华南理工大学自动化科学与工程学院

2023/1/111Semi-supervisedSupportVectorMachine(SVM)AlgorithmsAndTheirApplicationsinBrainComputerInterfaces(BCIs)

李远清

华南理工大学自动化科学与工程学院脑机接口与脑信息处理研究中心OutlineMyresearchtopicsinrecentyearsSemi-supervisedSupportVectorMachine(SVM)

Aselftrainingsemi-supervisedSVMalgorithmanditsconvergenceFeatureextractionbasedonRayleighcoefficientmaximizationAnextendedsemi-supervisedSVMalgorithmanditseffectivenessApplicationsinBrainComputerInterfaces(BCIs)1.

MyresearchtopicsinrecentyearsMotivation:Toextractinterestingcomponentsfromcomplexdatausingsomeprinciples

Complexdata:highlydimensional,highlynoisy,ill-conditioned,highlydynamical,insufficient,etc.,E.g.EEG,fMRIdata.

Principles:independence,sparseness,ML,MAP,informationmaximization,entropy,etc.1.MyresearchtopicsinrecentyearsIndependentcomponentanalysis(ICA)andblindsourceseparation(BSS)inill-conditionedcases

whereareknownmixtures,areunknownmixingmatrixandunknownsources.Task:recoversourcesonlybasedontheknownmixtures.1.MyresearchtopicsinrecentyearsMainResults:Inill-conditionedcases,anecessaryandsufficientconditiononextractabilityofsourceswasobtained;

thenumberofsourceswhichcanbeextractedwasestimated;severalmodelsandalgorithmswereestablished.[1]YuanqingLi,JunWang,IEEETrans.OnSignalProcessing,vol.50(5),pp.997-1007,2002.[2]YuanqingLi,JunWang,J.M.Zurada,IEEETrans.OnNeuralNetworks,Vol.11(6),pp.1413-1422,2000.[3]YuanqingLi,WangJun,AndrzejCichocki,IEEETrans.onCircuitsandSystems,vol.51(9),pp.1814-1823,2004.[4]YuanqingLi,JunWang,NeuralNetworks，Vol18/10pp1348-1356，2005.[5]YuanqingLi,etal.,SignalProcessing,vol84(12),pp.2245-2263,2004.1.MyresearchtopicsinrecentyearsSparserepresentationanditsapplications

whereareknowndatavector,arebasismatrix(unknown/known)andcoefficientvectorrespectively.Task:findsuchthatsatisfiestheaboveconstraintandisassparseaspossible..1.MyresearchtopicsinrecentyearsMainresults:Twosparsesolutions,0-normsolutionand1-normsolution,wereanalyzedusingprobabilitymethods.Severalprobabilityestimatesontheirequivalencewereobtained---ProbabilityframeworkBlindsourceseparationinill-conditioned:separateallsources.[6]YuanqingLi,Shun-ichiAmari,AndrzejCichocki,CuntaiGuan,IEEETrans.OnInformationTheory,vol.52,no.7,July2006.[7]YuanqingLi,Shun-ichiAmari,AndrzejCichocki,etal.,UnderdeterminedBlindSourceSeparationBasedonSparseRepresentation,IEEETrans.onSignalProcessing,vol.54,no.2,pp.423-437,Feb.2006.[8]YuanqingLi,AndrzejCichockiandShun-ichiAmari，NeuralComputation,vol.16,no.6,pp.1193-1234,2004.[9]YuanqingLi,AndrzejCichocki,etc.NeuralInformationProcessingSystemConference(NIPS),2003,Canada[10]YuanqingLi,AndrzejCichocki,etal.,IEEETrans,onNeuralNetworks,vol.19(12),2008.121.Myresearchtopicsinrecentyears(3)EEG,fMRIdataanalysisEventrelatedSynchronizationandde-synchronizationofEEGcomponentsobtainedbysparserepresentationwereanalyzed;Pre-processingofEEGsignalsbasedonsparserepresentation;VoxelselectioninfMRIdataanalysis.

[11]YuanqingLi,AndrzejCichocki,andShun-ichiAmari,IEEETrans.onNeuralNetworks,Vol.17,No.2,pp.419-431,Mar.2006.[12]YuanqingLiandetal.,VoxelselectioninfMRIdataanalysis:Asparserepresentationmethod,IEEETrans.onBiomedicalEngineering(accepted).

1.Myresearchtopicsinrecentyears(4)Semi-supervisedlearninganditsapplicationsinBCIsE.g.twosemi-supervisedlearningalgorithmswhicharebasedonSVMandEMrespectivelyweredevelopedforjointfeatureextractionandclassificationforsmalltrainingdataset.ThesealgorithmscanbeusedtoreducethetrainingeffortandimprovetheadaptabilityinBCIs

[13]YuanqingLi,CuntaiGuan,NeuralComputation,NeuralComputation，18,pp.2730-2761,2006.[14]YuanqingLi,CuntaiGuan,MachineLearning,vol.71,no.1.[15]YuanqingLi,HuiqiLi,CuntaiGuan,PatternRecognitionLetters,vol.29(9),pp.1285-1294,2008.7.[16]A.Cichocki,…,YuanqingLi,NoninvasiveBCIs:MultiwaySignalProcessingandArrayDecomposition,IEEEComputerMagazine,Vol.41(10),pp.34-42,2008.2.1Semi-supervisedSVM:Introduction(1)AstandardSVMclassifier(forsufficienttrainingdata)Subjecttowhereisatrainingsample(featurevector),isthelabelofthissample.cisaregularizationconstant.Theobjectiveiscalledstructuralrisk.Foranewfeature,ifthenitslabelis1,otherwise,-1.2.1Semi-supervisedSVM:Introduction(2)Whysemi-supervisedlearningwithfeaturere-extractionisimportant?Inmanyrealapplications,labellingdataistimeconsumingandexpensive(e.g.,BCItraining,diseasediagnosis,etc).Whenonlyasmallamountoflabeleddataandalargeamountofunlabeleddataareavailable,semi-supervisedlearning,whichresortstolabeledandunlabeleddatasimultaneously,canoftenprovideusasatisfactoryclassifier.2.1Semi-supervisedSVM:IntroductionInrecentyears,semi-supervisedlearninghasreceivedagreatdealofattentionduetoitspotentialforreducingtheeffortoflabelingdataUntilnow,existingsemi-supervisedlearningmethodshavebeendevelopedonlyforclassification.However,manyfeaturesareextractedalsobasedontrainingdatawithlabels(e.g.,LDA).Howtoextractreliablefeatureswhentrainingdatasetissmall?Thisproblemhasnotbeendiscussed.

2.1Semi-supervisedSVM:Introduction2.Semi-supervisedSVM(3)ThemaincontributionsinthisworkProposeaself-trainingSVMalgorithmandproveitsconvergence;Howtoextractreliable(orconsistent)featuresandperformclassificationinsmalltrainingdatacase?Thisproblemisfirstdiscussed.Anextendedsemi-supervisedlearningalgorithmisproposedforjointfeatureextractionandclassification.Convergenceandeffectivenessofareanalyzed.ApplicationsinEEGbasedBCIs2.2Aself-trainingsemi-supervisedSVMFlowchartofAlgorithm1(forpreparedfeatures)Notations:FI,smallinitialtrainingdataset,Y0,labelset,FT,testdataset,Yk,labelsetpredictedinthekthiteration.[Y.Li,etal.,PatternRecognitionLetters,vol.29(9),2008.7.]FI+Y0FTY1FI+FTY0+Y1SVMFTY2FI+FTY0+Yk-1FTYkSVMSVMiteration1Iteration2iterationk2.2Aself-trainingsemi-supervisedSVM2.2Aself-trainingsemi-supervisedSVM2.2Aself-trainingsemi-supervisedSVM2.2Aself-trainingsemi-supervisedSVMAsimulationexample:Trainingdataset:10samples,Testdataset:190samples.Accuracyratesincrease,objectivefunctiondecreases2.3FeatureextractionbasedonRayleighcoefficientmaximization

ManycommonlyusedfeatureextractionalgorithmscanbededucedbymaximizingRayleighcoefficient,whereSIandSNaresymmetricmbymmatricesdesignedsuchthattheycanmaximizethedesiredinformationandminimizetheundesirednoisealongthedirectionof.Bysolvingtheaboveoptimizationproblem,weobtainamatrixQwhichjointlydiagonalizeSIandSN.AsubmatrixofQisusedasatransformationmatrixforfeatureextraction.2.3FeatureextractionbasedonRayleighcoefficientmaximization(1)CommonSpatialPatternfeatureextraction(commonlyusedinBCIsandEEGdataanalysis)::thesecondordercorrelationmatricesconstructedbythedataoftwoclassesrespectively.(2)LineardiscriminantanalysisNotethatweneedthelabelstoconstructSIandSN.2.4Anextendedsemi-supervisedSVMalgorithmFlowchartofAlgorithm2[Y.Li,etal.,NeuralComputation，18,2006;Y.Li,etal.,MachineLearning,vol.71,2007.]Iteration2DI+Y0FI(1),FT(1)Y1DI+DTY0+Y1F.E.Y2DI+DTY0+Yk-1YkF.E.F.E.iteration1iterationkAlg.1FI(2),FT(2)Alg.1FI(k),FT(k)Alg.1Notations:DI,smalltrainingdataset,Y0,labelset,DT,testdataset,Yklabelsetpredictedinkthiteration.FI(k),FT(k)aretrainingandtestfeaturesetsextractedinthekthiteration.2.4Anextendedsemi-supervisedSVMalgorithm2.4Anextendedsemi-supervisedSVMalgorithm2.4Anextendedsemi-supervisedSVMalgorithm

Convergence:

WehaveprovedthatthesumofRayleighcoefficientsgenerallyincreasesintheiterationsofAlgorithm2andisbounded.Thatis,Algorithm2isconvergent.Thiswillbedemonstratedinourexperimentaldataanalysis.3.ApplicationsinBCIsIntroductiontoBCIsWhat?

AninterfacebetweenbrainandcomputerWhy?

Brain-ComputerInterface(BCI)providesanalternativecommunicationsandcontrolmethodforthosepeoplewithseveremotordisabilitiesNeuralrehabilitation3.ApplicationsinBCIsHowmany?

TherearetwoclassesofBCIs.InvasiveBCIsuseneurons’signalasinput,whichiscollectedbyimplantingmicro-electrodesinthebrain[2],whilenoninvasiveBCIsuseEEG,MEG,FMRIetc.asinputs(collectedfromtheoutsideofbrain)[1]

[1]Birbaumer,N.,Ghanayim,N.,etc.Aspellingdevicefortheparalysed,Nature,398,297-298,1999.[2]LeighR.Hochberg,etc.,Neuronalensemblecontrolofprostheticdevicesbyahumanwithtetraplegia,Nature,Vol.442,2006|

3.ApplicationsinBCIsHow?

脑机接口的意义:(1)

辅助脑科学的研究(验证手段);(2)残疾人神经功能辅助与康复,……。脑机接口信号流图3.ApplicationsinBCIs脑机接口：不经过外围神经和肌肉等正常路径、由大脑向外输出指令的脑－机通信系统。约10年历史，属于当今国际科学研究的前沿领域，在高端杂志（如Nature、Science、PNAS)有不少论文发表，受到很多国家的重视。应用前景:残疾人神经功能辅助与康复，如文字输入、鼠标、遥控器、假肢、康复机器人等；辅助脑科学的研究(验证手段);其它用途（游戏、宇航，危险环境等）……。3.ApplicationsinBCIsChallenges:Highcomplexityofbrainsignals(e.g.nonstationarity,

highmixtures,highdimension);DatacollectionforinvasiveBCIs;HighnoiseespeciallyfornoninvasiveBCIs;Trainingistimeconsumingandboring;Highdimensionalcontrol(difficulttoobtainseveralindependentcontrolsignals);Thenumberofusefulfeaturesissmall.E.g.firingrateisthemostcommonininvasiveBCIs.Nowweareconsideringspikepatterns.FeaturesusedinnoninvasiveBCIincludeCSP,P300,SLP,SVEP,power.(lessthan10).Etc.3.ApplicationsinBCIsDemos:Demo1(Trackhandmovementofamonkeyusingneurons’signal[JohnP.Donoghueetc.])Demo2(EEGbasedBCIspellerusingP300)Demo3(BCIsoccergameusingmotorimaginaries)Demo4

(2Dcursorcontrol)Demo5

(Rehabilitation)3.ApplicationsinBCIsExample1:P300basedspeller.3.ApplicationsinBCIsExample2:DatasetIVa,BCIcompetition2005(wonthesecond).Task:discriminatetwoclassesofmotorimaginaries(righthand,rightfoot)withsmalltrainingdataset.Trialnumbers:Initialtrainingdataset,40,testdataset,120,independentdataset,80.WeapplyAlgorithm2(withfeaturere-extraction)tothisdataset.3.ApplicationsinBCIsFeaturesinIteration1FeaturesinIteration6ConclusionsWeproposedtwosemi-supervisedSVMalgorithmsandprovedtheirconvergence.Algorithm1isaself-trainingalgorithm.Byembeddingfeaturere-extracti