R-Q型因子分析与对应分析

第30卷第1期物探化探计算技术2008年1月基金项目:中国地质调查局地质调查项目(200110200021)收稿日期:2006-11-08改回日期:2007-06-22:10011749(2008)01007803R-Q曾道明1,2,纪宏金1,高文1,刘强1(1.吉林大学地球探测科学与技术学院,长春130026;2.中国地质科学院地球物理地球化学勘查研究所,廊坊065000):R-Q型因子分析是一种多元统计方法,但也是一种被忽视的方法这里以简单方式证明了R-Q型因子分析对偶性,并给出一种方便的R-Q型因子得分计算公式利用地球化学数据解释的实例,对比了该方法与对应分析的应用效果结果表明,二种方法都能有效地识别数据中的样品与变量类型及其对应关系,并且二种方法都具有独特的优点这些方法为快速有效地解释勘查地球化学数据起到重要作用:多元统计分析;因子分析;对应分析;地球化学勘查;数据解释:P632:A0Benzcri[1],RQ,,[2,3],[4~8],,,,[9],R-Q[10]R-Q,,,,R-Q,R-QR-Q,,R-Q,Howarth[11],1R-QX=(xij)nmnm,xijijW=n-1/2XX=n1/2W(1)R=WTW,H=WWT,WTW,Hn[10],RR,HQRQR-QRr,r12r0,=diag(1,2,,r)(2)U=(u1,u2,,ur)=(uij)mr(3)UTU=I,IrRARFRAR=U1/2(4)FR=WU(5),ARTAR=1/2UTU1/2=(6)FRTFR=UTWTWU=UTUUTU=(7),HR,V=(v1,v2,,vr)=WU-1/2=(vij)nr(8)VTV=IQAQFQAQ=V1/2(9)FQ=WTV(10)RQAQ=V1/2=WU-1/21/2=WU=FR(11)FQ=WTV=WTWU-1/2=UUTU-1/2=U1/2=AR(12)RQ,(5)(10),FRFQ[10],FR=V,FQ=U,(11)(12),(6)(7),ARmpmp,FRnpnpARART=U1/21/2UT=UUT=WTW=R(13)FRFRT=V1/21/2VT=VVT=WWT=H(14)mARART,nFRFRT(6)(7),,,ARFR,,R,R-Q,AR,FRRF=XAR-1,(1)(4)(5)F=n1/2WU1/2-1=n1/2FR-1/2,FR=n-1/2F1/2(15)2R-Q,R-QHowarth25ZnFeMnCdCuPb[11]256(FORTRAN)R-Q,R1=3.393,2=2.114,3=0.285,4=0.171,5=0.027,6=0.01092%,,,1:1R-Q型因子分析的结果Fig.1TheresultofR-Qmodefactoranalysis(1)25,131516,2223,20(2),CuZnCd,;FeMnPb,(3)Howarth[11],131516CuZnCd,,,CuZnCd2223FeMnPb,FeMnPb,20,,,,1=0.2643,2=0.0334,3=0.0032,4=0.0015,5=0.0004,791期曾道明等:R-Q型因子分析与对应分析2对应分析的结果Fig.2Theresultofcorrespondenceanalysis98%,2,,:131516CuZnCd,,22FeMnPb,3R-Q,R-Q,,,R-Q,,R-Q,,R-Q,,,[10]R-Q,,,ImbrieQ[12],,,,R-Q,:(1)RQ,R-Q,RR-Q(2)R-Q,;(3),:[1]DAVIDM,CAMPIGLIOC,DRLINGlingR.ProgressinR-andQ-modeanalysis:correspondenceanalysisanditsapplicationtothestudyofgeologicalprocesses[J]Can.J.EarthSc.i,1974,11:131[2]TAOFENGMEI,XIALIAXIAN.Stepwisecorrespon-denceanalysisandstudyofphysicalcharacteristicsofChineseethnicgroups[J]JournalofBiomathematics,2003,18(2):139[3]GROENENPJF,VELDENM.Inversecorrespondenceanalysis[J]LinerAlgebraandItsApplications,2004,388:221[4],[J],1991,13(2):98[5]JIHONGJIN,ZHUYONGZHENG,WUXISHENG.CorrespondenceClusterAnalysisandItsApplicationinExplorationGeochemistry[J]Geochem.Explor.,1995,(55):137.[6],,[J](),1998,19(2):132[7],[J]()2000,21(1):11[8],,,[J],2004,21(4):248[9],,,[J](),2005,35(3):308[10]RQ[J],1985,7(4):332[11]HOWARTHR.J.,SINDING-LARSENR.Multivar-iateanalysis.In:R.J.Howarth(Ed),Statisticsanddataanalysisingeochemicalprospecting[M]HandbookofExplorationGeochemistry,Vo.l2.Elsevier,Amsterdam,1983[12]JORESKOGKG,KLOVANJE,REYMENTRA.MethodsinGeomathematics1,GeologicalFactorAna-lysis[M]Elsevier,Amsterdam,1976:曾道明(1982-),男,四川德阳人,硕士,主要致力于应用地球化学研究80物探化探计算技术30卷map-makingisbetterwiththehelpofinversedis-tanceinterpolation.Keywords:goldensoilengineeringdistric;tsoilgeo-chemicalmeasuring;methodsandaccuracyationTHEEFFECTOFSUPERFICIALCHARGEANDMINERALCOMPONENTOFSOILONNUCLIDESTRONTIUMSADSORPTIONINSOMERADWASTEBARRIERLIANGYan,ZHANGCheng-jiang,NISh-ijun,eta.l(Collegeofappliednucleartechnologyandauto-mationengineering,ChengduUniversityofTechnolo-gy,Chengdu610059,China).COMPUTINGTECH-NIQUESFORGEOPHYSICALANDGEOCHEMICALEXPLORATION,2008,30(1):0074Inordertoreducethepollutionofradwaste,weusuallyadoptfill-inmethodneartheradwaste.ThefactorthataffecttheadsorptionofStrontiumhassu-perficialcharge,mineralcomponen,tandbesidestheouterfactor,suchasadditivealsohasimpactoni.tInthisarticle,experimentstaticadsorptionisadop-ted,andthroughmeasuringtheconcentrationofStron-tiumtoacquiretheadsorptionratioofdifferentsoilsforselectingthebestadsorptionmateria.lTheou-tcomeofexperimentindicatesthatalthoughdifferentsoilsuperficialchargeinnuclidewastebarriercontainpositiveandnegativecharges,thesoilthatcontainmorenegativechargehasthehigheradsorptionratio;Andinthemineralcomponentsquartzisprimary,anditis,however,alsocomposedofsomestrongad-sorptionminerals,suchasmontmorillonite,illite.ThebrownarenaceouspowderTY29joinedwithsod-iumcarbonatehadthehighestKd(103)conten,twhichmeetstheneedofbarrier.Fortheotherfactorsthataffectadsorptionneedfurthervalidation.Keywords:radwaste;barrier;adsorption;adsorp-tionratio;nuclides'migrationTHER-QMODEFACTORANALYSISANDCORRESPONDENCEANALYSISZENGDao-ming1,2,JIHong-jin1,GAOWen1,eta.l(1.CollegeofGeo-explorationScienceandTechnolo-gy,JilinUniversity,Changchun130026,China;2.In-stituteofGeophysicalandGeochemicalExploration,MinstryofgeologyandMineralResources,Langfang065000,China).COMPUTINGTECHNIQUESFORGEOPHYSICALANDGEOCHEMICALEXPLORA-TION,2008,30(1):0078TheR-Qmodefactoranalysisisameaningfulmultivariatestatisticalmethod,butalsoanignoredmethod.Inthepaper,thedualityofR-Qmodefactoranalysisisproved,andaconvenientcomputingfor-mulaforR-Qmodefactorscoresisgivenwithasim-plemanner.Theapplicaioneffectofthemethodiscomparedwiththatofthecorrespondenceanalysisbyanexampleofgeochemicaldatainterpretation.Theresultsshowthatthetypesofsampleandvariableandtheircorrespondingrelationsinthegeochemicaldatacanbeeffectivelyrecognizedbytwokindsofmeth-ods,andthatbothmethodshaverespectivefeatures.Thesemethodsplaythesameimportantpartsinfastandeffectiveinterpretationoftheexplorationgeo-chemicaldata.Keywords:multivariatestatistical