數(shù)據(jù)分析習(xí)題

第五章數(shù)據(jù)剖析(梅長(zhǎng)林)習(xí)題(總9頁(yè))--本頁(yè)僅作為文檔封面，使用時(shí)請(qǐng)直接刪除即可----內(nèi)頁(yè)能夠依據(jù)需求調(diào)整適合字體及大小--第五章習(xí)題1.習(xí)題解：假定兩整體聽(tīng)從正態(tài)散布，且協(xié)方差矩陣12，誤判損失相同又先驗(yàn)概率按比率分派，經(jīng)過(guò)SAS計(jì)算獲得先驗(yàn)概率如表：ClassLevelInformationVariablePriorProbagroupNameFrequencyWeightProportionbilityG1G16G2G28即：P10.428571P20.571429又計(jì)算可得：x(1)25.316,x(2)22.0252.4161.187有計(jì)算的整體協(xié)防差距矩陣S為：PooledWithin-ClassCovarianceMatrix,DF=12Variablex1x2x1x2而且：lnS-2.38145計(jì)算廣義平方距離函數(shù)：d2(x)(xx(j))TS1(xx(j))lnSj2lnpjjj并計(jì)算后驗(yàn)概率：?22?2(x)?0.5dj(x)0.5dkj1,2eeP(Gj|x)k1回代鑒別結(jié)果以下:2PosteriorProbabilityofMembershipingroupObsFromgroupClassifiedintogroupG1G21G1G12G1G13G1G14G1G2*5G1G16G1G17G2G28G2G29G2G210G2G211G2G212G2G213G2G214G2G2因而可知誤判的回代預(yù)計(jì)：*Pr1/140.0714若依據(jù)交錯(cuò)確認(rèn)法，定義廣義平方距離以下：d2j(x)(xx((xj)))TS(x1)j(xx((xj)))lnS(x)j2lnpj逐一剔除,交錯(cuò)鑒別，后驗(yàn)概率按下式計(jì)算：?22?2?(x)(x)0.5dje0.5dkj1,2P(Gj|x)ek1經(jīng)過(guò)SAS計(jì)算獲得表所示結(jié)果。發(fā)現(xiàn)相同也是屬于G1的4號(hào)被誤判為G2，因此誤判率的交錯(cuò)確認(rèn)預(yù)計(jì)為p?c*1/140.07143PosteriorProbabilityofMembershipingroupObsFromgroupClassifiedintogroupG1G21G1G12G1G13G1G14G1G2*5G1G16G1G17G2G28G2G29G2G210G2G211G2G212G2G213G2G214G2G2p*p1d/2p21d/2此中?(x(1)x(2))TS1(x(1)x(2))=，dc(1|2)p2，又由于c(1|2)c(2|1)c，因此dlnP20.288，lnP1c(2|1)p1最后可得后驗(yàn)概率p為：習(xí)題解：（1）在12而且先驗(yàn)概率相同的的假定前提下，成立矩離判其他線性鑒別函數(shù)。利用SAS的procdiscrim過(guò)程第一計(jì)算獲得整體的協(xié)方差矩陣，如表：4PooledWithin-ClassCovarianceMatrix,DF=25Variablex1x2x3x4x5x6x7x8x12.-0.0.x20.4.x30.-0.3.1.1.0.x4-2.1.5.2.0.x51.5.8.3.x60.0.2.3.4.0.x70.x84.0.0.2.各個(gè)整體的馬氏平方距離見(jiàn)表：GeneralizedSquaredDistancetogroupFromgroupG1G2G10G20線性鑒別函數(shù)為：W1121.19957.006x12.179x20.389x31.818x45.670x50.046x69.578x71.916x8W-176.330308.269x13.069x2x-00.263x4x10.70234.58151.054x613.465x70.909x8獲得訓(xùn)練樣本回判法鑒別結(jié)果如表：ErrorCountEstimatesforgroupG1G2TotalRatePriors訓(xùn)練樣本的交錯(cuò)確認(rèn)鑒別結(jié)果：PosteriorProbabilityofMembershipingroupObsFromgroupClassifiedintogroupG1G217G1G2*19G1G2*5ErrorCountEstimatesforgroupG1G2TotalRatePriors2）假定兩整體聽(tīng)從正態(tài)散布，先驗(yàn)概率按比率分派且誤判損失相同，在兩總體協(xié)方差矩陣相同，即12的條件下進(jìn)行Bayes鑒別剖析，經(jīng)過(guò)SASdiscrim過(guò)程獲得結(jié)果：ErrorCountEstimatesforgroupG1G2TotalRatePriors交錯(cuò)確認(rèn)鑒別結(jié)果：PosteriorProbabilityofMembershipingroupObsFromgroupClassifiedintogroupG1G219G1G2*25G2G1*ErrorCountEstimatesforgroupG1G2TotalRatePriors在12，而且先驗(yàn)概率按比率分派的假定前提下利用SAS的procdiscrim過(guò)程進(jìn)行Bays鑒別剖析，這時(shí)以個(gè)整體的訓(xùn)練樣本獨(dú)自預(yù)計(jì)各整體的協(xié)方差矩陣，可到的訓(xùn)練樣本的回判和交錯(cuò)確認(rèn)結(jié)果：回判結(jié)果：ErrorCountEstimatesforgroupG1G2TotalRatePriors交錯(cuò)確認(rèn)鑒別結(jié)果：6PosteriorProbabilityofMembershipingroupObsFromgroupClassifiedintogroupG1G221G2G1*22G2G1*23G2G1*24G2G1*25G2G1*26G2G1*27G2G1*ErrorCountEstimatesforgroupG1G2TotalRatePriors3）在不一樣的假定前提，采納不一樣鑒別方法獲得待判樣本的鑒別結(jié)果：1.距離鑒別剖析獲得西藏、上海、廣東的鑒別結(jié)果：PosteriorProbabilityofMembershipingroupObsClassifiedintogroupG1G21G22G23G22.在協(xié)方差矩陣相同的前提下，Bayes對(duì)西藏、上海、廣東的鑒別結(jié)果：PosteriorProbabilityofMembershipingroupObsClassifiedintogroupG1G21G22G23G23在協(xié)方差不一樣矩陣相同的前提下，Bayes對(duì)西藏、上海、廣東的鑒別結(jié)果：PosteriorProbabilityofMembershipingroupObsClassifiedintogroupG1G21G12G13G13.習(xí)題7解：（1）假定兩整體聽(tīng)從正態(tài)散布且在兩整體協(xié)方差矩陣相同，即12，先驗(yàn)概率按相同的條件下進(jìn)行Bayes鑒別剖析，經(jīng)過(guò)SASdiscrim過(guò)程獲得結(jié)果：第一獲得線性鑒別函數(shù)：W98.847530.351x10.152x20.789x31.952x40.589x51108.102x60.312x7W-95.00029.878x1-0.152x20.227x31.395x40.065x5185.337x60.259x7回代誤判結(jié)果：PosteriorProbabilityofMembershipingroupObsFromgroupClassifiedintogroupG1G29G1G2*29G2G1*由計(jì)算結(jié)果發(fā)現(xiàn)，第9號(hào)樣本被誤判到G2,29號(hào)樣本被誤判到G1.誤判率為%ErrorCountEstimatesforgroupG1G2TotalRatePriors交錯(cuò)確認(rèn)鑒別結(jié)果：由計(jì)算發(fā)現(xiàn)總合有四個(gè)樣本被判錯(cuò)，分別是9、28、29、35號(hào)樣品。累計(jì)誤判率為%PosteriorProbabilityofMembershipingroupObsFromgroupClassifiedintogroupG1G29G1G2*28G2G1*29G2G1*35G2G1*ErrorCountEstimatesforgroupG1G2TotalRatePriors8（1）假定兩整體聽(tīng)從正態(tài)散布且在兩整體協(xié)方差矩陣相同，即12，先驗(yàn)概率按比率分派且誤判損失相同的條件下進(jìn)行Bayes鑒別剖析，經(jīng)過(guò)SASdiscrim過(guò)程獲得結(jié)果：第一獲得線性鑒別函數(shù)：LinearDiscriminantFunctionforgroupVariableG1G2Constantx1x2x3x4x5x6x7回代誤判結(jié)果PosteriorProbabilityofMembershipingroupObsFromgroupClassifiedintogroupG1G29G1G2*29G2G1*ErrorCountEstimatesforgroupG1G2T