441.06071.88680G93.15943.51261.55353.76022.05820G143.00581.56641.76672.58670.84562.55160G163.09853.33172.19283.98762.17511.69741.83820G173.1841.53892.35292.54821.60923.39090.88742.67230将G6 （南通）和 G14 归并为 G18，得图表如下：G1G2G3G5G9G16G17G18G10G21.99950G32.53442.340D=(d )= j8*8G52.68891.44462.20670G93.15943.51261.55353.76020G163.09853.33172.19283.98761.69740G173.1841.53892.35292.54823.39092.67230G183.00581.56641.76672.58673.76022.17511.60920.0000将G2 （无锡）和G5 （苏州）合并为G19得表如下：G1G3G9G16G17G18G19G10D=(d.)_ =G3G92.53443.15941.55350 j7*7G163.09852.19281.69740G173.1842.35293.39092.67230G183.00581.76673.76022.17511.60920G192.68892.343.76023.98762.54822.58670将G3 （盐城）和G9 （徐州）归并为G20，得表如下G1G16G17G18G19G20G10G163.09850D=(%)6*6=G173.1842.67230G183.00582.17511.60920G192.68893.98762.54822.58670G203.15942.19283.39093.76023.76020将G17和G18归并为G21，得表如下:D=（dj）5*5G1G16G19G20G21G10G163.09850G192.68893.98760G203.15942.19283.76020G213.1842.67232.58673.76020将G16和G20归并为G22,得表如下:D=（dij）4*4=G1G19G21G22G10G192.68890G213.1842.58670G223.15943.98763.76020将G19和G21归并为G23，得表如下:D=（dj）3*3=G1G22G23G10G22G233.159403.1843.98760将G1 （南京）和G22归并为G24,得表如下:G23G24D=（dj）2*2=G230G243.98760第四步，画出聚类谱系图。（见下页）聚类分析的局限性就是计算量过大，手工计算容易出错。用SPSS做会比较快捷，准确。SPSS生成 的树状图不包含聚类的久值。需要手工加入。入=2.5867入=1.6092.入=1.4446 入=0.8456.-入=0.6797 入=0.23510二亠瓷n二 $L唄进E劉辖E 一亠15Hco闌一亦4 罰1.-.;Ln吾入=3.1594入=2.1928入=1.5535入=0.6790入=0.4790