Iris數(shù)據(jù)判別分析.doc

Iris數(shù)據(jù)判別分析一、 提出問題R.A.Fisher在1936年發(fā)表的Iris數(shù)據(jù)中，研究某植物的萼片長、寬及花瓣長、寬。x1：萼片長，x2：萼片寬，x3：花瓣長，x4：花瓣寬。取自3個種類G1，G2，G3，每個種類50個樣品，共150個樣品。數(shù)據(jù)如下表所示。序號類別x1x2x3x41160331422364285622326528461543673156245363285115614634143736931512382622245159259324818101463610211261304614122602751161336530522014256253911153653055181635827511917368325923181513317519257284513203623454232137738672222263334716233673357252437630662125349254517261553513227367305223282703247142926432451530261284013311483116232359305118332552438113436325501935364325323361523414237149361413825430451539379386420401443213241367335721421503516643258264012441443013245377286720463632749184714732162482552644124925023331050372326028511483014352151381625336130491854148341925515030162561503212257361265614583642856215914330111601584012261151381946226731441463362284818641493014265151351426625630451567258274110681503416469146321427026029451571257263510721574415473150361427437730612375363345624763582751197725719421378372305816791543415480152421518137130592182364315518833603048188436329561885249243310862562742138725730421288155421428914931152903772669239136022501592154391749326629461394252273914952603445169615034152971441914298250203510992552437101002582739121011473213210214631152103369325723104262294313105374286119106259304215107151341521081503513310935628492011026022401011137329631811236725581811314931151114267314715115263234413116154371521172563041131182632549151192612847121202642943131212512530111222572841131233653058221243693154211251543913412615135143127372366125128365325120129261294714130256293613131269314915132364275319133368305521134255254013135148341621361483014113714523133138357255020139157381731401513815314125523401314226630441414326828481414415434172145151371541461523515214735828512414826730501714936333602515015337152（1） 進行Bayes判別，并用回代法與交叉確認(rèn)法判別結(jié)果；（2） 計算每個樣品屬于每一類的后驗概率；（3） 進行逐步判別，并用回代法與交叉確認(rèn)法驗證判別結(jié)果。二、 判別分析用距離判別法，假定總體 G1，G2，G3的協(xié)方差矩陣1=2=3=。計算各個總體之間的馬氏平方距離d2(Gi,Gj)形成的矩陣，其中dij2=d2Gi,Gj=(xi-x(j)TS-1(x(i)-x(j)線性判別函數(shù)是W1x=2.364x1+1.834x2-1.524x3-1.521x4-78.767W2x=1.510x1+0.558x2+0.665x3+0.419x4-70.541W3x=1.167x1+0.320x2+1.417x3+1.747x4-101.5012.1 Bayes判別假定1=2=3=。先驗概率按比例分配，即p1=p2=p3=50150=13求得的線性判別函數(shù)W1x，W2x，W3(x)中關(guān)于變量x1x4的系數(shù)以及常數(shù)項均與上面結(jié)果相同。廣義平方距離函數(shù)dj2x=x-xjTSj-1x-xj-2lnpj，j=1,2,3后驗概率PGjx=exp-0.5dj2xi=13exp-0.5di2x，j=1,2,3以下是SPSS軟件判別分析結(jié)果。分析觀察值處理摘要未加權(quán)的觀察值N百分比有效150100.0已排除遺漏或超出範(fàn)圍群組代碼0.0至少一個遺漏區(qū)別變數(shù)0.0遺漏或超出範(fàn)圍群組代碼及至少一個遺漏區(qū)別變數(shù)0.0總計0.0總計150100.0群組統(tǒng)計資料類別平均數(shù)標(biāo)準(zhǔn)偏差有效的 N (listwise)未加權(quán)加權(quán)1x150.263.7955050.000x234.104.3395050.000x314.621.7375050.000x42.461.0545050.0002x159.365.1625050.000x227.503.3645050.000x342.604.6995050.000x413.261.9785050.0003x165.886.3595050.000x229.743.2255050.000x355.525.5195050.000x420.462.9365050.000總計x158.508.253150150.000x230.454.571150150.000x337.5817.653150150.000x412.067.718150150.000群組平均值的等式檢定Wilks Lambda ()Fdf1df2顯著性x1.393113.3142147.000x2.63841.6762147.000x3.0591180.1612147.000x4.075902.5042147.000聯(lián)合組內(nèi)矩陣ax1x2x3x4共變異x127.1599.78316.7094.225x29.78313.5145.6103.464x316.7095.61018.5194.571x44.2253.4644.5714.547相關(guān)x11.000.511.745.380x2.5111.000.355.442x3.745.3551.000.498x4.380.442.4981.000a. 共變異數(shù)矩陣具有 147 自由度。共變異數(shù)矩陣a類別x1x2x3x41x114.40010.9731.509.939x210.97318.8271.304.994x31.5091.3043.016.607x4.939.994.6071.1112x126.6439.00018.2905.578x29.00011.3168.3884.173x318.2908.38822.0827.310x45.5784.1737.3103.9113x140.4349.37630.3296.158x29.37610.4007.1385.224x330.3297.13830.4595.797x46.1585.2245.7978.621總計x168.104-3.050125.84951.862x2-3.05020.893-31.831-11.530x3125.849-31.831311.628131.066x451.862-11.530131.06659.574a. 共變異數(shù)矩陣總計具有 149 自由度。變數(shù)已輸入/已移除a,b,c,d步驟已輸入Wilks Lambda ()統(tǒng)計資料df1df2df3確切 F統(tǒng)計資料df1df2顯著性1x3.05912147.0001180.1612147.000.0002x2.03922147.000297.9004292.000.0003x4.02732147.000243.5026290.000.0004x1.02542147.000191.1338288.000.000在每一個步驟中，輸入最小化整體 Wilks Lambda 的變數(shù)。a. 步驟的數(shù)目上限為 8。b. 要輸入的局部 F 下限為 3.84。c. 要移除的局部 F 上限為 2.71。d. F 層次、容差或 VIN 不足，無法進行進一步計算。分析中的變數(shù)步驟允差要移除的 FWilks Lambda ()1x31.0001180.1612x3.8741129.588.638x2.87437.484.0593x3.72941.949.043x2.78144.975.044x4.67129.889.0394x3.37944.010.040x2.64817.172.031x4.66022.391.033x1.3696.615.027不在分析中的變數(shù)步驟允差最低 允差要輸入的 FWilks Lambda ()0x11.0001.000113.314.393x21.0001.00041.676.638x31.0001.0001180.161.059x41.0001.000902.504.0751x1.445.44532.824.040x2.874.87437.484.039x4.752.75223.296.0442x1.375.37512.776.033x4.671.67129.889.0273x1.369.3696.615.025Wilks Lambda ()步驟變數(shù)數(shù)目Lambda ()df1df2df3確切 F統(tǒng)計資料df1df2顯著性11.059121471180.1612147.000.00022.03922147297.9004292.000.00033.02732147243.5026290.000.00044.02542147191.1338288.000.000分類處理摘要已處理150已排除遺漏或超出範(fàn)圍群組代碼0至少一個遺漏識別變數(shù)0已在輸出中使用150群組的事前機率類別在前分析中使用的觀察值未加權(quán)加權(quán)1.3335050.0002.3335050.0003.3335050.000總計1.000150150.000Bayes判別（用回代法）的結(jié)果見下表。分類結(jié)果a類別預(yù)測的群組成員資格總計123原始計數(shù)150005020500503005050%1100.0.0.0100.02.0100.0.0100.03.0.0100.0100.0a. 100.0% 個原始分組觀察值已正確地分類。下表是Bayes判別（交叉確認(rèn)法）的結(jié)果。分類函數(shù)係數(shù)類別123x12.3641.5101.167x21.834.558.320x3-1.524.6651.417x4-1.521.4191.747（常數(shù)）-78.767-70.541-101.501費雪 (Fisher) 線性區(qū)別函數(shù)分類結(jié)果a類別預(yù)測的群組成員資格總計123原始計數(shù)150005020482503014950%1100.0.0.0100.02.096.04.0100.03.02.098.0100.0a. 98.0% 個原始分組觀察值已正確地分類。2.2 逐步判別逐步判別的主要計算步驟如下：第一步：輸入原始數(shù)據(jù)矩陣X=x111x112x11mx121x122x12mx1n11xg11xg21xgng1x1n12xg12xg22xgng2x1n1mxg1mxg2mxgngm第二步：計算變量的總均值、組均值、總離差、組內(nèi)離差。Xk=xk1,xk2,xkm，k=1,2,mX=x.1,x.2,x.mW=WjlmmT=(tjl)mm第三步：給定挑選變量F檢驗門坎值（臨界值）F1,F2。第四步：逐步挑選變量。逐步挑選變量的思想與逐步回歸中一樣，現(xiàn)假設(shè)迭代已進行了S步，引進了r個變量，這r個變量號構(gòu)成的集合為Ir，剩下的m-r個變量號構(gòu)成的集合為Im-r。第五步：求判別函數(shù)。設(shè)迭代h步后，挑選變量結(jié)束，共選入r個變量進入判別式。FkX=lnqk+Cok+jIrCjkxj，k=1,2,gCjk=n-gjIrxkiWijh，k=1,2,gCok=-12jIrCjkxki，k=1,2,g其中，qk為第k個總體的先驗概率。判別系數(shù)的計算為Cjk=n-gjIrxkiWijh，k=1,2,gCok=-12jIrCjkxki，k=1,2,g其中，xki表示為k個總體的第i個變量的均值。第六步：判別歸類。將已知樣本進行回判，并算出錯判概率，然后將待判樣本進行歸類。得到結(jié)果如下表：逐觀察值統(tǒng)計資料個案編號實際群組最高群組第二高群組區(qū)別評分預(yù)測的群組P(Dd | G=g)P(G=g | D=d)重心的馬氏 (Mahalanobis) 距離平方群組P(G=g | D=d)重心的馬氏 (Mahalanobis) 距離平方函數(shù) 1函數(shù) 2pdf原始111.58321.0001.0782.000102.251-8.352.071233.68021.000.7712.00024.2046.471.577322.7822.996.4913.00411.3692.354-.416433.34521.0002.1292.00027.3876.3201.779532*.1412.7303.9223.2705.9113.691-.998611.91221.000.1842.00076.125-6.926.377733.2092.9993.1272.00116.8394.7372.059822.2872.9772.5003.0239.9633.132-1.460923*.1312.7604.0632.2406.3713.625.9351011.47821.0001.4742.000103.912-8.335.8911122.8322.997.3693.00312.1112.237-.3991223*.1622.8323.6382.1686.8414.337-.9211333.6552.995.8462.00511.3154.722.8021422.54421.0001.2193.00025.639.960-1.5241533.6452.992.8772.00810.5444.921-.1371633.8122.998.4162.00212.9595.261-.0391733.44921.0001.5992.00027.5486.5501.3421811.44321.0001.6272.00062.661-6.086.5281922.7792.998.4993.00212.7022.375-1.0152033.24321.0002.8332.00024.4305.7142.1922133.42121.0001.7282.00028.0116.5801.3842222.2932.9792.4523.02110.1812.409.6792333.11821.0004.2672.00032.7306.5532.3432433.20721.0003.1472.00029.7687.168-.3082533.3282.9352.2322.0657.5734.468-.4672611.56421.0001.1462.000103.265-8.360.4892733.45021.0001.5982.00018.6635.2751.7352822.73321.000.6213.00017.9901.388-.0212922.5122.9991.3393.00114.9401.731.4263022.64721.000.8723.00023.337.853-.4073111.48821.0001.4332.00068.257-6.533-.6803233.5612.9801.1572.0208.9284.558.2293322.49921.0001.3903.00026.151.944-1.6123433.5552.9861.1772.0149.7384.809-.2353533.35221.0002.0892.00021.7635.5411.9573611.91921.000.1692.00090.235-7.729.1533711.82721.000.3802.00094.309-7.940.1833822.4052.9471.8093.0537.5952.904-.0773933.7642.999.5392.00115.6275.2111.1384011.85721.000.3092.00075.989-6.973-.2124133.82521.000.3852.00018.2245.5691.1324211.30321.0002.3882.00067.317-6.2201.3014322.77421.000.5113.00022.6201.129-1.1214411.60721.000.9982.00071.573-6.730-.5844533.06521.0005.4522.00031.1877.302-1.0814633.2742.8492.5872.1516.0364.090-.0544711.57521.0001.1082.00068.776-6.562-.5074822.5712.9991.1213.00115.1582.328-1.6044922.19121.0003.3163.00034.340.133-1.6105033.00921.0009.3902.00047.3777.6392.7965111.67021.000.8012.00069.948-6.626-.3415211.85621.000.3102.00090.123-7.662.6615333.2422.8452.8372.1556.2293.912.4785411.42721.0001.7022.00063.049-6.207-.4555511.43921.0001.6482.00069.334-6.598-.8395611.88321.000.2492.00090.552-7.761-.0235733.0182.9317.9852.06913.1815.024-2.2555833.79721.000.4532.00021.2306.225.2755911.66921.000.8042.00082.308-7.344-.6786011.04021.0006.4552.000130.836-9.4761.5696111.54221.0001.2232.00070.142-6.479.9336222.58621.0001.0693.00020.4121.098.0876333.2032.7463.1922.2545.3473.831.2306411.65421.000.8502.00075.585-6.965-.6306511.90521.000.2002.00091.111-7.758.3266622.4862.9731.4423.0278.6002.718-.0516722.40421.0001.8123.00028.207.745-1.6516811.73321.000.6222.00070.758-6.591.5106911.80921.000.4232.00075.140-6.929-.2977022.6552.991.8453.00910.2722.467-.1857122.09021.0004.8253.00039.077-.421-1.1837211.02521.0007.3922.000119.382-8.6862.5727311.86421.000.2922.00092.048-7.786.4997433.67121.000.7992.00024.5306.417.8667533.15921.0003.6772.00030.2506.3272.2857633.8122.998.4162.00212.9595.261-.0397722.1542.9983.7383.00216.1632.778-2.3557833.1732.8843.5112.1167.5714.468-.9847911.89421.000.2232.00081.567-7.193.6738011.22821.0002.9562.000112.943-8.7171.2278133.90821.000.1932.00019.7246.022.4048233.6972.993.7222.00710.5984.892.0368333.1902.7843.3202.2165.8953.774.5768433.6172.999.9652.00113.9845.458-.4608522.20921.0003.1343.00033.948.105-1.4378622.97521.000.0513.00015.6021.899-.8808722.86221.000.2983.00020.6201.196-.6128811.08721.0004.8762.000120.483-8.9801.6808911.66421.000.8192.00073.727-6.856-.5559033.00321.00011.5482.00049.2118.743-.7679133.0202.6717.7982.3299.2234.468-2.0429211.50921.0001.3492.00086.699-7.3401.3819322.99321.000.0153.00017.3681.648-.8239422.9052.999.1993.00114.8581.827-.2979522.1912.9903.3093.01012.4622.1061.0489611.97921.000.0412.00082.315-7.313.0169711.00121.00013.4272.00051.548-5.164-2.7419822.18821.0003.3453.00029.933.958-2.3909922.25421.0002.7383.00031.658.468-1.80310022.63321.000.9143.00025.003.777-.82410111.92421.000.1592.00080.961-7.252-.17310211.54421.0001.2192.00069.006-6.577-.59510333.52321.0001.2952.00023.5515.9971.57810422.90721.000.1963.00019.3141.329-.54110533.41921.0001.7382.00017.8565.954-.75610622.5742.9991.1103.00114.8371.748.32210711.97921.000.0432.00084.024-7.406.02910811.83421.000.3632.00090.065-7.649.72610933.8822.999.2522.00113.3415.111.64611022.16921.0003.5583.00030.446.936-2.44411133.23221.0002.9222.00019.6016.140-1.10811233.1532.9993.7512.00118.9376.032-1.37411311.54621.0001.2092.00077.998-7.102-.85811422.7002.998.7143.00212.8922.034.05611522.53121.0001.2653.00016.7082.195-1.75511611.70821.000.6922.00097.452-8.050.62611722.79921.000.4503.00018.9331.305-.21111822.1462.8563.8463.1447.4133.595-1.33411922.6672.999.8113.00115.4092.218-1.48812022.82321.000.3893.00020.8801.143-.51512122.05921.0005.6623.00040.180-.647-.58912222.95121.000.1013.00018.3171.455-.57012333.59121.0001.0512.00025.8526.595.74012433.6692.998.8042.00213.7144.9361.12012511.17821.0003.4572.000106.319-8.2611.82512611.90421.000.2032.00087.234-7.512.62812733.07721.0005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