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外文资料--Using spectral components for predicting treatment.PDF

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外文资料--Using spectral components for predicting treatment.PDF

UsingspectralcomponentsforpredictingtreatmenteffectsontimeseriesmicroarraygeneexpressionprofilesQianXuBioengineeringProgramHKUSTClearwaterBay,Kowloon,HongKongEmailfleurxqust.hkHongXueDept.ofBiochemistryHKUSTClearwaterBay,Kowloon,HongKongEmailhxueust.hkQiangYangDept.ofComputerScienceandEngineeringHKUSTClearwaterBay,Kowloon,HongKongEmailqyangcse.ust.hkAbstractAnalyzingtimeseriesgeneexpressionprofilesisanincreasinglypopularmethodforunderstandingthebehaviorofawiderangeofbiologicalsystems.Onecouldstudythestatusofadiseasebyanalyzingtheinductionorrepressionactivityandeffectsfromanumberoraspecificgroupofgenes.Insuchascenario,itisoftennaturalforbiologicalresearcherstoposeoutthequestionofwhetheronecouldpredictthetreatmenteffectsbyusingsuchtimeseriesmicroarraygeneexpressionprofiles.However,suchproblemisabigchallengeconsideringtheirspecificnatureusuallysuchtimeseriesgeneexpressionprofilesareshortandthesamplingratesarenotuniform.Ourexperimentswitharealworlddatasetshowthattraditionalmachinelearningmethodssuchassupportvectormachinewillnotperformwellinsuchacase.Inthispaper,wedecomposeatimeseriesgeneexpressionprofileintofrequencycomponentsandapplymachinelearningalgorithmstohelpimprovethepredictionaccuracy.Experimentalresultsshowthatouralgorithmisbothaccurateandeffective.KeywordstimeseriesgeneexpressiontreatmentpredictionspectralcomponentsI.INTRODUCTIONGeneexpressionistheprocessbywhichinheritableinformationfromageneismadeintoafunctionalgeneproduct,suchasproteinorRNA.Whileinthefieldofmolecularbiology,geneexpressionprofilingisthemeasurementoftheactivityofthousandsofgenesatonce.Therefore,aglobalpictureofcellularfunctioncanbecreatedandanalyzedviatheexpressionprofiles.Formicroarraytechnology,itmeasurestherelativeactivityofpreviouslyidentifiedtargetgenes.Timeseriesexpressionprofiling,differentfromstaticexpressionprofiling,providesatemporalprocessoftheexpressionofgenes,whilestaticexpressionprofilingofgenesonlyprovidesasinglesnapshotofthegenesrelated.Fortimeseriesdata,itisintuitivetoseethatthesuccessivepointsarenotindependentidenticallydistributed,hence,whenanalyzingsuchdata,understandingthecorrelationbetweenthesuccessivedatapointsisalsoveryimportant.Oneoftheapplicationsofanalyzingtimeseriesmicroarraygeneexpressiondataistopredicttreatmenteffects.Formanychronicdiseases,treatmenteffectsareoftennonnegligibleandthesideeffectscausedbyimpropertreatmentareveryserious.Forexample,ourdatasetusedforanalyzinginthispaperreflectsthetreatmenteffectsofinterferonandribavirintoHCVHepatitisCVirusinfectedpatients.HCVisoneofthecausesofchronichepatitis,cirrhosis,andhepatocellularcarcinoma.ThecurrentmethodofHCVtreatmentisacombinationofpegylatedinterferonalphaandtheantiviraldrugribavirinfor24or48weeks.Nevertheless,usingthesetwokindsofdrugstogethermayleadtosideeffectsasthepatientsmaygetheadachesorevenmyeloiddisordersandneuropsychiatricsymptoms.Therefore,itisnaturaltoaskthequestionaboutwhetherwecouldpredictthetreatmenteffectsatanearlystage,insteadofafter24or48weekswhenthepatientsmayalreadyhaveshownthesymptomsofsideeffects.However,conventionalmethodsinbiologycannothandlesuchproblemsinasatisfyingway.In1,itissuggestedthatmachinelearningmethodscouldhelppredictthetreatmenteffectsoftimeseriesmicroarraygeneexpressionprofiles.Successfulanalysisandcomprehensionofwhatwashiddenbehindthesegeneexpressionprofilesisanimportantprobleminbioinformaticsandmanyresearchershaveproposedvariousalgorithmsforanalyzinggeneexpression.Earlierworkonanalyzingtimeseriesgeneexpressiondatafrequentlyusedmethodsthatarethesameforstaticexpression2.Later,algorithmsweredevelopedforspecificallytargetingtimeseriesdata3.However,timeseriesdatahavemanyspecificchallenges.Sinceitsveryexpensivetoperformtimeseriesexperiments,manytimeseriesareveryshort.Itisshownin4thatmorethan80ofalltimeseriesdatasetsinStanfordMicroarrayDatabaseSMDcontainlessthan8timepoints.Thenumberofgenesthathavebeenprofiledisratherlarge,usuallyoverthousands.Theconflictbetweensuchalargenumberofgenesandthesmalltimepointsposesanevengreaterchallengeforanalyzingsuchtimeseriesdata.AnotherchallengeisthatourspecificproblemofpredictingthetreatmenteffectsbasedonmicroarraytimeseriesgeneexpressionprofilesisaclassificationproblemNeverthelessatpresent,alargenumberofcurrentresearchinsteadfocusesonclusteringmethodsofthetimeseriesdata5,6.Eventhoughonecouldtrytousesomedensitybasedclustering9781424447138/10/25.00©2010IEEEmethodsandadaptthemtoaclassificationframework,manyoftheseclusteringalgorithmswilloverfitinourcase,whenthetimedatapointsareextremelysmall.Therefore,itisrathernecessaryanddifficulttodesignanalgorithmtoaccuratelypredictthetreatmenteffectsofshorttimeseriesmicroarraygeneexpressionprofiles.Therehavealsobeenmanypreviousresearchonclassifyinggeneexpressions,however,mostofthesemethodsfocusonstaticexpressions.UsingSupportVectorMachines,Fureyetal.7classifiedcancertissuesamples.Bicciatoetal.8usedPrincipalComponentAnalysisformulticlasscanceranalysis.Aspecificchallengefortimeseriesgeneexpressionclassification,aspointedoutby9,isthatthediseasedevelopmentortreatmentresponseisnotuniformandispatientspecific.Theoveralltrajectorymaybesimilarbetweenpatientsbutdifferentpatientswillprogressatdifferentspeeds,evengiventhesametreatment.Therefore,aclassifiershouldbeabletotakethevaryingresponseratesanddevelopmentspeedintoaccount.Hence,traditionalmachinelearningmethods,suchasSupportVectorMachines,willnotperformsowellforthisspecificproblem.Ourexperimentalresultsinthelatersectionwillalsoconfirmthisfinding.Inthispaper,wepresentanalgorithmforpredictingtreatmenteffectsbasedontimeseriesmicroarraygeneexpressiondatabytransformingtheoriginalgeneexpressiondatatoitsspectralcomponentcounterpart.Later,weemploytraditionalSVMforfurtherclassification.WecompareouralgorithmwithdirectlyclassifyontheoriginaldatasetinthetimedomainviaSVMinarealworlddatasetandconfirmthatouralgorithmissimpleandeffectivebyexperiments.Therestofthispaperisorganizedasfollows.InSection2,wewilldescribesomerelatedworksinclusteringgeneexpressiondatabothinstaticexpressionandtimeseriesexpressionclassificationwithtimeseriesgeneexpressiondataotherdataminingmethodsinanalyzingtimeseries.InSection3,wewilldescribeouralgorithmforpredictingtreatmenteffectsviaspectralcomponents.InSection4,wewillconductsomeexperimentsandshowtheeffectivenessofouralgorithm.Finally,wewillmakeconclusionsanddiscusssomepossibledirectionsforfutureresearch.II.RELATEDWORKA.ClusteringGeneExpressionDataManygeneralclusteringapproacheshavealreadybeenappliedtoclustergeneexpressiondata10.In11,Eisenetal.developedaclusteringmethodbasedonthewidelyknownhierarchicalclusteringalgorithm.AKmeansbasedclusteringalgorithmwasdevelopedbyHerwigetal.12toclustercDNAoligofingerprints.Thisalgorithmdoesnotrequireapredefinedspecifiednumberofclusters.TheHCS13algorithmrepresentsthedataasasimilaritygraphandthenrecursivelypatternsthecurrentsetofelementsintotosubsetsbyconsideringwhetherthesubgraphinducedbycurrentsetofelementssatisfiesthestoppingcriterion.However,thesealgorithmsarelargelybasedonthegeneralmethodofclusteringinthefieldofdatamining,withouttakingthespecificnatureoftimeseriesgeneexpressiondataintoconsideration.Takingthesequentialpropertyoftimeseriesgeneexpressiondataintoconsideration,manyclusteringalgorithmsspecificallydesignedfortimeseriesgeneexpressiondatahavebeenproposed.In14,aBayesianmethodformodelbasedclusteringofgeneexpressiondynamicswasproposed,whichrepresentsgeneexpressiondynamicsasautoregressiveequationsandsearchesthemostprobablesetofclustersgiventheavailabledata.Inthisway,thedynamicnatureoftimeseriesgeneexpressiondataistakenintoaccount.Inpractice,experimentsshowthatsuchanalgorithmworksforlongtimeseriesgeneexpressiondatabutnotforshorttimeseriesgeneexpressiondata.ZivBarJoseph5proposedaclusteringalgorithmusingsplinestoclusterthecontinuousrepresentationoftimeseriesgeneexpression,yetitstillcannothandleshorttimeseriesgeneexpressiondataverywell.In4,aclusteringalgorithm,whichusesasetofmodelprofilestoclustertheresultsoftheseexperimentsspecifically,designedforshorttimeseriesgeneexpressiondatawasproposed.Therearemanyotherclusteringalgorithmsdealingwithtimeseriesgeneexpressiondata.Forexample,ageneclusteringalgorithmbasedonmixtureofHMMwasproposedin6.GenesareassociatedwiththeHMMmostlikelytogeneratethetimecoursesofthecorrespondingexpressiondata.In15,amultistepapproachforclusteringtimeseriesgeneexpressiondatawasintroduced,consistingnonlinearPCA,probabilisticprincipalsurfacesbasedonNegentropy.In16,ageneexpressiondataisdecomposedintofrequencycomponentsandthecorrelationbetweenthedatafromapairofgenesismeasuredinthefrequencydomain.Anextensivereviewofclusteringmethodsingeneexpressiondataisbeyondthescopeandpagelimitofourpaper.B.ClassificationwithGeneExpressionDataAnotherimportanttopicrelatedtoourproblemistheclassificationproblemofgeneexpressiondata.Oneofthemostimportantproblemslyinginthiscategoryistumorclassification.Forexample,severalmulticategoryclassificationalgorithmshavebeenproposedinrecentyearsusingsupportvectormachines,showingthatsomemulticlassSVMsperformwellinisolatedgeneexpressioncancerdiagnosticexperiments17.Moreover,itcanbebelievedthatthefinalperformanceoftheclassifierswillimprovewhenwecombinetheclassificationresultsanddifferentkindsofclassifiers,hence,ensemblelearningalgorithmsmaybeusedinsuchascenario.In18,traditionalensemblelearningmethodssuchasbaggingandboostingwereappliedtotumorclassificationproblems.OtherapplicationsincludetheworkbyFureyetal.7toclassifycancertissuesamplesandBicciatoetal.8toanalyzemulticlasscancerusingPrincipalComponentAnalysis.However,aswehavementionedabove,thesegeneexpressionclassificationalgorithmscannotbedirectlyappliedtotimeseriesgeneexpressionclassificationsincetheydonothandlethetemporalrelationshipbetweendifferenttimeslicesofthegeneexpressiondata.C.TimeSeriesDataClassificationFurthermore,timeseriesdataclassificationtaskisalsohighlyrelevanttoourproblemsinceourworkfocusesondealingwithpredictingtreatmenteffectsintimeseriesgeneexpressionprofiledata.However,thegeneraltimeseriesdataclassificationalgorithmisoftenonlyappliedtolongtimeseriesandwillnotperformsowellinshorttimeseries.OneofthemostimportantworkintimeseriesdataclassificationisdynamictimewarpingDTWforaligningtimeseriesdataandmeasurethedissimilaritybetweendifferentsequences.19usedaDTWbaseddecisiontreeforclassifyingtimeseriessequences.In20,firstorderlogicruleswithboostingwasemployedforclassifyingtimeseries.MuchresearchworkinthisareahasbeenconductedbyEamonnKeogh.In21,amodificationofDTWonahigherlevelabstractionofthedata,namely,PiecewiseAggregateApproximationwasproposedandshowntobeoutperformingDTWbyoneortwoofmagnitude.Anewsymbolicrepresentationoftimeseries,SAX,wasproposedin22.Itallowsdimensionalityornumerosityreductionandalsoallowsdistancemeasurestobedefinedonthesymbolicapproachthatlowerboundcorrespondingdistancemeasuresdefinedontheoriginalseries.23proposedasemisupervisedtimeseriesclassificationalgorithmforthefirsttime,whereaccuratetimeseriesclassifiershavebeenbuiltwhenonlyasmallsetoflabeledexamplesareavailable.Therefore,selftrainingmethodsofusingunlabeleddatahasapotentialforsignificantbenefitsintimeseriesclassification.In24,iSAX,arepresentationthatsupportsindexingofmassivedatasetsuptoterabyteswasproposedandshowntobeabletoindexuptoonehundredmilliontimeseries.Itallowsbothfastexactsearchaswellasapproximatesearch.Despitethelargeamountofavailabilityofpapersintheareasofgeneexpressiondataclustering,geneexpressiondataclassificationandtimeseriesdataclassification,ourknowledge,nopaperhasbeenformallyproposedandtryingtosolvetheproblemoftimeseriesgeneexpressiondataclassificationandprediction.Thus,ourworkisthefirstoneaimingtodealwiththisprobleminthisarea.III.PROPOSEDMETHODSInthissection,wewilldescribeourproposedalgorithmforspectraltransformationofthetimeseriesgeneexpressiondataandclassificationinsuchacontinuousdomain.Wedefineatimeseriesgeneexpressiondataasavectorx.Thisvectorxcanberepresentedasx2Ksummationdisplayk1ckznk2Ksummationdisplayk1ckeσknjωkn1Insucharepresentation,thefollowingrelationshipwillholdinthat⎡⎢⎢⎣x0x1...x2K−1x1x2...x2K............xN−2K−1xN−2K...xN−2⎤⎥⎥⎦⎡⎢⎢⎣p2Kp2K−1...p1⎤⎥⎥⎦−⎡⎢⎢⎣x2Kx2K1...xN−1⎤⎥⎥⎦2Herepk1≤k≤2Karecoefficientsofthepolynomialpz2Kproductdisplayk1z−zk2Ksummationdisplayk0pkz2K−kp01.3Equation2istheAutoRegressiveARmodeloftimeseriesx,andinEquation1,thedampingratesσkandfrequenciesωkcanbedeterminedfromtherootsofthepolynomialinEquation3afterwehadcalculatedpkfromEquation2.Therefore,givenzkσkωk,wecancalculatezkandthenckcanbederivedinEquation1.Sincexisrealvalued,zkandckwilloccurincomplexconjugatepairs.Soweletckαkejρk.ThenwecanrewriteEquation1asxnsummationdisplaykxknϕk2Ksummationdisplayk1αkeϕkncosωknϕk0≤n≤N−1Hereαkandϕkaretheamplitudeandphaseofthekthspectralcomponent,thereforewecanrewritetheaboveequationintheformofeachspectralcomponent,whichisxknϕkαkeσkncosωknϕk.Byapplyingthesesteps,wecandirectlytransformthetimeseriesgeneexpressiondataintoitscorrespondingspectralcomponents.Weplantousethisspectralcomponentrepresentationforclassificationtaskbasedonthefollowingreasons.Firstly,wetakedependencebetweensuccessivedatapointsintoaccount.Itseasytoverifythisclaimfromtheabovetransformationsteps,afterthespectrumtransformation,eachspectralcomponentisnowrelatedtomanysuccessivedatapointsandthereforesucharepresentationovercomestheoriginaldrawbackoflooseconnectionbetweensuccessivedatapointsinthetemporaldomain.Secondly,wecanestimatetheparametersofallspectralcomponentsandcansetthephaseofeachcomponenttozero.Therefore,thephaseshiftproblemencounteredbytimeseriesgeneexpressiondatacanbesolved.Sucharepresentationisinsensitivetonoiseasdescribedin25.Sequentially,weclassifytheoriginaltimeseriesgeneexpressiondatabytheconventionalclassifiersupportvectormachineusingourspectralcomponentrepresentation.SinceSVMsareconventionalclassificationalgorithms,weomitthedetailsofdescribingSVMandtheinterestedreaderscanlookintotechnicaldetailsin26.IV.EXPERIMENTALRESULTSInthissection,wewilldescribethedatasetweusedinthispaper,analyzetheperformanceofourproposedmethodandcompareouralgorithmwiththebaselinemethod.Ourobjectiveistoshowthattraditionalandconventionalclassificationmethodscannothandlesuchshorttimeseriesgeneexpressiondataclassificationproblemwellandillustratetheadvantageofouralgorithmoverthebaseline.A.DatasetDescriptionsOurtimeseriesmicroarraygeneexpressiondatawaspublishedbyM.Taylor27,anditispubliclyavailablefordownload1withaccessionnumberGSE7123.Thisdatasetrecordsthegeneexpressiondataof33AfricanAmericansand36CaucasianAmericanpatientsgivenHCVgenotype1infectiononday1,2,4,7,14and28,withpegylatedinterferonandribavirintherapy.TheglobalgeneexpressioninperipheralbloodmononuclearcellsPBMCwasanalyzedvia22283probesinHGU133AGeneChip.Notethatthedatasetdoesnotincludesomepatientswhodidnothaveall6daytretmentgeneexpressionprofiledata,whichmaybecausedbyeitherlossofdataorbecausethepatientdidnotreceivespecifictreatmentduringthatday.Weonlyincludedthepatientswith6fulltreatmentsinourclassificationproblem,therefore,forAfricanAmericans,wehadpreserved28ofthem,whichhad19goodresponsesand9responseswhileforCaucasianAmericans,wehadpreserved30ofthem,with17goodresponsesand13poorresponses.WhetherthetreatmenteffectispositiveornotisdeterminedbythedifferenceoftheHCVRNAlevelatday0andthecorrespondingHCVRNAlevelatday28.Ifthetreatmentislabeledasagoodresponse,thenatleast1.4log10IU/mlofHCVRNAleveldecreaseisrequired.Otherwise,iftheHCVRNAleveldecreaseislessthan1.4log10IU/mlthenitisdenotedasapoorresponse.B.AnalysisofourresultsWeusedourproposedmethodfortransformingthetimeseriesgeneexpressiondataintospectralcomponentsandemployedsupportvectormachineforclassification.TheSVMpackageweareusingisSVMLightimplementedbyJoachims2.AndwehadusedRadialBasisFunctionRBFkernelKxi,xje−γxi−xj2inourexperiments.WeclassifiedourdatasetwithtuningparametersofγinRBFfunctionandcalculatedtheproportionofaccuratelyclassifieddatainbothAAAfricanAmericansandCACaucasianAmericans,showninthetablebelow.γAAAccuraciesTPNumberCAAccuraciesTPNumberγ0.2585.72493.328γ0.589.32593.328γ1.089.32590.027γ2.085.72496.729γ4.096.427100.030γ8.096.427100.030γ16.096.42793.328γ32.092.92696.729γ64.092.92696.729γ128.089.32590.027γ256.085.72493.328TABLEIPERFORMANCEONAAANDCACATEGORIESWITHTUNINGPARAMETERγAsshowninthetableabove,ouraccuraciesarequitehighandthealgorithmisrelativelystablesincethechange1http//www.ncbi.nlm.nih.gov/geo2http//www.cs.cornell.edu/People/tj/ofγwillnotaffectmuchoftheaccuracies.However,isthishighaccuracymainlycausedbysupportvectormachineclassificationframeworkorbytransformingthetimeseriesgeneexpressiondatatospectralcomponentsInthenextsubsection,toanalyzetheeffectivenessofourapproach,wewillcompareouralgorithmwiththeSVMapproach,wheretherepresentationofthetimeseriesmicroarraygeneexpressiondataisrepresentedinitsoriginaltemporaldomain.C.ComparisonwiththebaselineAsmentionedabove,inordertofigureoutwhetherthehighperformanceisachievedbyourproposedapproachusingspectracomponentsorisjustachievedbyclassificationalgorithmSVM,wecomparedouralgorithmwithSVMwherethetimeseriesgeneexpressionprofilesarerepresentedinitsoriginaltemporaldomain.ThefollowingtwotablesshowtheperformanceofSVMusingRBFkernelandPolynomialkernelrespectivelyonAAandCAcategorieswithtuningparameters.γAACategoryCACategoryγ0.2567.857156.6667γ0.567.857156.6667γ1.067.857156.6667γ2.067.857156.6667γ4.067.857156.6667γ8.067.857156.6667γ16.067.857156.6667γ32.067.857156.6667γ64.067.857156.6667γ128.067.857156.6667γ256.067.857156.6667TABLEIIPERFORMANCEOFSVMUSINGRBFKERNELONAAANDCACATEGORIESWITHTUNINGPARAMETERγFromtheresultsshowninthetableIIandtableIII,wedemonstratethattheresultsofapplyingSVMdirectlytopredicttreatmenteffectsbasedontimeseriesgeneexpressiondataarenotpromising.Theperformanceimprovementmainlyreliesonembeddingspectralcomponentsintoouralgorithm.V.CONCLUSIONANDFUTUREWORKInthispaper,wehadproposedanalgorithmusingtimeseriesgeneexpressiondatatopredicttreatmenteffectsinadvance.Ouralgorithmwasbasedonspectralcomponenttransformationtogetherwithsupportvectormachinesoastodealwiththechallengeofclassifyingwithshorttimeseriesgeneexpressiondata.OurexperimentalresultswithrealworlddatasetfocusingonusingpegylatedinterferonandribarivintherapyonHCVinfectedpatientshaveconfirmedtheeffectivenessofouralgorithms.Weplantoextendourworkinthefollowingdirections.Firstly,itisnoteworthythattimeseriesdatahasstrongcorrelationsbetweensuccessivetimepoints.However,transformingtheoriginaldataontospectraldomainmaylosesuchkindofinformation.Itisnaturaltoaskthequestionaboutwhetheritispossibletoemployothergraphicalmodelsinmachinelearning

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