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ContentslistsavailableatScienceDirect

Biomedical

Signal

Processing

and

Control

j ou rn a l h o m e p a g e :w w w . e l s e v i e r . c o m / l o c a t e / b s p c

Study

on

the

usage

feasibility

of

continuous-wave

radar

for

emotion

recognition

Carolina

Gouveia

a,b,∗

,

Ana

Tomé

a,c

,

Filipa

Barros

d,e

,

Sandra

C.

Soares

d,e,f

,

José

Vieira

a,b,c

,

Pedro

Pinho

b,g

aDepartamentodeEletrónica,Telecomunicac¸õeseInformática,UniversidadedeAveiro,Portugal bInstitutodeTelecomunicac¸ões,Aveiro,Portugal

cInstitutodeEngenhariaEletrónicaeTelemáticadeAveiro,UniversidadedeAveiro,Portugal

dCenterforHealthTechnologyandServicesResearch(CINTESIS.UA),DepartmentofEducationandPsychology,UniversityofAveiro,Aveiro,Portugal eWilliamJamesCenterforResearch(WJCR),DepartmentofEducationandPsychology,UniversityofAveiro,Aveiro,Portugal

fDepartmentofClinicalNeuroscience,DivisionofPsychology,KarolinskaInstitute,Stockholm,Sweden gInstitutoSuperiordeEngenhariadeLisboa,Portugal

a

r

t

i

c

l

e

i

n

f

o

Articlehistory: Received16April2019 Receivedinrevisedform 22December2019 Accepted24December2019 Availableonline9January2020 Keywords:

Continuouswaveradar Emotionrecognition Patternrecognition Support-vectormachine K-nearestneighbour RandomForest

a

b

s

t

r

a

c

t

Non-contactvitalsignsmonitoringhasawiderangeofapplications,suchasinsafedriveandinhealth care.Inmentalhealthcare,theuseofnon-invasivesignsholdsagreatpotential,asitwouldlikelyenhance thepatient’sadherencetotheuseofobjectivemeasurestoassesstheiremotionalexperiences,hence allowingformoreindividualizedandefficientdiagnosesandtreatment.Inordertoevaluatethe possi-bilityofemotionrecognitionusinganon-contactsystemforvitalsignsmonitoring,wehereinpresenta continuouswaveradarbasedontherespiratorysignalacquisition.Anexperimentalsetupwasdesigned toacquiretherespiratorysignalwhileparticipantswerewatchingvideosthateliciteddifferentemotions (fear,happinessandaneutralcondition).Signalwasregisteredusingaradar-basedsystemanda stan-dardcertifiedequipment.Theexperimentwasconductedtovalidatethesystemattwolevels:thesignal acquisitionandtheemotionrecognitionlevels.Vitalsignwasanalysedandthethreeemotionswere iden-tifiedusingdifferentclassificationalgorithms.Furthermore,theclassifierperformancewascompared, havinginmindthesignalacquiredbybothsystems.Threedifferentclassificationalgorithmswereused: thesupport-vectormachine,K-nearestneighbourandtheRandomForest.Theachievedaccuracyrates, forthethree-emotionclassification,werewithin60%and70%,whichindicatesthatitisindeedpossible toevaluatetheemotionalstateofanindividualusingvitalsignsdetectedremotely.

©2020TheAuthors.PublishedbyElsevierLtd.ThisisanopenaccessarticleundertheCCBY-NC-ND license(http://creativecommons.org/licenses/by-nc-nd/4.0/).

1. Introduction

Emotionsare adaptive andmultidimensional responses

trig-geredbymeaningfuleventsand/orstimuli,thataffectthewaywe

think,feel,behaveandinteractwithothersinourdailylife[1,2].

Theseresponsesencompasschangesindifferentsystemsincluding

cognition,physiology,motivation,motorexpressionandsubjective

sensations,henceallowingforeffectiveself-regulationprocesses

andprovidingcrucialresourcestoasuccessfuladaptationtothe

environment[3,4].Thechangescanthenbeexpressedbydifferent

means,suchasviaverbalcommunication,facialexpressionsand

∗ Corresponding authorat:DepartamentodeEletrónica,Telecomunicac¸õese Informática,UniversidadedeAveiro,Portugal.

E-mailaddress:[email protected](C.Gouveia).

bodymotion[5],aswellasbymoresubtlecues,includingbiological

signs(increasedheartrateandrespiration)[6].

Although automatic emotion recognition represents a

chal-lengingprocess,it canprovideusefulinformationregarding the

individuals’well-beingand,generallyspeaking,contributeto

sys-tems’enhancement,accordingtotheuser’sneeds.Forexample,it

canbeusefultoadjustmedicalandpsychologicaltreatmentsor

evenaidindetectingtheveracityofinformationinforensic

inves-tigations.Additionally,emotionidentificationcanbeacrucialasset

intheHuman–ComputerInteraction(HCI)field,onceitenablesthe

adjustmentofthedesignanditsfunctionalfeaturestotheusers’

needs[5,7–9].

Emotionrecognitionthrough physiologicalsigns hasalready

beenreported,namelybyusingbreathing rate,bloodflow, skin

conductance,electroencephalogram(EEG),andelectrocardiogram

(ECG)[6],[8].However,mostofthesephysiological-basedsystems

stillrelyonthedirectcontactwithsensorsanditisrecognizedthat

https://doi.org/10.1016/j.bspc.2019.101835

1746-8094/©2020TheAuthors.PublishedbyElsevierLtd.ThisisanopenaccessarticleundertheCCBY-NC-NDlicense(http://creativecommons.org/licenses/by-nc-nd/4. 0/).

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theindividual’sawarenessofthemonitoringprocessmayinfluence

theresults[6].Moreover,theuseinreallifecontexts,whichisof

greatvaluetoallowfortheestablishmentofindividualizedprofiles,

canalsointerferewiththesignal.Therefore,non-contactsystems

canbeadvantageousintheseapplications,astheycanremotely

monitorvitalsigns.

Recently, emotion recognition algorithms using vital signs

acquiredbyradarsystems,wasdonein[7,9],witha

continuous-wave (CW)radar and a frequency-modulated continuousradar

(FMCW)radar,respectively.In[9],theheartbeatsignalwastracked

andused toidentifypositive and negativeemotions(joy,

plea-sure,sadnessandanger),thatresultedfrommemoriestriggered

bymusicorphotos.Thesupport-vectormachine(SVM)

classifica-tionalgorithmwasimplemented,and72.3%ofaccuracyratewas

achieved,consideringthedatasetof12volunteers.Additionally,

[7]presentedanapplicationusingtheK-nearestneighbour(KNN)

asclassifier,usingtherespiratorysignaldetectedbyaheterodyne

CWradar,withanaccuracyrateof67.4%.Inthiscase,theclassifier

wastrainedalsotoidentifyfouremotions,nowincludingan

emo-tionallyneutralcondition(joy,sadness,fearandneutral).Adataset

from5subjectswasused,withwaveformfeatures(suchasmean

orstandarddeviation)andspectralfeaturesobtainedthroughthe

powerspectraldensitycomputationinseveralfrequencyintervals,

from0to0.4Hz.

SimilarstudiesusingCWradarswerecarriedoutin[10,11],but

focusedonthementalstressresponse.In[10],theSVMclassifier

wasusedtoidentifyifasubjectwasundermentalstress,physical

stressorinsteadystate.Theuseddatasetencompassedwaveform

andspectralfeatures,extractedfromthebreathingsignal,similarly

to[7].Thestressstatewasidentifiedwithabinarystrategy,withan

accuracyof77.5%and77.9%,forthesteadystate/mentalstresscase

andthesteadystate/physicalstresscase,respectively.Thebinary

strategywasalsotestedforthesteady/stressstatein[11],butusing

neuralnetworks(NN).Inthiswork,featureswereextractedfrom

therespiratorysignal.However,authorshadtolimittheamountof

data,whichledtoalimitednumberoffeaturesusedontheinput

oftheNN(asinglefeatureandcombinationsoftwofeatureswere

used).

Inthiswork,aradarsystembasedonasoftwaredefinedradio

(SDR)technology wasemployedto acquiretherespiratory

sig-nalsresultingfromtheinductionofthreedifferentemotions:fear,

happinessandanemotionallyneutralstatetoserveasacontrol

condition.Alongwiththerespiratorysignal,wealsoaimedat

cap-turingothertypesofbodymotionthatoccurnaturallyduetothe

individual’sreactiontospecificemotions.Thesebodymovements,

thathavebeenseenasasourceofdistortioninsimilarworks,hold

importantinformationregardinghumanresponsivenesstospecific

emotions.Asinpreviousworks,inwhichtheauthorsinduced

emo-tions[6,8],inthepresentstudyweusedfilmclipstoelicitspecific

emotions.Eachparticipantwasexposedtoasetofvideosinducing

thethreespecificemotions,whichwerepresentedinthree

differ-entsessions,separatedbyatleastoneweek,in ordertoisolate

thespecificemotions.Volunteersdidnothavepriorknowledgeof

video’scontentthatweregoingtowatchinthatday.

Fortheemotionrecognitionusingasetoffeaturesextracted

fromthesesignals,threedifferentclassificationalgorithmswere

used,inordertoevaluatewhich providedresultswiththebest

accuracy:SVM,KNNandtheRandomForest.Furthermore,afeature

selectionwasperformedtoincreasetheaccuracy.Therespiratory

signalsofthevolunteerswereacquiredusingsimultaneously,the

CWradarsystem,fromnowoncalledBio-Radar,andacertified

measurementequipment(BIOPAC),withachest-bandtransducer.

Bycomparingtheperformanceofclassifierswithsignalsacquired

usingbothsystems,weaimedatinvestigatingifsignalsremotely

measuredcanbeusedforemotionidentification.Thiswaspossible

toproveindeed,since theclassification resultsconcerning

Bio-RadarandBIOPACsignalswereinthesameorderofmagnitude.The

bio-radarsystemwascalibratedusingachest-wallsimulator

devel-opedforthispurposeandalreadyvalidatedusingthesamecertified

measurementequipment,in[12].Thebestresult,regardingthe

Bio-Radarsignal,wasachievedfortheRandomForestclassifier,being

65.2%and67.1%,beforeandafterthefeatureselection.

Thiswork is dividedas follows: in Section 2,the Bio-Radar

operationmodeisexplainedandtheexperimentalprocedureis

described.Thesignalprocessingalgorithmperformedbeforethe

classificationstageisexplainedindetail.Thissectionendswiththe

validationoftheBio-Radarsignalacquisition,wheresomeuseful

signalcharacteristicsareidentified.Thereafter,theclassifier

imple-mentationisexplainedinSection3,whichstartswiththefeatures’

extractionprocedureandexplainstheclassifierimplementation.

Thecross-validationmethodsarepresentedinSection4alongwith

theresults.ResultsarelaterdiscussedinSection5,througha

perfor-mancecomparisonbetweendifferentclassifiers.Weintendtofocus

speciallyintheclassifierperformanceconsideringbothmeasuring

systemsandinspectiftheiraccuracydiffersorifitisequivalent.

Finally,conclusionsarepresentedinSection6.

2. Experimentalprocedure

2.1. Continuouswaveradaroperationprincipal

Dopplerradarsforvitalsignsmeasurement,alsodefinedasthe

Bio-Radarsystems,consistinatechnologycapabletoacquirethe

respiratory and thecardiac signals, withoutinterfering directly

withtheindividual.Forthispurpose,ituseselectromagneticwaves,

whicharetransmittedtowardsthechest-wallofthesubjectunder

monitoring,andthereflectedechoisreceived.FromtheDoppler

effect,itispossibletorelatethereceivedsignalpropertieswith

thedistancechangebetweentheradarantennasandthesubject’s

chest-wall,whichmovesaccordingtothecardiopulmonary

func-tion.The CW radar continuouslytransmits a sinusoidalcarrier,

generateddigitally,andreceivestheechofromthereflectingtarget.

DuetotheDopplereffect,thereisaphasechangeasthesubject’s

chest-wallmovestowardsorawayfromtheradarand,hence,a

phasemodulationinthereceivedsignaliscreated[13].The

math-ematicalmodeloftheBio-RadarchannelresponseanditsMATLAB

simulationaredetailedin[14].

TheBio-RadarimplementedinthisworkisdepictedinFig.1

andit wasdeveloped in[13].It consistsin areal-time

measur-ingsystemimplementedwiththeLabVIEWsoftware.Signalswere

acquiredusingtwoantennas,onefortransmissionandtheother

forreception,andafront-endbasedinaSDRsystem.Theseradars

allowthedigitalconfigurationofitsinputandoutput(receiverand

transmitter),regardingtherequiredfrequencyandsamplingrate

ofthecurrentapplication.Intheframeworkofthisapplication,the

SDRusedwasanUSRPB210.Itoperatesinalimitedrangeof

car-riers(70MHzto6GHz)and,therefore,weselected5.8GHzasthe

carrierfrequency.

2.2. Vitalsignsacquisition

Theexperimentwasconductedwithninevolunteers,inthree

differentdays,spacedbyatleasttwodays(hence,awithin-subject’s

experimentaldesign).Theexperimentconsistedinmeasuringthe

respiratorysignalofeachsubjectandothermotioncharacteristics

relatedtohisemotionalstate,whiletheywerewatchingdifferent

setsofshortvideosthateliciteddifferentemotions(fear,

happi-ness andneutral emotion),similarly totheworks presented in

[15,16].Forexample,happinesswasinducedbycomedyvideos,

theneutralstatewasinducedbydocumentaryvideosand,finally,

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Fig.1.Bio-Radarprototype:(a)hardwareset-upcomposedbyaSDRfront-endand twoarrayantennas,(b)signalacquisitionusingtheLabVIEWsoftware.

inthisexperimentwerepreviouslyselectedinpilotstudies,where

foreachvideoitwasverifiedhowintensewasthetriggered

emo-tion.Oneachtestingsessiononeemotionwasinducedbyusing

thesedifferenttypesofvideos.Duringtheexperiment,videoswere

shownaccordingtoanincreasingorderofemotionintensification,

inordertoallowforacontinuousinductionandaneffective

engage-mentofthesubjectthroughoutthesession.Participantsdidnot

havepriorknowledgeaboutthetypeofvideosthattheywereabout

towatch,toavoidforpotentialconfounds.Eachtestingsessiontook

around30minutes.

Sincethemaingoalofthisworkistovalidatetheusageofa

Bio-Radarsysteminemotionrecognition,respiratorysignalwas

acquiredusingBio-Radarandacertifiedmeasuringequipment,the

BIOPACMP160DataAcquisitionSystemwithAcknowledgment5

Software(fromBIOPACSystems,Inc.).TheBIOPACsystemis

con-nectedtoanacquisitionboard, whichhaveseveralmodulesfor

differenttypesofsignalacquisition,suchasECG,breathingand

bloodpressure.ThemoduleRSP100Cisfocusedintheprocessing

ofdataacquiredfromarespirationtransducerchestband,placed

aroundthechestcavityofthesubjectattest.Thistransducer

mea-surestherespiratoryeffortbyanalysingtheinstantaneousthoracic

perimeter[12].

The Bio-Radar signal is a lowpass signal with a bandwidth

equalto0.2–2Hz,whichcomprisestherespiratorybandwidthfor

ahealthyadult(0.2–0.4Hz)[17],thehyperpneacases(0.4–0.8Hz)

andthecardiacsignaturealongwithotherrandommotionsfrom

thebody (0.8–2Hz)[18].The receivedsignalhad tobevisually

inspectedduringthereal-timeacquisition,onceitwasrequired

todo aphaseadjustmentinrealtime,forseveralreasons.First,

thelocaloscillatorintheUSRPboardstabilizesinadifferentphase

valueeverytimethesystemrestarts,whichchangesthemeanvalue

ofthephaseandhencethearcpositioninthecomplexplane.The

distancebetweenthesubjectand theradaralsodeterminesthe

arcposition.Furthermore,thesubjectisnottotallystillduringthe

monitoringperiodandcannotkeepthesameamplitudeof

chest-wallmotion(infact,changesinamplitudeastheresultofdifferent

emotions,isexactlywhatwewanttocapture),henceweexpect

thatthemeanvalueofthephasechangesduringtheexperiment.

Ifthenominalphaseisnearor−inthebeginningofthe

exper-iment,itcanreacheasilythosevalues andwraps willoccur.In

thosecases,thephaseshouldbecorrectedbychangingthephase

ofthetransmittedsignal,digitallyandinrealtime.Theeffectof

thisphasecorrectionprocedureispresentedinFig.2.Thisfigure

hasawrapmarkedas‘W’andthreedifferentsegments(‘S1’,‘S2’

and‘S3’),whichresultfromthephaseadjustmentinthattime,to

avoidnewwrapoccurrences.

Regarding the acquisition details, the Bio-Radar signal is

receivedwithasamplingrateequaltofs1=100kHzandis

down-sampledinreal-timetofs2=1kHz.ThisisperformedinLabVIEW

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Fig.3.BlockdiagramoftheBio-Radarsignalpre-processingbeforetheclassificationstage.

anditwasnecessarytoeasethevisualizationinreal-timeandto

decreasetheamountofdatatobestored,whichcanbeprocessed

inMATLABwithlowcomputationaleffort.TheBIOPACsignalis

acquiredwithasamplingrateequaltofs2.

2.3. Bio-Radarsignalprocessingalgorithm

Consideringthephaseadjustmentthatwasnecessaryto

per-formduringthesignalacquisition,thesignalprocessingalgorithm

implementedintheBio-Radarsignalshouldbeperformedwith

care.Inthissense,thealgorithmexecutesthefollowingsteps(see

blockdiagramfromFig.3).

SignalsareacquiredusingaSDR,whichhasanIn-phaseand

Quadrature(IQ)demodulatoranddeliversonitsoutputthe

com-plexbaseband signal,g(n),witha samplingfrequency equal to

fs2.Thus,thefirststepistodoasecondstageofdownsampling,

oncethesignals thatwe aredealing arelowpass signals.

Com-plexsignalgd(n) hasa newsamplingrateequal to fs3=100Hz.

Also, the BIOPAC signal is downsampled to this new sample

rate.

ThenextstepistoremovetheDCcomponentofthecomplex

signal.Inorder todo this,an algorithm wasdeveloped,having

inmind that thesignals extractionresultsfromthearctangent

computation.Inotherwords,itisnecessarytoguaranteethatthe

arc in the complex planedoes not cross the value.

Further-more,thephase transitions duetothephase correctionshould

alsoberemoved.Fig.4 shows analgorithm toperformthe DC

removal, that avoids the wrap occurrence and removes phase

transitions.

Thealgorithmstartedtoinspectiftherearephasetransitions

duetoouradjustments.Inthosecases,thesignalisdividedin

sub-segments(thecorrespondentsub-segmentpriorthetransitionand

afterthetransition)andthephasesarealigned.Then,withamore

uniformedsignal(regardingthemeanphasevalue),theellipse

fit-tingmethod[19]isappliedtoremovetheDCcomponentofthe

signal.Fig.5depictstheellipsefittingmethodanditsimportance

intheextractedsignal.First,theellipsethatbestfitstothearcis

determinedanditscentreiscomputed.Then,thecentre

coordi-natesaresubtractedfromthesignalinordertore-centreitbackto

theorigin.Fig.5(b)showsthatifthereceivedsignalhashighDC

component,thephasedemodulatedresultisdistortedand

atten-uated.Ontheotherhand,thesignalcanrecoveritsnormalform

aftertheDCremoval.

Inthisstage,itisrequiredtoinspectifthearcislocatedaround

thevalue.Inthiscase, thearc shouldberotatedtoavoidthe

wrapoccurrenceafterthearctangentcomputation.Evenwiththe

arclocatedfarfromthevalue,meanvaluefluctuationsduetothe

subjectrandommotioncanimplythatthearccrossestheorigin

ofthecomplexplane.Inthesecases,asmalloffsetisaddedjustto

avoidwraps,butitshouldbesmallenoughthemaintainthesignal

informationunchanged.

AftertheDCremoval,theresultingcomplexsignalisp(n).The

respiratory signal is recovered from p(n), by performingphase

demodulationwiththearctangentcomputation,resultinginthe

realsignalb(n).

Later,therespiratorysignalb(n)isdividedinsub-segmentswith

oneminutedurationforthefeatureextractionforclassification.

Fig.4. FlowchartofthealgorithmimplementedtoremovetheDCcomponent.

2.4. Bio-Radarsignalvalidation

Intheintroductorysection,wereferredtothenumerous

advan-tages of thevital signs acquisition using non-contact methods,

consideringtheemotionrecognitionframework.Nonetheless,one

needstoverifythatthesameresultsareachievedbyboth

con-ventionalsensorsandcontactlessmeans, andthat thiscanalso

contributefortheclassifiersperformanceenhancement.Forthis

purpose,vitalsignsweremeasuredusingtwomeasurement

set-upssimultaneously:theBio-Radarprototypefortheremotesignals

acquisitionandtheBIOPACsystem,astheconventional

measure-mentequipment.Fig.6showstwosignalsamplesobtainedduring

theFearstatetest,acquiredsimultaneouslywiththesetwo

sys-tems.Inthissample,itispossibletoobservethatthesubjectwas

frightenedtwiceandtheseeventsarerepresentedbytwopeaks

withhigheramplitudes,whencomparedwiththerestofthe

sig-nal(markedwitharedpointinthefigure).Immediatelyaftereach

momentoffright,itispossibletoidentifyanincreaseinthe

heart-beatrateintheBio-Radarsignal,duringtheexhaleperiods.This

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Fig.5.Ellipsefittingmethod:(a)consideringthearcformedinthecomplexplane,theellipsethatbestfitstothearcisestimatedalongwithitscentre,(b)signalafterphase demodulationwithDCcomponent,(c)thearcisre-centredbysubtractingthecentrecoordinatesfromthesignal,(d)signalafterphasedemodulationwithoutDCcomponent.

Fig.6. RespiratorysignalacquiredduringtheFearstate:bytheBio-Radarsystem(top)andbytheBIOPACsystem(bottom).Peakswithreddotswerethemomentswhere subjectgotfrightened.Segment‘A’containsanincreaseoftheheartbeatrateandtheremainsegments(‘B’and‘C’)signthebodymotionofthesubject.(Forinterpretation ofthereferencestocolorinthisfigurecitation,thereaderisreferredtothewebversionofthisarticle.)

capturedintheBIOPACsignal.Fig.7showsazoom-inofthefirst

momentoffright,consideringthesignalpresentedinFig.6.Inthis

figure,theincreaseofheartbeatrateismoreclearintheBio-Radar

signalratherintheBIOPAC.

Theradarsystemcanalsodetecttherandommotionofthe

sub-ject,thatoccursnaturallyduetothesuddenreactionsofvideos

(suchaslaughorfright),orforcomfortingpurposes.Infact,this

ran-dommotionalongwithothersignalsignaturesthatarisefromthe

emotionalinduction,serveastoolsfortheproperemotion

recogni-tion.Forexample,thesubject’sdiscomfortcanbeobservedinthe

Bio-RadarsignalfromFig.6.Ifhe/shemovesslightlyhis/her

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Fig.7.Zoom-inoftherespiratorysignalintheFearstate,duringthefirstfrightexperience:bytheBio-Radarsystem(top)andbytheBIOPACsystem(bottom).

Fig.8.Specificationofthesegmentationprocessforthedifferentfeaturecategories.

markedas‘B’and‘C’.Ontheotherhand,thistypeofeventisnot

evidentintheBIOPACsignal.

3. Classificationprocedure

3.1. Featuresextractions

Featureswereextractedfromoneminuteobservations.Forthis

purpose,thesignalwasdividedinoneminutesegments,performed

bySegmentationblock,asdepictedinFig.8.The“rawsignal”atthe

blockinputistheresultofphasedemodulation.Insidetheblock,

thissignalpassesthroughdifferentdataprocessing,accordingly

withthefeatures’categoriesthataregoingtobeused.

Duringthemonitoringperiod,changestotherespirationpattern

areexpectedaccordingtothenaturalreactionofthebodydueto

emotions,andotherbodymotions.Thus,statisticalandwaveform

characteristicscanbeidentified.In addition,thespectral

evalu-ationisalsocarriedout,not onlyfor therespiratorybandwidth

0.2–0.4Hz,butalsoforhigherfrequenciesthatcanrevealheartbeat

detectionorsuddenmotionsfromthesubject.

Forspectral features,theinputdataisonly dividedin1min

sub-segments,withoutanypriorprocessing.Ontheotherhand,

forstatisticalandwaveformfeatures,afilterwasappliedinthefull

signalbeforethesub-segmentationprocess.Thefilterusedwasa

2ndorderButterworthwithabandpassequalto0.05–1.5Hz.The

usageofthisfilterisimportanttocentretherespiratorysignalin

Table1

Featuresspecification:statisticalandwaveformfeatures.

Statisticalandwaveformfeatures

FT1 Meanvalue

FT2 Variance

FT3 Waveformwidth

FT4 Timebetweenpeaks

FT5 Respiratoryrate

zero,andtoavoidbiasedresultsonthemeanvalueduetodifferent phases,asshowedinFig.2.

Atotalof12featureswereextractedfromthesegmentedsignals

andtheyarepresentedinTables1and2.

Statisticalfeaturesencompasses:

• FT1–themeanvalueofthesegment;

• FT2–thevarianceconsideringtheaverageofallsegment

sam-ples.

Waveformfeaturesincludes:

• FT3–thewaveformwidth,whichisthemeanvalueofallpeak

widthsinthatsegment.Thewidthisdefineddistancebetween

thepointswheresignalinterceptsareferenceline.Inthiscase,

thereferencelineislocatedbeneaththepeakathalfofthepeak

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Table2

Featuresspecification:spectralfeatures

Spectralfeatures

FT6 PowerSpectraldensityinthe

range0—0.1Hz

FT7 PowerSpectraldensityinthe

range0.1–0.2Hz

FT8 PowerSpectraldensityinthe

range0.2–0.3Hz

FT9 PowerSpectraldensityinthe

range0.3–0.4Hz

FT10 PowerSpectraldensityinthe

range0.4–0.9Hz

FT11 PowerSpectraldensityinthe

range0.9–1.5Hz

FT12 Ratioofthepowerspectral

densityvaluesbetween

low-frequencyand

high-frequencyrange

• FT4–thetimebetweenpeaks,wherethenumberofsamples betweentwopeaksiscountedanditsmeanvalueiscomputed • FT5 – the respiratory rateof the full segment,which canbe

obtainedbythroughtheestimationofthemaximumcomponent inpowerspectraldensity.

Finally,spectralfeaturesFT6-FT11aretheamplitudesofspectral componentsinthedifferentfrequencybands.Thisisalsoobtained throughthepowerspectraldensity,usingaslidingHamming win-dowwith50%ofoverlap.ThelastfeatureFT12relatesthespectral componentswithinthelowband(0.1–0.5Hz)andthehighband (0.6–1.5Hz).Itisexpectedthatthelowbandexpressesonlythe res-piratorypresenceandthehighbandexpressesarestlessbehaviour. Sincefeatures have differentnaturesand theirrange of val-uesaredifferentfromeachother,anormalizationisrequired.In thiscase,thez-scorenormalizationwasappliedtoallfeatures,as describedby

˜

xi=xi−mi

i (1)

where ˜xiisthenormalizedfeature,xiisthefeaturetobenormalized,

miisitsmeanvalueandiisitsstandarddeviation.

3.2. Classifiers

Inthiswork,threedifferentclassifierswereimplementedand theirperformancewascompared.Thesameclassification proce-durewasappliedforboththeBIOPACandtheBio-Radarsignals, inordertovalidatetheusageofthedevelopedprototypeforthis scope.

Theclassificationwasperformeddefiningdifferentproblems: binaryandmulticlass,bothusingadatasetwith221observations foreachemotion.Forthebinaryproblem,onlypairsofemotions wereconsidered,thereforethedatasetlengthhad442 observa-tions. On theother hand, themulticlass case considered three elicitedemotionsand afinaldatasetlengthequal to663 obser-vations.

Noticethattheseobservationswerechosenaftervisual inspec-tionofthesignal,whennoisysegmentsarediscarded.Thisresulted inanimbalanceddataset,sinceitwasnotpossibletohavethesame numberofobservationsforeachperson,ateachemotion.Thus,the numberofobservationswaslimitedtotheminimumdurationtime ofallexperiments,inordertobalancethedataset.

Threeclassificationalgorithmswerechosen–SVM,KNNand RandomForest, consideringtheirgood performance withshort datasets[20].Moreover,SVMandKNNwerealsousedinliterature (in[9,7],respectively)andsincethegoalofthisworkisto

rein-forcethepossibilitytouseradarsystemsinemotionrecognition,

Table3

Accuracyrateresultsforthebinaryclassification.

Happyvs.neutral Happyvs.fear Neutralvs.fear

SVM 70.8% 68.8% 72.2% Bio-Radar 79.2% 73.5% 81.7% BIOPAC KNN 72.6% 72.4% 72.4% Bio-Radar 75.8% 71.0% 79.2% BIOPAC Random Forest 77.4% 73.8% 77.8% Bio-Radar 83.9% 73.3% 83.0% BIOPAC Table4

Accuracyrateresultsformulticlassclassification.

SVM KNN RandomForest

Bio-Radar 58.1% 58.2% 65.2%

BIOPAC 65.2% 61.4% 69.1%

thatsamealgorithmsastheonesimplementedinliteratureshould beused.Inaddition,RandomForestispresentedasanalternate option.

Thesealgorithmswereimplementedforbothbinaryand multi-classclassification.TheaccuracyresultsareshowninTables3and4

,respectively,andarediscussedinSection5.Theirimplementation

consideredthefollowingfunctionalprinciples:

• SVMwasappliedwithaRadialBasisFunction(RBF)kernel[20],

inbothbinaryandmulticlassproblems.

–Regardingthemulticlasscase,sinceSVMalgorithmsarebased

inbinaryclassificationonly,adecisionstrategybasedinvoting

wasappliedinordertoreducethemulticlassprobleminaset

ofbinaryproblems.Inthissense,one-versus-one(OVO)

strat-egyselectstheclassthroughthemajorvote,withinC(C1)/2

binaryclassifiers(SVMs)thatcanbetodealwiththeCclasses.

• TheKNNalgorithmusestheEuclideandistanceasmeasureof

proximityandtheclosestneighbour(withk=1)forthedecision

rule[21].Thesameclassifiercharacteristicswereusedforboth

binaryandmulticlassproblems.

• Finally,theRandomForestalgorithmconsistsinanensembleof

decisiontreestrainedinparalleltogiveacontributetothefinal

decision.Thisensembleclassifierwasimplementedwiththe

Bag-gingmode,i.e.,eachtreewastrainedwithabootstrapsampleof

thedataset,withoutnormalization[20,22].Inordertoprevent

thedeepgrowoftrees,aminimumleafsizewasassignedtofive

observations.Theout-of-bagscorewasthenusedtochoosethe

numberoftrees(seeFig.9)and70treeswereselected.

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Table5

Accuracyrateresultsformulticlassclassificationwithalimitednumberoffeatures.

SVM KNN RandomForest

Bio-Radar 63.3% 66.2% 67.1%

BIOPAC 63.3% 76.5% 75.1%

–ThefeatureimpactcanalsobestudiedfromtheRandomForest method.Forthispurpose,therelevanceofthefeatureselection oneachnodewasanalysedandthesixmorerelevantfeatures werechosentocreate anewdataset.Theclassifiers perfor-mance,withthelimitednumberoffeatures, ispresentedin Table5.

4. Results

SVMandKNNweretrainedandtestedusingtheLeave-one-out

cross-validationstrategy.Notethatthedatasetissmall.

Leave-One-OutisanextremecaseofK-foldcross-validation.Consideringthat

thedatasethasNobservations,thisstrategyusesN−1

observa-tionsfortrainingandtheleftoutoneinstancefortesting[20].With

thismethodwehaveNcombinationsoftrainingsetswithdifferent

singleinstancesfortesting.Thefinalresultshowshowmanytimes

thepredictionwasrightonidentifyingthecorrectlabel.Therefore,

thebinomialdistributioncanbeusedtomodeltheaccuracyofthe

classifier.

InthecaseofRandomForest,theout-of-bagobservations

(sam-plesnotincludedinthebootstrapsample)canbeusedtoestimate

theperformanceoftheclassifier[22].

Consideringtheproceduredescribed intheprevioussection,

theachievedresultsforeachclassifierarepresentedinthetables

bellow.First,Table3presentstheresultsregardingthebinary

clas-sificationproblem.

Then,Table4presentstheresultsachievedformulticlass

prob-lem.

Finally, RandomForest classifier allowed theexecution of a

preliminarystudyregarding thefeatureimportance. Thisstudy

revealedwhichfeatureshadmoreinfluenceontheachievedresults

andthisinformationcanbeusedtopresumablyincreasethe

accu-racyresults,bydecreasingthenumberoffeaturesusedindataset.

Table5showstheobtainedresultsafterimplementingthe

classifi-cationalgorithmswithasmallernumberoffeatures.

5. Discussion

Inthissection,theresultsachievedforbothbinaryand

multi-classproblemsarediscussed.

5.1. Binaryproblem

Inthiscase,byanalysingtheobtainedaccuracies,itispossible

toverifythatresultsfrombothBio-RadarandBIOPACsignalswere

similar.Generally,theHappyvs.fearcaseistheonethatpresents

loweraccuracy,withadifferenceoflessthan10%,ifwecompare

withtheotherbinarycases.Thiscanbeexplainedbythesimilar

responsesforthesetwoemotions,leadingtoanapproximated

fea-tureresult,whichhinderstheclassidentification.Thealgorithm

withbetterperformancewastheRandomForestandtheworst

accuracyresultswereobtainedwiththeSVMclassifier,whichalso

presentedthebiggestdeviationbetweenBio-Radarand BIOPAC

signals,withamaximumdriftof10%,approximately.

Asidefromtheseresultsandinordertoproperlyvalidatethe

Bio-Radarsystemusage,theMcNemartest wasperformed[20],

withthemid-p-valuetest.Thistesthelpstounderstandwhichtype

ofsignalcouldbeusedtoidentifymoretruelabelsaccurately,or

iftheclassifieraccuracyissimilarusingbothsignals.Itverifiesif

thenullhypothesisisacceptedorrejected.Inthiscase,thenull

hypothesisstandsthattheclassifierwiththedifferentsignalshave

thesameaccuracyofpredictingcorrectlytheprovidedclasslabels.

TheMcNemartestwasperformedforeveryclassification

algo-rithm(SVM,KNNandRandomForest)andforeverybinarycase.

Toapplythetest,thepredictedvaluesofthetestsetofthe

leave-one-outstrategyloop,arestoredforallclassifiers.Then,thenull

hypothesisistested,e.g.,ifthepredictedlabelsoftwoclassifiers

havetheequalaccuracyforpredictingthetruelabels.Thetestwas

appliedwith5%significanceleveltocomparetheresultsof

classi-fiers,withinputtheBIOPACsignalsandradarsignals,respectively.

Sincebothpositiveandnegativeemotionsservemotivational

purposes(rewardorwithdrawal,respectively),similarautonomic

nervoussystemresponsesfavourenvironmentaladaptation

pur-poses, as to prepare the organism for appropriate behavioural

responses[23].Althoughthisremainsacontroversialtopicinthe

literature,severalstudieshavecorroboratedthisview,byshowing

anincreasedphysiologicalarousal(e.g.,increasedheartrate)not

onlyinnegativeemotionalstates(whichtrigger“fightorflight”

responses)butalsoinpositiveemotionalstates[24].Thecurrent

resultssupportsuchviewforrespiratorysignalscapturedusingthe

Bio-Radar.

5.2. Multiclassproblem

Theresultsformulticlassclassification(presentedinTable4),

wereagainsimilarwithinthedifferentclassifiersandthedifferent

acquisitionsystems.

Withadetailedanalysisitispossibletoobservethattheresults

fortheKNNandRandomForestclassifierwereapproximatelythe

sameforBio-RadarandBIOPACsignals,withonly3.2%and3.9%of

difference,respectively.Thedifferencewasslightlymoreevident

fortheSVM,with7.1%ofdifference.Forthemulticlasscase,the

bestclassificationalgorithmwastheRandomForest,with65.2%of

accuracyfortheBio-Radarsignaland69.1%fortheBIOPACsignal.

Consistentlywiththepreviousresults,theBIOPACsignalresultedin

betteraccuracyresultsthantheBio-Radar.However,theMcNemar

testperformedforeveryclassificationalgorithm,didnotrejected

thenullhypothesisatthe5%significancelevel,whichsustainthat

differencesbetweenaccuracyresultswithBio-RadarandBIOPAC

signalsarenotrelevant.

Analternatewaytoevaluatetheresultsisbycomputingthe

confidenceintervaloftheaccuracyresults.Forthispurpose,the

normalapproximationofbinomialconfidenceintervalwas

com-putedthroughby:

ˆ p±z



ˆ p(1− ˆp) N (2)

where ˆpistheprobabilityofcorrectdecision,Nisthetotalnumber

ofobservationsandzistheequivalent1−˛

2 quantileofthe

stan-darddeviation.Inthiscase,˛=0.05wasconsidered,whichresults

inz=1.96.Infact, ˆp isalsoanestimateofaccuracy,itcanbeobtain

throughtherelation Ns

N,whereNsisthenumberofcorrect

deci-sions[25].Fig.10showstheperformanceofeachclassifierusing

theBio-RadarandBIOPACsignals,andtheirdistributionthrough

thecomputedintervals.

Resultsaredisposedinconsecutivepairsof‘name/signal’,with

therespectiveclassifiernameandsignaltype,where‘bR’stands

forBio-Radarand‘bP’standsforBIOPAC.Byanalysingthisgraph

itispossibletoobservethatresultsunderthesameclassifier

devi-ateslightlybetweenthedifferentsignals,bykeepinganinterval

(9)

Fig.10.Classificationaccuracyfordifferentclassifiersconsideringthedifferent sig-nals,Bio-Radar‘bR’andBIOPAC‘bP’,respectively.

5.3. Resultsafterfeatureselection

As mentioned previously, the Random Forest method also

allowstochecktherelevanceofthefeaturesinthedecision.Table5

showstheobtainedresults,foreachclassifierimplemented,with

themostrelevantfeatures.

IntheBio-RadarcasetheselectedfeatureswereFT6,FT7,FT12,

FT4,FT9andFT2(disposedindecreasingorderofimportance).In

theBIOPACcase,theselectedfeatureswereFT9,FT7,FT2,FT3,FT10

andFT8.Thereweresomecommonfeaturesusedbybothsystems,

suchasthevariance(FT2)andthepowerspectraldensityinthe

rangeof0.1–0.2Hz,(FT7)andintherangeof0.3–0.4Hz(FT9).These

featurescandepictmodificationsonthebreathingsignal

character-istics,i.e.,thechangeofthewaveformovertimeandthedynamic

rangevariationofthebreathingrateofahealthyperson,whichcan

occurduetorandommotionsortosuddenchangeofemotional

state(causedbylaughsorfrights).Itshouldbealsohighlightedthe

featuresthatwereselecteddifferentlyinthedifferentsignalcases.

Forexample,FT4,thatmeasuresthetimebetweenpeaksandFT12,

thatrepresentstheratiobetweenlowfrequencycomponentsand

highfrequencycomponents,wereonlyselectedontheBio-Radar

basedsystem.Thesefeaturescanencompasseithertheheartbeat

(mostlydetectedinapneaperiods),andrandombodymotionsthat

arenoteasilydetectedbytheBIOPAC,asseenpreviously.

Withthelimitednumberoffeatures,theresultsincreasedin

general(besideSVM for theBIOPACcase). Thisdeterminesthe

importanceoftheselectedfeaturesandprovestheirrelationwith

thecurrentemotionalstateofthesubject.

6. Conclusion

ThisworkaimedtovalidatetheusageoftheBio-Radarsystem

fortheemotionrecognitionthroughtheremotedetectionofvital

signs,inthiscasetherespiratorysignal.Threedifferentalgorithms

foremotionsidentificationwereappliedandcompared.Emotional

responseswereextractedfromvitalsignsacquiredsimultaneously

byanon-contactsystembasedonaCWDopplerradaranda

certi-fiedmeasuringequipment(BIOPAChereinusedasaconventional

method).Byanalysingbothsignalsvisually,itispossibletoobserve

thattheBio-Radarsystemwasmoresuccessfulonidentifyingthe

actualemotionalstateoftheindividual,thantheBIOPACsystem,

sinceitcandetectmoresubtlecharacteristics.Theexecuted

classi-fieralgorithmsweretheSVM,KNNandtheRandomForest,which

wereappliedtobothsignals.Regardingbinaryclassification,itwas

possibletoobserveadifficultytodistinguishbetweentheHappy

and the Fear emotional states, when compared withthe other

binarycases.Inbinaryandmulticlassclassificationproblems,the

BIOPACsignalpresentedbetterresults.Importantly,anddespite

themarginaldifferences,bothBio-RadarandBIOPACsignals

pre-sentedsimilarperformances,between65%and80%.Withina5%of

significancelevel,thesameclassifierusingthesedifferentsignals

havethesameaccuracy,accordingtoMcNemartestresult.

Gen-erally,theobtainedaccuracyresultsincreasedwhenthenumber

offeatureswaslimitedtothesixmoreimportantones,afterthe

featureimportanceevaluation.

In sum, thecurrent studycontributes toshowthat the

Bio-Radarcanindeedbeusedintheemotionrecognition,withasimilar

performancetothoseconventionalmethodsusedforvitalsignal

detection.Webelievethatitispossibletoenhancetheachieved

results,byimprovingtheset-upintwolevels.Firstly,regardingthe

monitoringscenario,thepresenceofmetallicsurfacesshouldbe

minimized,oncetheycorruptthereceptionoftheelectromagnetic

signals.Secondly,intermsofsignalprocessing,thedevelopment

ofstrategiestoremovetheDCcomponentinreal-timeandalso

totracktheoptimaldetectionpoint(i.e.,thecentreofthesubject’s

chest-wall),duringtheexperiment,cancontributefortheaccuracy

ofsignals’reception.Moreover,itisknownthatthecardiacsignal

couldalsobeseparatedfromtherespiratorysignal[26,27].Since

theirspectralcomponentsareclosedtoeachotherandthe

ampli-tudeofrespiratorysignalisaround10timesbiggerthanthecardiac

signal,theirseparationisachallengingtask.Thecardiacsignalhas

usefulinformationthatcouldhelpintheemotionalstate

identi-fication,thereforeitshouldbeexploredmethodsforanefficient

signaldecomposition.

Theseresultsrepresentanimportantsteptowardstheuseof

emotion recognitionsystemswithnon-invasive equipmentand

reinforces thenotionthat thesesystems representa promising

toolin severalcontexts,withmental healthcarerepresentinga

prime example,giventhepivotalroleof emotiondysregulation

inpsychiatricdisorders.Thistypeofsystemmayacttoprovide

individualizedprofilesand,therefore,moretailored-based

inter-ventions,hencereducingtheburdenofsuchdisorders.

Authors’contribution

Carolina Gouveia:conceptualization; software;investigation;

formalanalysis;datacuration;writing–originaldraft.

AnaTomé:conceptualization;methodology;validation;writing

-review&editing;supervision.

Filipa Barros:conceptualization; methodology;investigation;

resources;writing–review&editing.

SandraC.Soares:conceptualization;methodology;resources;

validation;writing–review&editing;supervision.

JoséVieira:methodology;validation;writing–review&

edit-ing;supervision.

PedroPinho:validation;writing–review&editing;supervision.

Acknowledgments

Thisworkis fundedbyFCT/MECthroughnationalfundsand

whenapplicableco-fundedbyFEDER–PT2020partnership

agree-ment under the project UID/EEA/50008/2019 and by National

PortugueseFundsthroughFCT–Fundac¸ãoparaaCiênciae

Tec-nologiaunderthePh.D.grantSFRH/BD/139847/2018.

Conflictofinterest:Nonedeclared.

References

[1]N.H.Frijda,Emotionexperienceanditsvarieties,Emot.Rev.1(3)(2009) 264–271.

(10)

[2]K.R.Scherer,Whatareemotions?andhowcantheybemeasured?Soc.Sci. Inform.44(4)(2005)695–729.

[3]L.F.Barret,Emotionsarereal,Emotion(Washington,DC)12(2012)413–429,

http://dx.doi.org/10.1037/a0027555.

[4]A.H.Fischer,A.S.R.Manstead,Socialfunctionsofemotion,Handb.Emot.3 (2008)456–465.

[5]S.Koelstra,etal.,Deap:adatabaseforemotionanalysisusingphysiological signals,IEEETrans.Affect.Comput.3(1)(2012)18–31.

[6]M.Raja,S.Sigg,ApplicabilityofRF-basedmethodsforemotionrecognition:a survey,2016IEEEInternationalConferenceonPervasiveComputingand CommunicationWorkshops(PerComWorkshops)(2016)1–6,http://dx.doi. org/10.1109/PERCOMW.2016.7457119.

[7]Q.Gao,J.Yan,H.Zhao,C.Ding,H.Hong,X.Zhu,Non-contactemotion recognitionviaCWDopplerradar,IEEEAsia-PacificMicrowaveConference (APMC)(2018)1468–1470.

[8]S.Katsigiannis,N.Ramzan,Dreamer:adatabaseforemotionrecognition throughEEGandECGsignalsfromwirelesslow-costoff-the-shelfdevices, IEEEJ.Biomed.HealthInformatics22(1)(2018)98–107.

[9]M.Zhao,F.Adib,D.Katabi,Emotionrecognitionusingwirelesssignals, Proceedingsofthe22ndAnnualInternationalConferenceonMobile ComputingandNetworking3(1)(2016)95–108.

[10]L.Anishchencko,Challengesandpotentialsolutionsofpsychophysiological statemonitoringwithbioradartechnology,Diagnostics8(4)(2018)73.

[11]J.Fernandez,L.Anishchencko,Mentalstressdetectionusingbioradar respiratorysignals,Biomed.SignalProcess.Control43(2018)244–249.

[12]C.Gouveia,D.Malafaia,J.N.Vieira,P.Pinho,Bio-radarperformanceevaluation fordifferentantennadesigns,URSIRadioSci.Bull.2018(364)(2018)30–38.

[13]C.Gouveia,Bio-Radar,UniversidadedeAveiro,Aveiro,Portugal,201712 (Master’sthesis).

[14]C.Gouveia,J.N.Vieira,P.Pinho,Areviewonmethodsforrandommotion detectionandcompensationinbio-radarsystems,Sensors19(3)(2019)604.

[15]J.Groot,etal.,Asniffofhappiness,Psychol.Sci.26(6)(2015)684–700.

[16]J.Ferreira,V.Parma,L.Alho,C.F.Silva,S.Soares,Emotionalbodyodorsas context:effectsoncardiacandsubjectiveresponses,Chem.Senses43(5) (2018)347–355.

[17]G.Yuan,N.A.Drost,R.A.McIvor,Respiratoryrateandbreathingpattern, McMasterUniv.Med.J.10(1)(2013)23–25.

[18]V.L.Clark,J.A.Kruse,Clinicalmethods:Thehistory,physical,andlaboratory examinations,JAMA264(21)(1990).

[19]O.Gal,EllipseFitUsingLeastSquaresCriterion,2018(Accessed)http://it. mathworks.com/matlabcentral/fileexchange/3215-fit-ellipse.

[20]E.Alpaydin,IntroductiontoMachineLearning,TheMITPress,Massachusetts InstituteofTechnology,Cambridge,MA,2004.

[21]P.-N.Tan,M.Steinbach,A.Karpatne,V.Kumar,IntroductiontoDataMining, 2nded.,Pearson,2018.

[22]Mathworks,Treebagger,2019(Accessed)https://www.mathworks.com/help/ stats/treebagger.html.

[23]J.Panksepp,AffectiveNeuroscience:TheFoundationsofHumanandAnimal Emotions,NewYorkOxfordUniversityPress,2004.

[24]N.R.Giuliani,K.McRae,J.J.Gross,Theup-anddown-regulationofamusement: experiential,behavioral,andautonomicconsequences,Emotion8(5)(2008) 714.

[25]T.M.Mitchell,MachineLearning,McGrawHill,1997.

[26]N.Petrochilos,M.Rezk,A.Høst-Madsen,V.Lubecke,O.Boric-Lubecke,Blind separationofhumanheartbeatsandbreathingbytheuseofadopplerradar remotesensing,IEEEInternationalConferenceonAcoustics,Speechand SignalProcessing1(2007)1–333.

[27]H.Zhang,etal.,Theseparationoftheheartbeatandrespiratorysignalofa DopplerradarbasedontheLMSadaptiveharmoniccancellationalgorithm, 6thInternationalSymposiumonComputationalIntelligenceandDesign1 (2013)362–364.

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