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ChemometricsandMultivariateResolutionanditsApplicationinanalysisofTCM中南大学中药现代化研究中心梁逸曾ChemometricsChemometricsisanewchemicaldisciplinethatusesthetheoryandmethodsfrommathematics,statistics,computerscienceandotherrelateddisciplinestooptimizetheprocedureofchemicalmeasurement,andtoextractchemicalinformationasmuchaspossiblefromchemicaldata.Chemometricscouldbedefinedasadisciplineoffundamentaltheoryandmethodologyofchemicalmeasuring.化学计量学运用数学、统计学、计算机科学、以及其他相关学科的理论与方法,优化化学量测过程,并从化学量测数据中最大限度地获取有用的化学信息,可以说是一门化学量测的基础理论与方法学。BriefHistoryofChemometricsSvanteWolduseditfirstlyforapplyingscientificprojectin1970inSweden;WoldandKowalskifoundedtheInternationalChemometricSocietyin1974;AnalyticalChemistrypublishedspecialreviewon“Chemometrics”everytwoyearsince1978;Twospecialchemometricinternationaljournalsnamed“J.Chemom.”and“ChemLab”appearedin1987frombothAmericanandEurope.ContentsinchemometricsChemometricsconsistsoffundamentalandmethodologyofchemicalmeasurements.NecessaryfundamentalknowledgeofstatisticsandlinearalgebraVectorandMatrixIsMathematicsreallyusefulforchemists?Dataexploding;Extractchemicalinformationfromthedata;RevolutionofInformationtechnique;ProgressinComputerability;VectorinanalyticalchemistryAllthespectra,chromatogramsandetc.canbenumeratedintoagroupofnumbers,whichiscalledavectorinmathematics.HyphenatedInstruments,suchasHPLC-DAD,GC-MS,GC-IR,HPLC-MSTwo-waydatacontainingbothchromatographyandspectra;Datamatrixwithmorethan10Megabytes;DatabaseoflotsofchemicalstandardsThemixturespectrumoftwodifferentchemicalcompoundsaandbaccordingtotheLambert-BeerlawGeometricsenseofvectoradditionGeometricsenseofvectorsubtractionDirectionandlengthofvectorThedirectionofavectorisdecidedbyallitselements,sincethedifferentratiosbetweenthemcandefinesdifferentdirectionsinlinearsubspace;Thelengthofavectorisalsodecidedbymagnitudesofitselements,sincewehave,||a||=(a12+….+an2)1/2differentratiosbetweenthemcandefinesdifferentdirectionsinlinearsubspaceSubtractionoftwovectorsdefinesthedistancebetweenthetwopointsinndimensionalspaceNumericalmultiplicationofvectorska=kakakan12ThespectraofdifferentconcentrationsInnerproductandouterproductbetweenthevectorsInnerordotproductbetweentwovectorsproducinganumberatb=[a1,a2,...,an]bbbn12=aibiGeometricsenseofinnerproductbetweentwovectorsInnerproductandprojectionbetweenvectorsOuterproductbetweentwovectorsproducingabilinearmatrix,whichisofspecialimportanceinmultivariateresolutionabt=aaan12[b1,b2,...,bn]=abababababababababnnnnnn111212122212Rankofamatrix:AmatrixAoforder(nm),itsrankisthemaximumnumberofthelinearlyindependentrowvectors(columnvectors)init,denotedbyrank(A).Ithasthefollowingfeatures:At=(A-1)t0rank(A)min(n,m)rank(AB)min[rank(A),rank(B)]rank(A+B)rank(A)+rank(B)rank(AtA)=rank(AAt)=rank(A)IfmatrixAisasquarematrixofordern,thenwhenandonlywhendet(A)isnotequaltozeros,rank(A)=nWhatisthechemicalmeaningofrankofamatrix?Linearlyindependent?Rankofamatrix=thenumberofthechemicalcomponentsinthemixture?Mixturenumberandcompoundnumber?Apartofarealtwo-waydatameasuredforCortexCinnamomi(肉桂)Lambert-BeerLaw1TpTmnmnmpnpiiiicseCSXETheproblemhereforchemiststosolveisthat,withthemeasurementmatrixathand,oneneedstofindout:Thenumberofabsorbingchemicalcomponents:AThespectrumofeachchemicalcomponent:si(i=1,2,…,A)(firststepofqualifications)Theconcentrationprofileofeachchemicalcomponent:ci(i=1,2,…,A)(firststepforquantification)Isitpossible?Yes,ifwehavethetwo-waydata!!MixturespectraandcompoundspectraThisisatwocompoundsystem;Tworedvectorsarethecompoundspectra;Sevenbluevectorsaremixturespectra;LinearlyindependentThetwospectraarefromtwodifferentchemicalcompounds,sotheyareindependentwitheachotherSevenspectraareallfromthespectraofthetwochemicalcompounds,sotheyaredependentupontheconcentrationsofthetwocompoundsinthemixtureMixturenumberandcompoundnumberRankofamatrix=thenumberofthechemicalcomponentsinthemixture?Unchangedarechemicalcompounds;Rankofamatrixisalsocertain,whichisnotchanged;Thus,ifwecollectallthespectratoformamatrix,therankofwhichshouldbe2.Howcanwefindtherankofamatrixwithmeasurementnoise?Whatarenoisesandhowdotheyinfluencethedataanalysis?Thus,weneedstatisticsandalsoalgebra;Usefultechnique:Principalcomponentanalysis!!Thisisreallyadifficultproblem!Now,let’sgothroughthisproblemstepbystep.ForanymatrixAnm(nm),onecanalwaysusethetechniquecalledsinglevaluedecomposition(SVD)toobtainitseigenvaluesandeigenvectors.TheSVDtechniqueistodecomposethematrixintothreematrices,thatisA=USVtHereUisacolumnorthogonalmatrix,sayeverycolumnisorthogonalwitheachother,thatis,UtU=In;Sisadiagonalmatrixwitheverydiagonalelementasaneigenvalueofthematrix;Vtisaroworthogonalmatrix,sayeverycolumnisorthogonalwitheachother,thatis,VtV=Im。SinglevaluedecompositionA=USVtQuestion2Wehaveadatamatrixathand,weneedtoknowtherearehowmanychemicalcomponentsinit.Whattechniquedoyouwanttouse?Principalcomponentanalysis?Canweusesingularvaluedecompositiontosolvetheproblem?Multivariatecalibrationandmultiva
本文标题:中南大学中药现代化研究中心
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