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plspartialleastsquaresanalysispls偏最小二乘法@#@pls(partialleastsquaresanalysis):
@#@pls(偏最小二乘法)@#@PLS(PARTIALLEASTSQUARESANALYSIS)IntroductionPartialLeastSquares(PLS)Analysiswasfirstdevelopedinthelate60sbyHermanWold,andworksontheassumptionthatthefocusofanalysisisonwhichaspectsofthesignalinonematrixarerelateddirectlytosignalsinanothermatrix.Ithasbeendevelopedextensivelyinchemometrics,andhasrecentlybeenappliedtoneuroimagingdata.Intheapplicationtoimagingdata,ithasbeenusedtoidentifytask-dependentchangesinactivity,changesintherelationsbetweenbrainandbehaviour,andtoexaminefunctionalconnectivityofoneormorebrainregions.PLShassimilaritiestoCanonicalCorrelationinitsgeneralconfiguration,butismuchmoreflexible.ThisGUIisthefirstmajorreleaseofPLSforneuroimaging.Ithasbeenindevelopmentforsometime,andalthoughthisversionappearsstable,therearealwaysthingsthatcanbeimproved.Wearealsoplanningseveralenhancements,suchasunivariatetestingofmeansandcorrelations,advancedplottingroutinesandhigher-orderanalyses.Pleasecheckourwebsiteregularlytoseeifthereareupdates.PLScomputesamatrixthatdefinestherelationbetweentwo(ormore)matricesandthenanalyzesthatcross-blockmatrix.InthecaseofTaskPLS,thecovariancebetweentheimagedatasetandasetofdesigncontrastscanbecalculated(anequivalentprocedureisdescribedbelow).ThecovarianceimagesareanalyzedwithSingularValueDecomposition(SVD)toidentifyanewsetofcovarianceimagesthatcorrespondtothestrongesteffectsinthedata.ForBehaviourPLS,task-specificcorrelationsofbrainactivityandbehaviourarecomputed(acrosssubjects),combinedintoasinglematrix,whichisthendecomposedwithSVD.Theresultantpatternsidentifysimilaritiesanddifferencesinbrain-behaviourrelations.CreatingDatamatRegardlessofwhichtypeofPLSistobeconducted,thedatamustbeinaformsuchthatalldataforallsubjectsandtasksthataretobeanalyzedarecontainedinasinglematrix.Forimagedataingeneral,itisassumedimageshavebeenstandardizedinsomemannersothattheyareallthesameshapeandsize.ForPETandMRIdata,PLSworksbestifyouusethesmallestsmoothingfilterpossible(e.g.,nomorethantwicethevoxelsize).ForERPdata,anyfiltering,orreplacingdatainbadchannels,etc.mustalsobedonebeforecreatingthePLSdatamatrix.TheSessionProfilepartofourprogramloadsbrainimagesorERPwaveforms,stringseachoneoutintoavectorandthenstacksthevectorsoneontopoftheothertomakethelargedatamatrix(calleddatamatinthePLSprograms).Eachimage(alsocalledsubjectdatafile)representsonesubjectunderonecondition.Forbrainimages,thescriptalsoeliminatesvoxelsthatarezeroornon-brainusingathreshold,whichisspecifictoeachtypeofimagedata.Removingthezeroandnon-brainvoxelsreducesthesizeofthedatamatconsiderablyandstreamlinesthecomputations.Unfortunately,thiscanrestrictthedatasetifimagesliceswerenotprescribedinthesamewayforallsubjects.Tomakelifeeasy,amaskiscreatedbasedonthevoxelsthatarecommonforallsubjects.Afterthedatamatisreduced,avector(‘coords’)isgeneratedtoremapthereduceddatamatintoimagespaceagain.PETImages:
@#@ThecodeiswrittenassumingyouusedtheSPM99sterotaxictemplatewith4x4x4mmvoxels,whichcreatesimageshaving34sliceseachwith40voxelsintheXand48voxelsintheYdimensions.ForPETscans,thethresholdtodefinebrainvoxelsis1/4ofthemaximumvalueforaparticularsubject.ThefinaldatamatwillhaveSbyCrowsandVcolumns(whereSisthenumberofsubjectsandCisthenumberofscansorconditions,Visthenumberofcommonbrainvoxelsintheimagedataset).ERP:
@#@ForERPdata,allchannelsofasubjectdatafilearestrungoutintoasinglevectorandthevectorsarethenstackedoneontopoftheother.ThedatamatwillhaveSbyCrowsandEbyTcolumns(whereSisthenumberofsubjects,Cisthenumberofconditions,Eisthenumberofchannels,andTisthenumberoftimepointsinthesubjectdatafile).If,aftercreatingthedatamat,itbecomesclearthataparticularsetofERPchannelsisbadformostofthesubjects,thosechannelscanbeeliminatedfromtheanalysisusingtheGUI.Aswell,singlesubjectdatacanalsobeeliminatedfromtheanalysisusingtheGUI.fMRI:
@#@CreatingthedatamatforfMRIdatasetscombinesthetwoapproachesabove.Thisallowsyoutoruntheanalysiseitheroneachsubjectorasagroup.Commonvoxelsacrosssubjectsand/orrunsareidentified,thenasinglerowvectoriscreatedforeachsubject,separatelyforeachcondition.ThedatamatwillbeSbyCrowsandVbyTcolumns(whereSisthenumberofsubjects,Cisthenumberofconditions,Visthenumberofcommonvoxels,andTisthenumberofimagesdefinedbytheusertoaccountforthelaginthehemodynamicresponse).TaskPLS:
@#@AnalysisusingGrandMeanDeviationTheTaskPLSisdesignedtoidentifywhole-brain(scalp)patternsofactivitythatdistinguishtasks.InTaskPLS,apatternmayrepresentacombinationofanticipatedeffectsandsomeunanticipatedones.TheGrandMeanDeviationanalysisisbasedonrepresentingtaskmeansasthedeviationaroundthegrandmeancomputedforeachvoxeland/ortimepoint.Thedataarethusaveragedwithinatask,leavingoutthewithin-taskvariability.(WeareexploringthepossibilityofaconstrainedPLSsolution,whereasetofaprioricontrastsareusedtodefinethesolutionspace).NexttheSVDalgorithmisusedtogetthefollowingthreecomponents:
@#@brainlv(orsalience),singularvalue(s),anddesignlv(saliencefordesign).Thedesignscoresandbrainscores(orscalpscoresinERP)areobtainedfromtheformulabelow:
@#@designscoresLV(n)=designlvbrainscoresLV(n)=datamat*brainlvThesaliencesfordesign(designlv)andbrain(brainlv)areorthonormal,orstandardized.Tomakecomparisonsacrosslatentvariableseasiertovisualize,wecomputeunstandardizedsaliences.Thisisaccomplishedbyweightingthesaliencesbytheirsingularvaluesforthelatentvariable.AlleigenimagesandERPsalienceplotsusetheunstandardizedsaliences.TaskPLSisrunbyclickingtheRunPLSAnalysisbutton.Allresultsaresavedintoaspecifiedfile.Theresultswillincludealldatamentionedabove,andotherusefulinformation.TheTaskPLSresultscanbedisplayedbyclickingtheShowPLSResultbuttoninthemainGUIwindow.ForPETandBlockedfMRI,thesaliences(eigenimages)andbootstrapratioimagesaredisplayedinamontagethatincludesalltheslicesfortheLV.ForEvent-RelatedfMRI,theresultsaredisplayedinamontageasfollows:
@#@eachrowrepresentsonelagpoint,thusthenumberofrowsequalsthespecifiedtemporalwindow;@#@eachcolumnrepresentstheslicesintheimage.ForERPs,theLVsaliencesaredisplayedasascalpplot,includingonlytheselectedelectrodesandepoch.Intheresultswindow,youwillalsofindoptionstodisplay:
@#@scatterplotsofbrain(scalp)scoreswithdesignscores,designLVbarplots,andbarplotsofthesingularvaluesandpermutationtestresults.BehaviourPLS:
@#@AnalysisusingBehaviourDataTheBehaviourPLSfirstcalculatesacorrelationvectorofbehaviourandbrainwithineachtask,thenstacksthesevectorsintoasinglematrixthatisdecomposedwithSVD.BehaviourPLShasthepotentialtoidentifycommonalitiesanddifferencesamongtasksinbrain-behaviourrelations.Thebehaviourmatrixcontainsoneormorebehaviouralmeasuresthatarethoughttorelatetothemeasuredbrainactivity.Thenumberofrowsinthebehaviourmatrixanddatamatshouldbethesame,withaseparatecolumnforeachbehaviouralmeasure.SincethismatrixiscreatedoutsideoftheGUI,itisimportantthattheorderofsubjectsandconditionsbeidenticaltotheorderdefinedusingtheGUItocreatethedatamat.AsfortheTaskPLS,theresultswindowinitiallycontainsplotsoftheunstandardizedsaliences.Withintheresultswindow,youcanalsodisplayscatterplotsofbrain(scalp)scoreswithbehaviour,barplotsshowingthemagnitudeofthebrain-behaviourcorrelationwithconfidenceintervals,andbarplotsofthesingularvaluesandpermutationtestresults.Inthebrain(scalp)scoresbybehaviourplots,thelinearfitisalsoplottedtobetterviewthescatteraroundthecorrelation.TestsofSignificancePERMUTATIONTEST:
@#@Thesignificanceofthelatentvariable,asawhole,isassessedusingpermutationtests.Weassessthemagnitudeofthesingularvaluesbyaskingthequestion:
@#@Withanyotherrandomsetofdata,howoftenisthevalueforsaslargeastheoneobtainedoriginally?
@#@Togeneratethisanswer,subjectsarerandomlyreassigned(withoutreplacement)todifferentconditions,andthePLSisrecalculated.OrthogonalprocrustesrotationisappliedtotheresultingBehavLVorDesignLVtocorrectforreflectionsandrotationsoftheresampleddata,andthesingularvaluesarerecalculatedbasedonthisrotation(MilanandWhittaker1995).Iftheprobabilityofobtaininghighersingularvaluesislow,thelatentvariableisconsideredtobesignificant.Forbothtaskandbehaviour,500permutationsaregenerallysufficient,althoughprobabilityestimatesaretypicallystableatabout100permutations.BOOTSTRAP:
@#@Bootstrapestimationisusedtoassessthereliabilityofthebrainsaliences.Inthiscase,subjectsareresampledwithreplacement.Anewdatamat,andforBehaviourPLS,anewbehaviourmatrixarecreated,andthePLSisrecalculated.Thus,unlikeforthepermutationtest,theassignmentofsubjectstoconditionsismaintained,butthesubjectscontributingtotask-relatedeffectsvary.Asforthepermut