pls partial least squares analysispls偏最小二乘法.docx

pls partial least squares analysispls偏最小二乘法.docx

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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