模糊聚類分析實(shí)驗(yàn)報(bào)告

實(shí)驗(yàn)報(bào)告（一）實(shí)驗(yàn)內(nèi)容模糊聚類在土地利用分區(qū)中的應(yīng)用實(shí)驗(yàn)?zāi)康谋敬紊蠙C(jī)實(shí)習(xí)主要以指導(dǎo)學(xué)生掌握“如何應(yīng)用模糊聚類方法進(jìn)行土地利用規(guī)劃分區(qū)”為目標(biāo)。實(shí)驗(yàn)方法本次試驗(yàn)是在Excel中實(shí)現(xiàn)。利用《土地利用規(guī)劃學(xué)》P114頁數(shù)據(jù)，使用“歐氏距離法”、建模糊相似矩陣，并進(jìn)行模糊聚類分析實(shí)現(xiàn)土地利用分區(qū)。實(shí)驗(yàn)步驟獲取原始數(shù)據(jù)通過對2000年如東縣土地利用總體規(guī)劃及各部門規(guī)劃資料的分析得到8個(gè)評價(jià)單元的13項(xiàng)指標(biāo)體系賦值如下。將數(shù)據(jù)錄入sheet1(A1：M8)工作區(qū)中。表1：2000年如東縣土地利用規(guī)劃指標(biāo)地區(qū)P1P2P3P4P5P6P7P8P9P10P11P12P131掘港區(qū)10060.581.740.215.552.5319.485853.594513801050076002掘東區(qū)99.9666.912.280.39.412.2518.8169525456289820041003且鎮(zhèn)區(qū)10057.229.210.3810.172.4220.656334.41747345750037004豐利區(qū)99.9552.694.150.3812.744.2425.7576027.19745375770038005拼茶區(qū)99.9758.195.120.5214.032.5919.5275721.42648404740036006雙甸區(qū)10060.493.70.113.952.9218.8467820.48618360700033007岔河區(qū)10061.793.190.1212.812.7619.3360924.98826425850049008馬塘區(qū)10062.243.90.0513.692.9817.1458532775420102005500指標(biāo)數(shù)據(jù)標(biāo)準(zhǔn)化本次實(shí)驗(yàn)采用了標(biāo)準(zhǔn)差法對數(shù)據(jù)進(jìn)行標(biāo)準(zhǔn)化，首先需求取原始矩陣各個(gè)指標(biāo)的均值和標(biāo)準(zhǔn)差。選取A10單元格輸入公式=AVERAGE(A1：A8)，用數(shù)據(jù)填充A10：M10得到樣本數(shù)據(jù)的均值。在單元格A11中輸入公式=STDEV（A1：A8），用數(shù)據(jù)填充A11：M11得到樣本數(shù)據(jù)的方差。如下表2。表2：13個(gè)指標(biāo)值得均值和標(biāo)準(zhǔn)差99.98560.013754.161250.2562512.793752.8362519.92375688.12529.88375658.25374.7583754562.50.0213814.1573582.3001580.1650922.0564320.6182222.545489101.043710.70495142.806344.579781306.851428.223選取A13單元格輸入公式=(A1-A$10)/A$11，并用數(shù)據(jù)填充A13：M20區(qū)域得到標(biāo)準(zhǔn)化矩陣如下表3。表3：標(biāo)準(zhǔn)化數(shù)據(jù)矩陣0.7015610.136204-1.05265-0.340721.340307-0.49537-0.205761.6812022.214513-1.451270.1177661.6260472.126768-1.169271.658806-0.817880.265004-1.64545-0.94828-0.437540.06804-0.45621-1.41625-1.92352-0.13391-0.323830.701561-0.6722.1949580.749582-1.27587-0.67330.265666-1.238320.4228180.621471-0.66734-0.66955-0.6039-1.63698-1.76164-0.004890.749582-0.026142.2706252.2888530.711326-0.251640.6074660.005608-0.51651-0.53388-0.70156-0.438680.4168191.5975940.601163-0.39832-0.158610.681635-0.79064-0.071780.656127-0.74607-0.673910.7015610.114556-0.20053-0.946440.562260.135469-0.42575-0.1002-0.87845-0.28185-0.33087-1.05215-0.883970.7015610.427255-0.42225-0.82530.007902-0.12334-0.23326-0.78308-0.458081.1746681.1271930.095650.2363080.7015610.535496-0.11358-1.24930.4358280.232522-1.0936-1.02060.1976890.8175411.0150341.3964880.65641求取模糊相似矩陣本次試驗(yàn)是通過歐氏距離法求取模糊相似矩陣。其數(shù)學(xué)模型為：r選取A23單元格輸入公式=SQRT((A$13-A13)^2+(B$13-B13)^2+(C$13-C13)^2+(D$13-D13)^2+(E$13-E13)^2+(F$13-F13)^2+(G$13-G13)^2+(H$13-H13)^2+(I$13-I13)^2+(J$13-J13)^2+(K$13-K13)^2+(L$13-L13)^2+(M$13-M13)^2)求的d11，B23中輸入公式=SQRT((A$14-A13)^2+(B$14-B13)^2+(C$14-C13)^2+(D$14-D13)^2+(E$14-E13)^2+(F$14-F13)^2+(G$14-G13)^2+(H$14-H13)^2+(I$14-I13)^2+(J$14-J13)^2+(K$14-K13)^2+(L$14-L13)^2+(M$14-M13)^2)q求的d如此在C23、D23、E23、F23、G23、H23依次輸入公式，用數(shù)據(jù)填充A23：H30區(qū)域求的標(biāo)準(zhǔn)化矩陣的d值矩陣。選取A32單元格輸入公式=1-A23/MAX($A$23:$H$30)，用數(shù)據(jù)填充A32：H39區(qū)域的模糊相似矩陣如下表4。易得模糊相似矩陣R具備自反性和對稱性。將模糊相似矩陣復(fù)制到sheet2工作表A1：H8區(qū)域。選取A10單元格輸入公式=MAX(MIN($A1,A$1),MIN($B1,A$2),MIN($C1,A$3),MIN($D1,A$4),MIN($E1,A$5),MIN($F1,A$6),MIN($G1,A$7),MIN($H1,A$8))，用數(shù)據(jù)填充A10：H17區(qū)域得到模糊相似矩陣的合成矩陣R2如下表5。模糊相似矩陣R2≠R,所以相似矩陣R并不是原始矩陣的模糊等價(jià)矩陣表4：模糊相似矩陣R10.1237770.01187300.1700740.1917410.2298980.314170.12377710.2583310.0872070.3250920.3843160.266430.1972360.0118730.25833110.2185980.4156960.4021310.3913340.29029500.0872070.21859810.3956450.2717010.2279040.1070360.1700740.3250920.4156960.39564510.5256230.4471510.3109680.1917410.3843160.4021310.2717010.52562310.599270.4683960.2298980.266430.3913340.2279040.4471510.5992710.7232760.314170.1972360.2902950.1070360.3109680.4683960.7232761表5：模糊相似矩陣R10.2298980.2902950.2279040.3109680.314170.314170.314170.22989810.3843160.3250920.3843160.3843160.3843160.3843160.2902950.38431610.3956450.4156960.4156960.4156960.4021310.2279040.3250920.39564510.3956450.3956450.3956450.3109680.3109680.3843160.4156960.39564510.5256230.5256230.4683960.314170.3843160.4156960.3956450.52562310.599270.599270.314170.3843160.4156960.3956450.5256230.5992710.7232760.314170.3843160.4021310.3109680.4683960.599270.7232761求取模糊等價(jià)矩陣求取模糊等價(jià)矩陣需對模糊相似矩陣進(jìn)行一系列的合成用算。R?R2=RoR?R4=R2oR2?……?R2k=RkoRk?……若存在正整數(shù)k，使得：R2k=Rk，則R2k是模糊等價(jià)矩陣，這樣:可通過R2k對X上的元素進(jìn)行聚類。與第一次合成運(yùn)算同理對R2和R4進(jìn)行合成運(yùn)算后得表6，表7。易得R8=R4，所以R16為原始矩陣的等價(jià)矩陣，可通過利用R16對樣本元素進(jìn)行聚類。表6：模糊相似矩陣R410.314170.314170.314170.314170.314170.314170.314170.3141710.3843160.3843160.3843160.3843160.3843160.3843160.314170.38431610.3956450.4156960.4156960.4156960.4156960.314170.3843160.39564510.3956450.3956450.3956450.3956450.314170.3843160.4156960.39564510.5256230.5256230.5256230.314170.3843160.4156960.3956450.52562310.599270.599270.314170.3843160.4156960.3956450.5256230.5992710.7232760.314170.3843160.4156960.3956450.5256230.599270.7232761表7：模糊相似矩陣R810.314170.314170.314170.314170.314170.314170.314170.3141710.3843160.3843160.3843160.3843160.3843160.3843160.314170.38431610.3956450.4156960.4156960.4156960.4156960.314170.3843160.39564510.3956450.3956450.3956450.3956450.314170.3843160.4156960.39564510.5256230.5256230.5256230.314170.3843160.4156960.3956450.52562310.599270.599270.314170.3843160.4156960.3956450.5256230.5992710.7232760.314170.3843160.4156960.3956450.5256230.599270.7232761模糊聚類分析本次實(shí)驗(yàn)運(yùn)用直接法進(jìn)行分類。將模糊等價(jià)矩陣復(fù)制到sheet5工作表中。取，寫出，其中，當(dāng)=1時(shí)，在A10單元格中輸入公式=IF(A1>=1,1,0)，用數(shù)據(jù)填充A10：H17區(qū)域得到=1的截矩陣R1，如下表8。將樣本分為8類，即將每一樣本分為1類，此為最細(xì)的分類。表8：=1的截矩陣R11000000001000000001000000001000000001000000001000000001000000001以下構(gòu)造截矩陣的方法與上同。當(dāng)=0.7時(shí)，如下表9。將樣本分為七類，即將第7，第8分為1類，其他6個(gè)樣本各分為1類。表9：=0.7的截矩陣R0.71000000001000000001000000001000000001000000001000000001100000011=0.55時(shí)，如表10。將樣本分為6類，即將第6、第7、第8分為1類，其他5個(gè)樣本各分為1類。表10：=0.55的截矩陣R0.551000000001000000001000000001000000001000000001110000011100000111=0.5時(shí)，如表11。將樣本分為5類，即將第5、第6、第7、第8分為1類，其他4個(gè)樣本各分為1類。表11：=0.5的截矩陣R0.51000000001000000001000000001000000001111000011110000111100001111=0.4時(shí)，如表12。將樣本分為4類，即將第3、第5、第6、第7、第8分為1類，其他3個(gè)樣本各分為1類。表12：=0.4的截矩陣R0.41000000001000000001011110001000000101111001011110010111100101111=0.39時(shí)，如表13。將樣本分為3類，即將第3、第4、第5、第6、第7、第8分為1類，其他2個(gè)樣本各分為1類。表13：=0.39的截矩陣R0.391000000001000000001111110011111100111111001111110011111100111