模糊聚類分析實驗報告

實驗報告（一）實驗內容模糊聚類在土地利用分區(qū)中的應用實驗目的本次上機實習主要以指導學生掌握“如何應用模糊聚類方法進行土地利用規(guī)劃分區(qū)”為目標。實驗方法本次試驗是在Excel中實現(xiàn)。利用《土地利用規(guī)劃學》P114頁數(shù)據(jù)，使用“歐氏距離法”、建模糊相似矩陣，并進行模糊聚類分析實現(xiàn)土地利用分區(qū)。實驗步驟獲取原始數(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個評價單元的13項指標體系賦值如下。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指標數(shù)據(jù)標準化本次實驗采用了標準差法對數(shù)據(jù)進行標準化，首先需求取原始矩陣各個指標的均值和標準差。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個指標值得均值和標準差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)域得到標準化矩陣如下表3。表3：標準化數(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是通過歐氏距離法求取模糊相似矩陣。其數(shù)學模型為：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$14-M13)^2)q求的d如此在C23、D23、E23、F23、G23、H23依次輸入公式，用數(shù)據(jù)填充A23：H30區(qū)域求的標準化矩陣的d值矩陣。選取A32單元格輸入公式=1-A23/MAX($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求取模糊等價矩陣求取模糊等價矩陣需對模糊相似矩陣進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是模糊等價矩陣，這樣:可通過R2k對X上的元素進行聚類。與第一次合成運算同理對R2和R4進行合成運算后得表6，表7。易得R8=R4，所以R16為原始矩陣的等價矩陣，可通過利用R16對樣本元素進行聚類。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驗運用直接法進行分類。將模糊等價矩陣復制到sheet5工作表中。取，寫出，其中，當=1時，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，此為最細的分類。表8：=1的截矩陣R11000000001000000001000000001000000001000000001000000001000000001以下構造截矩陣的方法與上同。當=0.7時，如下表9。將樣本分為七類，即將第7，第8分為1類，其他6個樣本各分為1類。表9：=0.7的截矩陣R0.71000000001000000001000000001000000001000000001000000001100000011=0.55時，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個樣本各分為1類。表10：=0.55的截矩陣R0.551000000001000000001000000001000000001000000001110000011100000111=0.5時，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個樣本各分為1類。表11：=0.5的截矩陣R0.51000000001000000001000000001000000001111000011110000111100001111=0.4時，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個樣本各分為1類。表12：=0.4的截矩陣R0.41000000001000000001011110001000000101111001011110010111100101111=0.39時，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個樣本各分為1類。表13：=0.39的截矩陣R0.391000000001000000001111110011111100111111001111110011111100111