ECG信号自动诊断中回归建模法特征提取的研究

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Vol.33,No.5ACTAAUTOMATICASINICAMay,2007

StudyofFeatureExtractionBasedonAutoregressive

ModelinginECGAutomaticDiagnosis

GEDing-Fei1

HOUBei-Ping1

XIANGXin-Jian1

AbstractThisarticleexplorestheabilityofmultivariateautoregressivemodel(MAR)andscalarARmodeltoextractthefeaturesfromtwo-leadelectrocardiogramsignalsinordertoclassifycertaincardiacarrhythmias.TheclassiﬁcationperformanceoffourdiﬀerentECGfeaturesetsbasedonthemodelcoeﬃcientsareshown.Thedataintheanalysisincludingnormalsinusrhythm,atriaprematurecontraction,prematureventricularcontraction,ventriculartachycardia,ventricularﬁbrillationandsuperventriculartachycardiaisobtainedfromtheMIT-BIHdatabase.Theclassiﬁcationisperformedusingaquadraticdiscriminantfunction.TheresultsshowtheMARcoeﬃcientsproducethebestresultsamongthefourECGrepresentationsandtheMARmodelingisausefulclassiﬁcationanddiagnosistool.

KeywordsAutoregressivemodel,ECGfeatures,classiﬁcation,automaticdiagnosis.

1Introduction

Oneofthemostimportanttasksisthereliabledetec-tionandclassiﬁcationofthearrhythmiasforautomaticmonitoringanddiagnosis.Amongthosethreateningar-rhythmias,ventriculartachycardia(VT)andventricularﬁbrillation(VF)aremostdangerousbecausetheyproducethehaemodynamicdeterioration.Otherarrhythmiaslikeprematureventricularcontraction(PVC)etc.arenotsolethal,butarealsoimportantfordiagnosingtheheartdis-eases.Variousstudieshavebeenproposedforclassiﬁcationofvariouscardiacarrhythmias,suchasanalysisofpeaksintheshort-termautocorrelationfunction[1],time-frequencyanalysis[2],nonlineardynamicalmodelingmethod[3,4],to-talleastsquaresbasedPronymodelingalgorithm[5],cor-rectionwaveformanalysis[6],andartiﬁcialneuralnetworksfordecimatedECGanalysis[7].Generally,thesetechniquesclassifyonlytwoorthreearrhythmias,thereforethereisaneedforextendingtheidentiﬁcationtechniqueforalargernumberofarrhythmiasandeasyreal-timeimplementation.Multivariateautoregressive(MAR)modelingprovidesanapproachtoanalysethebio-signals.Forexample,MARmodelingwaswidelyusedtomodelheartrate(HR),bloodpressure(BP)andrespiration(RESP)forassessmentofinteractionbetweenthem[8].MARmodelingwasusedtoextractthefeaturesfromthehumanelectroencephalogramwithwhichmentaltaskscanbediscriminated[9].However,inthestudyofECGarrhythmiarecognitionproblems,re-searcheshavenotdonetoomuchusingMARmodelandmultipleleadECGs.Scalarautoregressive(AR)modelinghasbeenwidelyutilizedtomodelbio-signalsforthepur-poseofanalysis,suchasARmodelingofscalartimesignalsbasedonKalmanﬁlterforcalculatinginstantaneousmea-suresoflineardependence[10],ARmodelingusedtomodelheartratevariability(HRV)andforpowerspectrumesti-mationofECGandHRVsignals[11],ARcoeﬃcientsusedasECGfeaturesforclassiﬁcationofcardiacarrhythmiasus-ingfuzzyARTMAP[12].ItisnotedthatnormalECGQRScomplexesareusuallyprominentinECGleadIIandnor-malbeatsarefrequentlydiﬃculttodiscerninECGleadVIalthoughectopicbeatswilloftenbemoreprominent.Thus,two-leadECGsignalscontainmoreinformationthan

ReceivedJanuary16,2006;inrevisedformMay24,2006

SupportedbyNaturalScienceFoundationofZhejiangProvinceofP.R.China(Y104284)

1.SchoolofInformationandElectronicEngineering,ZhejiangUni-versityofScienceandTechnology,Hangzhou310012,P.R.ChinaDOI:10.1360/aas-007-0462

one-leadECGsignals,andtheclassiﬁcationresultscanbeimprovedbyusingtwo-leadECGsignalssigniﬁcantly.

Thepurposeofthepresentworkistoexplorethefeasi-bilityofMARandARmodelingtoextracttheclassiﬁca-tionfeaturesfromtwo-leadECGsignalsinordertoclassifymoretypesofcardiacarrhythmiaswithhigheraccuracy.Inthisstudy,MARandARmodelingwereperformedontheECGdataincludingnormalsinusrhythm(NSR),atriaprematurecontraction(APC),PVC,VT,VFandsuper-ventriculartachycardia(SVT).TherewerefourECGrep-resentationsbasedonthemodelcoeﬃcients,andtheclassi-ﬁcationwasperformedusingquadraticdiscriminantfunc-tion(QDF)basedclassiﬁer.Threehundredsamplepat-ternseachfromthesixclasseswereselectedforanalysis.Atrainingdatasetconsistedof150samplepatternseachfromthesixclasses,andtheremainingdatawasusedfortesting.TheresultsshowedthattheMARcoeﬃcientscouldclas-sifybetterthanotherthreerepresentations.Thus,MARmodelingisausefulclassiﬁcationanddiagnosistoolforthecardiacarrhythmias.

2.1

Methods

Preprocessing

ThedataintheanalysiswasobtainedfromtheMIT-BIHdatabase.TheNSR,PVCandAPCweresampledat360Hz,theVTandVFweresampledat250Hz,andtheSVTwassampledat128Hz.ThedataincludingNSR,PVC,APCandSVTwassubsampledinorderthatallthetwo-leadECGsignalsintheanalysishadafrequencyof250Hz.AllECGdatahavebeenﬁlteredtoremovethenoiseincludingrespiration,baselinedriftandwanderingetc.Thehigh-passﬁlterisofalinearphasecharacteristicbasedonthefrequencyof250Hz.Thecutoﬀfrequencyofthehigh-passﬁlteris2Hz.Thus,thedriftcausedbyres-pirationatabout0.2Hzissuﬃcientlyremoved.Theothernoisecausedbythemotionfromtheelectrodeisalsomin-imized.

TheRpeaksoftheECGsweredetectedusingTompkin󰀁salgorithm[13].AnormalECGreferstotheusualcaseinthehealthadultswheretheheartrateis60∼100beatsperminute.Inthecurrentstudy,thesamplesizeofthevarioussegmentswas0.9seconds.0.3secondsbeforeRpeakand0.6secondsafterRpeakwerepickedformodeling.Itisad-equatetocapturemostoftheinformationfromaparticularcardiaccycle.

No.5GEDing-Feietal.:StudyofFeatureExtractionBasedonAutoregressiveModeling···

463

2.2

MARandscalarARmodeling

[8A,9]

commonformofaMARmodeloforderPisgivenby.

X(k)=−

PA(i)X(k−i)+e(k)(1)i=1

whereX(k)isa2-dimensionalcolumnvectorofobserva-tionsattimek,e(k)isa2-dimensionalcolumnvectorof

unknown,zero-mean,uncorrelatedrandomvariable,A(i),fori=1,2,...,Pisthe2×2matricesofMARmodelcoef-ﬁcientstobeestimated.

ItisimportanttodeterminethemodelorderwhichbestﬁtsthedatawhenconstructingaMARmodel.Themodelwasestimatedfrom225pointsofdata(0.9seconds)fromtwoECGleadsinthisresearch.Themodelorderselectionwasperformedonthesixtypesoftwo-leadECGsignalsin-cludingintheanalysis.Pre-selectedmodelordersfromonetoeightwereinvestigatedformodelorderselection.Burg󰀁salgorithmwasusedtoestimatetheMARcoeﬃcients.Thecriterionusedtoevaluatethemodelorderselectionwasthesum-squarederror(SSE)inthiswork[10].

ScalarARmodelingwasperformedoneachofthetwoECGleadsforthesixtypesofECGsignals.TheARmodelorderwasestimatedbasedontheSSE,andwascalculatedoverallestimatesinthe225-pointwindowsegmentedfromsinglelead.

2.3ECGfeatures

Inthisstudy,fourdiﬀerentrepresentationsofECGsig-nalswereusedforclassiﬁcation:theMARcoeﬃcients,theK-LMARcoeﬃcients,thescalarARcoeﬃcientsbasedontwo-leadECG,andthescalarARcoeﬃcientsbasedonsingle-leadECG.

2.3.1ECGfeaturesbasedonMARandK-LMAR

coeﬃcients

AMARprocessoforderPhasbeenappliedtothetwo-leadECGsignalsfromthesixclasses.ThenumberofMARcoeﬃcientsrepresentingatwo-leadECGsegmentwas4P.Inordertoreducetheredundancyoffeatures,K-LMARcoeﬃcientswascomputedandusedasfeatures.TheK-Ltransformcanreducethedimensionoffeaturespacebyprojectingtheoriginalfeaturevectorsontoasmallnum-berofeigenvectors.TheK-Ltransforminthisstudywasperformedasfollows[14]:

1)Calculatethewithin-classscattermatrix.2)Calculatetheeigenvaluesandeigenvectorsofthewithin-classscattermatrix.3)Thesetofmeigenvectorswhichcorrespondtothemlargesteigenvalueswaschosentotransfertheorigi-naldata,thecorrespondingeigenvectorsinthisstudywasdeterminedbytheindexiforwhichri/rmax≤0.001,wherei=1,2,...,4P,ri󰀁sareinthedescendingorder.4)Gener-atetheK-Ltransformbyprojectingeach4P-dimentionalpatternontothesechoseneigenvectors.Thusthedimen-sionofthefeaturesbasedonK-LMARcoeﬃcientswasm.

2.3.2ECGfeaturesbasedonscalarARcoeﬃ-cients

AscalarARprocessoforderPhasbeenperformedoneachECGleadfromthesixclasses.ThescalarARco-eﬃcientswereestimatedfromeachleadandconcatenatedtogethertoformthefeaturevectorsfortheclassiﬁcation.ThenumberofthescalarARcoeﬃcientsrepresentingatwo-leadECGsegmentwas2P,thenumberofthescalarARcoeﬃcientsrepresentingasingle-leadECGsegmentwasP.

2.4

QDF-basedclassiﬁcation

TheECGfeaturesdescribedasabovewereutilizedtoclassifythecardiacarrhythmias.Thevariouscardiacar-rhythmiashavebeenclassiﬁedbyastage-by-stageQDF-Basedalgorithmincurrentresearch.TheQDFisgivenby[14]

yi=Xiβ+εi(2)wherex=[x1,x2,...,xd]representsad-dimensionalECG

featurevector,yiisanobservedresponse,εiistheQDFerror,βisa(d(d+3)/2+1)-dimensionalcolumnvector.Xiisa(d(d+3)/2+1)-dimensionalrowvector,thatis

Xi=[1,x1,x2,...,xd,x21,x22,...,x2

d,2x1x2,2x1x3,...,2x1xd,2x2x3,2x2x4,...,2x2xd,...,2xd−1xd]

TheECGfeaturevectorofaparticularECGsegmentwasmappedtoaresponse(1or–1).AssumethetotalnumberoftheECGsegmentsusedforclassiﬁcationataparticularstageisD.Thefollowingequationcanbegiven

˜=Aββ+E(3)

whereY

˜=[y1,y2,...,yD]TisaD-dimensionalcolumnvec-toroftheobservedresponses,andmadeupof“1”and“-1”,whichcorrespondtodiﬀerentclassesrespectively,A=[X1,X2,...,XD]TisaD×(d(d+3)1/2+1)matrix,E=[ε1,ε2,...,εD]TisaD-dimensionalcolumnvectoroftheerrors.

Theleastsquaresestimatoris

β=(ATA)−1ATY

˜(4)

Thequadraticdiscriminantfunctionoftheclassiﬁeris

YI=Xiβ

(5)

Table1showstheclassiﬁcationalgorithmfortheMAR

andK-LMARcoeﬃcients.Thesimilarclassiﬁcational-gorithmcanbeconstructedforthescalarARcoeﬃcients.ThecriterionbasedonstandarddeviationandEuclideancenterdistance(SDECD)wasusedtomeasurethesepara-bilitybetweentwoclasses.AssociatedvalueofSDECDwascomputedtodeterminethegroupingsoftheclassesateachstageinordertoperformthestage-by-stageclassiﬁcation.TheSDECDcanbeexpressedas[14]

d(µ1i−µ2i)2

i=1(6)

3(1Pddσ1ii+

Pdσ2ii)

i=1

di=1

whereσ1iiandσ2ii(i=1,2,3,...,d)representthestan-darddeviationsofvariables,µ1=[µ11,µ12,...,µ1d]Tand

µ2=[µ21,µ22,...,µ2d]Taretheexpectedvectors.

Duringthetrainingphase,theestimatorβwascomputedbyequation(4)usingtheselectedtrainingsetsateachstageoftheclassiﬁcation.Duringthetestingphase,theoutputresponseateachstageoftheclassiﬁcationwascomputedusingthefeaturevectorsandthepreviouslyestimatedβbyequation(5).Athresholdvalueofzerowasusedtoclas-sifytheoutputresponseataparticularstage.Theaveragesensitivityandspeciﬁcitywerecomputedforalltheclassesformeasuringtheperformanceoftheclassiﬁcation[15].

464

Table1

ACTAAUTOMATICASINICA

ClassiﬁcationalgorithmforMARandK-LMARcoeﬃcients

Vol.33

Stage1

Stage2GroupsMemberDecision-GroupsMemberDecision-shipmakingshipmakingNSR1Y1>0NSR-1Y2<0APC1Y1>0APC-1Y2<0PVC1Y1>0PVC-1Y2<0VT/VF1Y1>0VT/VF

Y2>0

SVT

-1

Y1<0

Results

3.1

MARandscalarARmodelingResults

InordertoevaluatetheperformanceoftheMARmodel-ing,theSSEwascomputedoverallestimatesinthelengthofmodeledECGsignals.TheresultsshowedthattheSSEdecreasedinitiallywiththemodelorderP,butremainedalmostconstantformodelordergreaterthanorequaltothree.However,MARmodeloforderfourwasselectedforextractingthefeatures.Thisisbecausemoredetailscanbeincorporatedintothemodelorder,whichmightbemissingfromalower-ordermodel.Ontheotherhand,thenumberoftheMARcoeﬃcientsandcomputationforhigherorderswouldincreaserapidly.SotheMARmodeloforder4isaﬁtterselection.

ScalarARmodelinghasbeenperformedforthepurposeofclassiﬁcation.AﬁtterscalarARmodeloforder4wasfoundtomodeltheECGusingSSEcriterioncalculatedfromsingle-leadECGsandoverallestimatesinthe225-pointwindow.ThisresultwasconsistentwiththeotherresearchesonthescalarARmodelorderselection[16].3.2

Classiﬁcationresults

AMARmodeloforder4andascalarARmodeloforder4wereselectedtomodeltheECGsignalsinthecurrentre-search.TheMARcoeﬃcientscomputedwithorder4,theK-LMARcoeﬃcientsandthescalarARcoeﬃcientsesti-matedwithorder4wereusedforQDF-basedclassiﬁcation.3.2.1ClassiﬁcationresultsbasedonMARand

K-LMARcoeﬃcients

TheECGfeatureswereextractedbyapplyingMARpro-cessoforder4tothetwo-leadECGsignals.Thisresultedinthe16MARcoeﬃcientstorepresentatwo-leadECGsegmentinthisresearch.Table1showstheclassiﬁcationalgorithmforthiscase.ThevaluesofSDECDbetweentheseclasseswerecomputedfordeterminingthegroup-ingsofclassesateachstage.Table2showsthevaluesofSDECDbasedontheMARcoeﬃcients.OnecanseethatAPC/NSR/PVC,VT/VFandSVTformonegrouprespec-tivelyduetosmallvaluesofSDECDwithinthesamegroupandlargevaluesbetweendiﬀerentgroups.Therefore,SVTwasseparatedfromAPC/NSR/PVCandVT/VFinstageone(Y1).ThemembershipofSVTwasdeﬁnedas“-1”,andthemembershipofAPC/NSR/PVCandVT/VFwasde-ﬁnedas“+1”.Theleastsquaresestimatorβwascomputedasequation(4).TheoutputresponseY1wascomputedasequation(5).ThevalueofY1wasusedtodeterminetheclasses.Similarly,VT/VFandAPC/NSR/PVCweredis-tinguishedbetweeneachotherinthesecondstage(Y2).

Stage3Stage4GroupsMemberDecision-GroupsMemberDecision-shipmakingshipmakingAPC/NSR-1Y3<0NSR1Y5>0PVC/NSR

1Y3>0PVC-1Y5<0VT-1Y4<0NSR1Y6>0VF

Y4>0

APC

-1

Y6<0

Stagethree(Y3andY4),four(Y5andY6)wereusedtodif-ferentiatebetweenAPC,NSR,PVC,VTandVFasshowninTable1.

Onehundredandﬁftycaseseachfromthesixclasseswereselectedatrandomtoestimateβintrainingphase,andtheremainingwereusedfortestingintestingphase.TheclassiﬁcationresultsbasedontheMARcoeﬃcientsontestingdataaregiveninTables3and4.Table3showsaclassiﬁcationresultsbasedontheMARcoeﬃcientsforasampletrainingset.Table4showstheperformanceofclassiﬁcationbasedontheMARcoeﬃcientsforthevariousclasses,whichwereaveragedover20runs,eachrunwithdiﬀerenttrainingandtestingdatasets.

Table2

ValuesofSDECDbasedonMARcoeﬃcientsbetween

thediﬀerentclasses

ClassesSVTAPCPVCNSRVTVFSVT01.65871.37751.57181.62872.8733APC1.658700.96691.23251.53972.8077PVC1.37750.966901.17391.43742.2122NSR1.57181.23251.173901.96312.2082VT1.62871.53971.43741.963101.0671VF

2.8733

2.8077

2.2122

2.2082

1.0671

Table3

ClassiﬁcationresultsbasedonMARcoeﬃcientsfora

sampletrainingset

ClassesSVTAPCNSRPVCVTVFSVT14800200APC01473000NSR01149000PVC00014910VT00001500VF

150

Table4

PerformanceoftheclassiﬁcationbasedonMAR

coeﬃcients

ClassesSVTNSRAPCPVCVFVTSensitivity98.6%99.3%98.0%99.3%100%100%Speciﬁcity

100%

98.0%

99.3%

98.6%

100%

99.3%

No.5GEDing-Feietal.:StudyofFeatureExtractionBasedonAutoregressiveModeling···465

Thenumberoftheeigenvectorswaschosentobe10ac-cordingtothechoicecriterionofeigenvectorsdescribedinsection2.Thus,10-dimensionalfeaturevectorsbasedonK-LMARcoeﬃcientswereobtainedafterK-Ltransforma-tion.The10-dimensionalfeaturevectorsweretrainedandtestedthesamewayasintheMARcoeﬃcientsbasedclas-siﬁcationexperiments,theclassiﬁcationresultsbasedontheK-LMARcoeﬃcientsonthetestingdataaregiveninTable5.

Table5

PerformanceoftheclassiﬁcationbasedonK-LMAR

coeﬃcients

ClassesSVTNSRAPCPVCVFVTSensitivity97.3%99.3%96.6%95.3%98.6%96.6%Speciﬁcity

96.6%

93.3%

99.3%

98.0%

99.3%

97.3%

3.2.2

ClassiﬁcationresultsbasedonscalarARco-eﬃcients

AscalarARprocessoforder4wasperformedoneachECGleadfromthesixclasses.Thus,thenumberofthescalarARcoeﬃcientstorepresentatwo-leadECGseg-mentwas8.AsimilaranalysismethodwasemployedforthescalarARcoeﬃcientclassiﬁcation.TheclassiﬁcationresultsbasedonthescalarARcoeﬃcientsandtwo-leadECGsegmentsareshowninTable6.

Table6

PerformanceoftheclassiﬁcationbasedonscalarARcoeﬃcientsandtwo-leadECGsegments

ClassesSVTNSRAPCPVCVFVTSensitivity96%99.3%96.6%98.0%98.6%97.3%Speciﬁcity

99.3%

94.6%

99.3%

96.0%

99.3%

98.0%

TheclassiﬁcationresultsbasedonscalarARcoeﬃcientsandsingle-leadECGaregiveninTable7.Itisforthepurposeofcomparisonbetweenone-leadECGsignalandtwo-leadECGsignalbasedclassiﬁcation.

Table7

Performanceoftheclassiﬁcationbasedonsingle-lead

ECGsignals

ClassesSVTNSRAPCPVCVFVTSensitivity90.0%98.6%94.6%92.6%99.3%92.0%Speciﬁcity

95.3%

86.0%

99.3%

92.0%

97.3%

98.0%

4Discussions

Themainobjectiveofthisstudywastomodeltwo-leadECGsignalsforextractingfeaturesinordertoexplorethefeasibilitytoclassifymoretypesofcardiacarrhythmiasus-ingMARandARmodeling.ThemodelingresultsshowedthattheMARorderof4wassuﬃcienttomodeltheECGsignalsforthepurposeoftheclassiﬁcation,scalarARor-derof4wasalsosuﬃcientforthesamepurpose.ItwasreportedthatthesuﬃcientMARmodelorderwas25formodelingHR,BP,andRESPforthepurposeofassessmentofinteractionbetweenthemin[8].

ExtracalculationwasinvolvedincalculatingK-Ltrans-formofMARcoeﬃcients.Thisrepresentationmaynotbeworthconsideringforareal-timesystem.Theclassiﬁca-

tionofthescalarARcoeﬃcientsextractedfromtwo-leadECGsproducedthesimilarpercentagesoftheaccuracycomparedtoclassiﬁcationoftheK-LMARcoeﬃcients.TheclassiﬁcationofthescalarARcoeﬃcientsextractedfromsignal-leadECGsgavethelowestclassiﬁcationac-curacy.Thus,theMARcoeﬃcientswouldbethemosteﬃcientECGsignalrepresentation.Usingtwo-leadECGsignalscanimprovetheclassiﬁcationaccuracysigniﬁcantlycomparedwithsingle-leadECGsignals.

ThecurrentstudyclassiﬁessixtypesofECGarrhyth-mias,andsomeoftheproposedtechniquesuseonlyasmallernumberofarrhythmiasthanthecurrentstudy.Forexample,twoARcoeﬃcientsandthemean-squarevalueofQRScomplexsegmentwereutilizedasfeaturesforclas-sifyingPVCandNSRusingafuzzyARTMAPclassiﬁer,sensitivityof97%andspeciﬁcityof99%wereachievedin[12],thetotalleastsequare-basedPronymodelingtech-niquewasusedfordetectingSVT,VTandVF,accuracyofSVT,VTandVFwere95.24%,96%and97.78%in[5].TheclassiﬁcationalgorithmsbasedonMARmodelingareeasytoimplement.Inthisstudy,thesamplesizeofthevarioussegmentswas0.9secondsonly,anditwas3to7secondsand5to9secondsforthecomplexitymeasure-basedtechniquein[3]andthePronymodelingtechniquein[5],respectively.

TheMARmodelmightnotbesuitedtoECGsignalsunderallconditionssinceMARmodelisalinearmodelingtechnique,nonlinearparametricmodelingmightimprovetheresults.Futureworkwouldinvolvereal-timedatacol-lectioninordertotestourhypothesisanddeterminetheprecisionofourmethodology.

5Conclusions

MARcoeﬃcientsextractedbyfusingtwoECGleadscouldbeusedasfeaturestoclassifycertaincardiacar-rhythmiaseﬀectivelyincriticalillpatientsforreal-timeautomaticdiagnosispurpose.

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GEDing-FeiReceivedhismasterde-greesfromNanyangTechnologicalUniver-sity,Singaporein2003.Nowheisanas-sociateprofessorinZhejiangUniversityofScienceandTechnology.Hisresearchin-terestcoverspatternrecognitionanddatamining.Correspondingauthorofthispa-per.E-mail:gedingfei@hotmail.com

HOUBei-PingReceivedhisPh.D.de-greefromZhejiangUniversityin2005.Hisresearchinterestcoversmachinevision,im-ageprocessing,andpatternrecognition.

XIANGXin-JianProfessorofZhe-jiangUniversityofScienceandTechnology.Hisresearchinterestcoversintelligentcon-trolandapplicationofpatternrecognition.

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ECG信号自动诊断中回归建模法特征提取的研究