expressedastheresponsestrengthsforfeaturesofthatpatternegvoxelssingleneuronsormodeldimensionsHyperalignmenttransformationofindividualrepresentationalspacesintoamodelrepresentationalspaceinwhich ID: 156557
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AndrewC.Connolly,1andJ.SwaroopGuntupalli11DepartmentofPsychologicalandBrainSciences,CenterforCognitiveNeuroscience,DartmouthCollege,Hanover,NewHampshire03755;email:james.v.haxby@dartmouth.edu,andrew.c.connolly@dartmouth.edu,swaroopgj@gmail.com2CenterforMind/BrainSciences(CIMeC),UniversityofTrento,Rovereto,Trentino38068,ItalyAnnu.Rev.Neurosci.2014.37:435Ð56FirstpublishedonlineasaReviewinAdvanceonJune25,2014TheAnnualReviewofNeuroscienceisonlineatneuro.annualreviews.orgThisarticleÕsdoi: expressedastheresponsestrengthsforfeaturesofthatpattern,e.g.,voxels,singleneurons,ormodeldimensionsHyperalignment:transformationofindividualrepresentationalspacesintoamodelrepresentationalspaceinwhicheachdimensionhasacommontuningfunctionREPRESENTATIONALSPACERepresentationalspaceisahigh-dimensionalspaceinwhicheachneuralresponseorstimulusisexpressedasavectorwithdifferentvaluesforeachdimension.Inaneuralrepresentationalspace,eachpatternfeatureisameasureoflocalactivity,suchasavoxelorasingleneuron.Inastimulusrepresentationalspace,eachfeatureisastimulus components,ormeasuresofsynchronybetweensources.Thecomputationaladvantagesofrepresentationalvectorspacesextendbeyondneuralrepre-sentationalspacestorepresentationalspacesforstimuliorcognitivestates.Forexample,avisualstimuluscanbemodeledasasetoffeaturesbasedonresponsepropertiesofneuronsinV1,ashigher-ordervisualfeatures,orasasetofsemanticlabels.SoundsÑvoicesandmusicÑcanbemod-eledassetsofacousticfeatures,wordscanbemodeledassetsofsemanticfeatures,actionsassetsofmovementandgoalfeatures,etc.Oncethedescriptionofthestimulusisinarepresentationalspace,variouscomputationalmanipulationscanbeappliedforrelatingstimulusrepresentationalspacestoneuralrepresentationalspaces.Allthemajorvarietiesofneuraldecodingandencodinganalysesfollowfromthisconversionofpatternsofbrainactivityorstimulitosinglepointsinhigh-dimensionalrepresentationalvectorspaces.MVPclassiÞcationusesmachinelearningmethodstodeÞnedecisionboundariesinaneu-ralrepresentationalspacethatbestdistinguishasetofresponsevectorsforonebrainstatefromothers.RSAanalyzesthesimilaritybetweenresponsevectorsasdistancesintherepresentationalspace.Stimulus-model-basedencodingpredictsthelocationoftheneuralresponsevectorforanewstimulusonthebasisofthecoordinatesofthatstimulusinastimulusfeaturespace.Stimulus-model-baseddecodingtestswhethertheencoding-basedpredictionallowscorrectclassiÞcationofneuralresponsevectorstonewstimuli.Buildingamodelofaneuralrepresentationalspacethatiscommonacrossbrainsrequireshyperalignmenttorotatethecoordinateaxesofindividualrepresentationalspacestominimizethedifferenceinthelocationsofresponsevectorsforthesamestimuli.Thus,stimuliandothercognitiveeventsarerepresentedasvectorsinneuralrep-resentationalspacesaswellasinstimulusrepresentationalspaces,andthecomputationaltaskforunderstandingrepresentationbecomesoneofcharacterizingthegeometrieswithinspacesandrelatingthegeometriesofthesespacestoeachother.Numerically,asetofresponsevectorsinarepresentationalspaceisamatrixinwhicheachcol-umnisalocalpatternfeature(e.g.,voxel)andeachrowisaresponsevector(Figure1).Thevaluesineachcolumnreßectthedifferentialresponsesofthatpatternfeaturetoconditionsorstimuli. vectorsAnMVPclassiÞcationanalysisbeginswithdividingthedataintoindependenttrainingandtestdatasets(Figure2).ThedecisionrulesthatdeterminetheconÞnesofeachclassofneuralresponsevectorsaredevelopedontrainingdata.Theborderbetweensectorsfordifferentconditionsiscalledadecisionsurface.ThevalidityoftheclassiÞeristhentestedontheindependenttestdata.Forvalidgeneralizationtesting,thetestdatamustplaynoroleinthedevelopmentoftheclassiÞer,includingdatapreprocessing(Kriegeskorteetal.2009).EachtestdataresponsevectoristhenclassiÞedasanotherexemplaroftheconditionassociatedwiththesectorinwhichitislocated.ClassiÞeraccuracyisthepercentageoftestvectorsthatarecorrectlyclassiÞed.AmorerevealingassessmentofclassiÞerperformanceisaffordedbyexaminingtheconfusionmatrix.AconfusionmatrixpresentsthefrequenciesforallclassiÞcationsofeachexperimentalcondition,includingthedetailsaboutmisclassiÞcations.ExaminationofmisclassiÞcationsaddsinformationaboutwhichconditionsaremostdistinctandwhicharemoresimilar.ThisinformationisanalyzedusingadditionalmethodsinRSA(seenextsection).ExaminationofclassiÞcationaccuracyforeachconditionseparatelycanalerttheinvestigatortowhetheraverageaccuracyisreallydependentonasmallnumberofconditions,ratherthananaccuratereßectionofperformanceacrossallormostconditions.Thus,averageclassiÞcationaccuracyisausefulmetricbutdiscardsinformationthatcanbediscoveredbyexaminingtheclassiÞcationconfusionmatrix.Confusionmatricesareshownin Percent classi! Figure5Threeexamplesofrepresentationalsimilarityanalysis(RSA).(a)Dendrogramderivedfrommultiplesingle-unitrecordingsinmacaqueinferiortemporal(IT)cortex(fromKianietal.2007)showshierarchicalcategorystructurewithremarkabledetailtothelevelofdifferentclassesofanimalbodytype.( Figure6).CorticalÞeldscanalsobeidentiÞedbyvirtueofhavingsimilaritystructuresthat00.85Mean correlationa MVP classi!cationb Between-subject correlation of DSMs112Number of subjects112Number of subjectsc DSM cluster 1 - LOCd DSM cluster 2 - early visualFigure6MVPAsearchlightanalyses(Kriegeskorteetal.2006)foridentifyingcorticalÞeldsofinterest(fromConnollyetal.2012a).MVPclassiÞcationaccuracies(a)andconsistencyinlocalsimilaritystructuresacrosssubjects(b)identifysimilarlylargeswathsofthevisuallyresponsivecortex.ClusteringofvoxelsbasedonsimilaritiesbetweenlocallydeÞnedsearchlightdissimilaritymatrix(DSMs)providesameanstoidentifycorticalÞeldswithuniquesharedstructuresuchasthelateraloccipitalcomplex(LOC)(c)andtheearlyvisual howRSAmaybeusedtotestawell-controlledmodel.OneofthegreatadvantagesofRSAisthatitstripsaclusterofresponsevectorsoutofafeature-basedrepresentationalspaceintoarepresentationalspacebasedonrelativedistancesamongvec-tors.Thisformatallowscomparisonofrepresentationalgeometriesacrosssubjects,acrossbrainregions,acrossmeasurementmodalities,andevenacrossspecies.Thesecond-orderisomorphismacrossthesespacesisaffordedbythefeature-independentformatofDSMs.Forexample,between-subjectsimilarityofDSMshasbeenexploitedtoaffordbetween-subjectMVPclassiÞcation(Abdietal.2012b,Raizada&Connolly2012).Thefeature-independentsecond-orderisomorphism,however,doeshavesomecost.Strippingrepresentationalspacesoffeaturesmakesitimpossibletocomparepopulationcodesintermsoftheconstituenttuningfunctionsofthosefeatures.Thus,onecannotinvestigatewhetherthespacesindifferentsubjectssharethesamefeaturetuningfunctionsorhowthesetuningfunctioncodesdifferfordifferentbrainregions.Onecannotpredicttheresponsetoanewstimulusinasubjectonthebasisoftheresponsestothatstimulusinothersubjects.Onecannotpredictthetuningfunctionforindividualneuralfeaturesintermsofstimulusfeatures,precludinginvestigatorsfrompredictingtheresponsepatternvectorforanewstimulusonthebasisofitsfeatures.Thenexttwosections sumofthesepatternsofweights(Figure8a).ModelsofVTcortexbasedonsingledimensions,suchascontraststhatdeÞnecategory-selectiveregions,aremodeledwellinthe35-dimensionalmodelspace(Figure8b),butthesesingledimensionsaccountforonlyasmallportionofthevarianceinresponsestoadynamicandvariednaturalstimulussuchasthemovie.Forexample,thecontrastbetweenresponsestofacesandresponsestoobjects,whichdeÞnesthefusiformfacearea(FFA)(Kanwisheretal.1997),accountsforonly12%ofthevariancethatisaccountedforbythe35-dimensionalmodel.Thisresultindicatesthatmodelsbasedonsimple,univariatecontrastsareinsufÞcientasmodelsofneuralrepresentationalspaces.Theuseofacomplex,dynamicstimulusisessentialforderivingtransformationmatrixparam-etersthataffordgeneralvalidityacrossawiderangeofstimuli.Transformationmatricescanalsobecalculatedonthebasisofresponsestomorecontrolledexperiments,suchasthecategoryper-ceptionexperiments.Thesetransformationmatricesarevalidformodelingtheresponsevectorsforstimuliinthatexperimentbut,whenappliedtodatafromotherexperiments,donotaffordBSCofnewstimuli(Haxbyetal.2011).Thisresultindicatesthatdatafromalimitedsamplingofbrainstates,suchasthosesampledinastandardcategoryperceptionexperiment,donotprovideasufÞcientbasisforbuildingacommonmodelofaneuralrepresentationalspace.STIMULUS-MODEL-BASEDENCODINGANDDECODINGForMVPclassiÞcation,RSA,andhyperalignment,aresponsevectortobedecodediscomparedwithresponsevectorsforthatsamestimulusmeasuredinthesamesubjectorinothersubjects.Thesemethodscannotpredicttheresponsepatternforanovelstimulusorexperimentalcondition.Stimulus-model-basedmethodsextendneuraldecodingtonovelstimulibypredictingtheresponsetostimulusfeaturesratherthantowholestimuli.Thestimuliusedtoproducetrainingdataforstimulus-model-baseddecodingareanalyzedintoconstituentfeatures.FeaturesetsusedforthistypeofanalysisincludemodelsofV1neuron 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