Accuracy comparison of dimensionality reduction techniques to determine significant features from IMU sensor-based data to diagnose vestibular system disorders

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

Accuracy

comparison

of

dimensionality

reduction

techniques

to

determine

significant

features

from

IMU

sensor-based

data

to

diagnose

vestibular

system

disorders

Serhat ˙Ikizo˘glu

_,

_Saddam

_Heydarov

a_{ControlandAutomationEngineeringDept.,IstanbulTechnicalUniversity,Istanbul,Turkey} b_{ElectronicsTechnologies,IstanbulGelisimUniversity,Istanbul,Turkey}

a

r

t

i

c

l

e

i

n

f

o

Articlehistory: Received7July2019

Receivedinrevisedform4March2020 Accepted5April2020

Availableonline29May2020 Keywords:

Diseaseidentification Gaitanalysisfeatureselection Featuretransformation

IMU(InertialMeasurementUnit)sensors Machinelearning

Vestibularsystemdisorders

a

b

s

t

r

a

c

t

ThisstudyisasignificantstepgonetodevelopMachineLearning(ML)algorithmtoapplytogait

sen-soryinformationcollectedfrompeopletoidentifyVestibularSystem(VS)disorders.AlthoughMLis

widelyusedasdiagnostictoolinmedicaldecision-making,thereisnotmuchresearchdoneon

appli-cationofMLmethodstoidentifyVSimperfections.Inthispaper,wecomparedtheaccuraciesoftwo

dimensionality-reductiontechniquestousewithSVMwithGaussianKernel:FeatureSelection(FS)and

FeatureTransformation(FT)methods.T-testandSequentialBackwardSelection(SBS)wereusedforFS

andPrincipalComponentAnalysis(PCA)andKernelPrincipalComponentAnalysis(KPCA)with

polyno-mialandGaussiankernelswereusedasFTmethod.Bothmethodswereappliedtothedatasetformedby

22featurescollectedfrom37people,ofwhom21werehealthyand16subjectshadVS-disorders.The

highestaccuracyamongFTmethodswas89.2%,whileitwas81.1%forFSmethod.SVMwithGaussian

Kernel,trainedwiththedatasetofreduceddimensionality,hadcomputationtimeoffewhundredsof

milliseconds,whichmakesreal-timedataprocessingpossible.Theimportanceofthisworkwillobviously

increasewiththeincreaseinthenumberofinitialfeatures.Asanextstep,weaimtoincreasedataset

anduseadditionalfeaturesextractedfrompressuresensorsplacedunderthefeet.Wealsoaimtouse

timedomaincharacteristicsofthefeaturestoincreaseoverallaccuracyasanextstep.

©2020ElsevierLtd.Allrightsreserved.

1. Introduction

THISworkisthecontinuationofthestudywehavedonebefore

tocomparetheaccuracyofthreeMLmethodsappliedtothe

sen-soryinformationtakenfrompeoplewithVestibularsystem(VS)

disordersandhealthyindividuals[1].

VSincludesthepartsofinnerearandbrainandprocesses

infor-mationtakenfromhumansensors.Itisaveryimportantpartof

humanbalancesystem.Todiagnosedisordersrelatedtohuman

balance systems, clinicians use mobile balance equipment and

analyserecordedbodysway[2].Thecurrentsystemhasits

draw-backsintermsofconsumedtimeandfeasibility.Automateddisease

classificationcan,ontheotherhand,reducetimedramaticallyand

resultinfastandreliablediagnosisofVSdisorders.

MLiswidelybeingusedin thefield ofdiseaseidentification

wherefasterandreliableresultsarerequired.JayminP.etal.[3]

∗ Correspondingauthor.

E-mailaddresses:ikizoglus@itu.edu.tr(S. ˙Ikizo˘glu),sheydarov@gelisim.edu.tr

(S.Heydarov).

usedMLforheartdiseasepredictionsandappliedDecisionTree

methodwith10-foldcrossvalidationusingWEKAtool.Theyalso

madecomparisonbetweendifferentDecisionTreealgorithmsand

reportedtheiraccuracies.In[4],SrivatsaS.andParthibanG.applied

MLtodatasetformedbyinformation takenfromdiabetic

peo-pleinordertopredictheartdisease.TheyfirstusedNaiveBayes

methodfordataminingpurposetofindoutthosewhosufferfrom

heartrelatedproblems.TheyfurtherusedSupportVectorMachines

(SVM)withGaussianKernelwith10-foldcrossvalidationas

classi-ficationmodel.MehmetK.and TolgaE.[5]usedand Multilayer

Perceptron (MLP)for diabetes identification.They appliedSVM

linear, SVM withpolynomial kernel and SVM withradial basis

functionandMLPtothefeaturesextractedfromthedataobtained

fromUCIwebpage.Theycomparedaccuracyofthesealgorithms

andreportedSVMlineartobethemostaccurateoneamongthe

comparedalgorithms.SubhaR.etal.[6]gavebriefreviewabout

MLtechniquesappliedtocardiovasculardiseaseidentificationand

statedtheimportanceoftheclassifierandthefeatureschosenfor

trainingmodelinordertoreachaccurateidentificationofthe

dis-ease. Lalaantikaetal. [7] developed and tested MLmethodfor

predictionofglobalhypokinesia,heartrelateddisease,throughMRI

https://doi.org/10.1016/j.bspc.2020.101963

images.Theyextractedalloftheirfeaturestotraintheirmodel

fromMRIimagesandreportedthattheirmodelperformedwith

highestaccuracyonindependenttestset.Trambaiolli,L.Retal.

[8]usedMLalgorithmforAlzheimer-Disease(AD)identification.

TheymadeuseofSVMalgorithmandextractedfeaturesfromlarge

datasetformedbyEEGsignals.Theyalsocomparedtheaccuracy

ofSVMalgorithmfordifferentfeaturecombinations.KhanA.and

MuhammedU[9]gavea reviewaboutMLapproachesfor

diag-nosisofAD.Intheirreview,theycompareddifferentapproaches

andstatedthe4-stepmodel-aspre-processing,featureselection,

classificationandclassthreshold-tobeusedasreferenceforAD

diagnosis.

Machinelearninghasalsoanapplicationareainthefieldofgait

analysis.MüllerH.etal.[10]appliedMLtogaitanalysisdatataken

fromhospitalsparticipatinginMD-PAEDIGREEtoclassifydatato

threecategories:healthy,peoplewithNeurologicaland

Neuromus-cularDiseases(NND)orpeoplewithJuvenileIdiopathicArthritis.

TheycomparedtheaccuraciesofRandomForest,Boosting,

Mul-tilayerPerceptronandSVMclassifiersandreportedtheaccuracy

ofRandomForest,SVMandMultilayerPerceptrontobe100%and

96.4%forBoostingclassifier.Theyalsostatedthatthetrainingand

testingtimeofallmodelswereofmillisecondsproviding

oppor-tunitiesforreal-timeapplication.In[11],NuttakiC.investigated

theuseofMLfordistinctlyidentifyinggender-specific

character-istics.Theyusedmobilesmartphoneswithbuilt-inaccelerometers

aswearablesensorswornonsubject’sshoulder,elbow,wrist,hip,

kneeandankletocollectgaitdata.Theyextractedstridelengthand

width,steplengthandwidth,andtorqueofeachjointasfeatures

andappliedNaïveBayes,J48treeandSVMasMLclassifierstothe

datasetformedbythesefeatures.ThereportedaccuraciesforNaïve

Bayes,J48andSVMwere99%,58%and99.2%,respectively.Theyalso

pointedoutthatthestudycanbeextendedtoidentifykey

biomark-ersfornormalanddiseasedconditions.WuJ.[12]usedthemanifold

learningalgorithmappliedtogaitdatatoimprovegait

classifica-tionperformance.HeusedIsometricFeatureMappingalgorithmas

nonlinearfeatureextractionmethodtodecreasethesizeofthe

fea-turematrixformedbygaitdatathatwascollectedfromthestrain

gaugeforceplatformembeddedin10mlongwalkwaypath.After

that,heappliedSVMasMLmodeltotesttheaccuracy.He

ana-lysedgaitdataofyoungandelderlypeopleandreportedthatSVM

combinedwithnonlinearfeatureextractionmodelperformed

bet-terwhencomparedtolinearSVM.Hestatedthatmanifoldlearning

algorithmcanbeusedtofindlow-dimensionalgaitdatainsidehigh

dimensionalfeaturematrixthatcanimprovemodelaccuracyand

ithaspotentialforfutureclinicalapplications.Anotherresearch

donebyLeMoyne.R,etal.[13],usesMLtoclassifylegsaffectedby

hemiplegicdisparity.TheyappliedMLmodeltothegaitdatathat

wasextractedthroughforceplatemeasurements.Theground

reac-tionforceparametersfromforceplatemeasurementswereused

toderivefeaturesandLogisticregressionwasappliedtothe

fea-turematrixtoidentifyaffectedandunaffectedleg.Thereported

accuracywas100%.

Featureextractionmethodis alsowidely usedtodetermine

relevant features and toremove redundant ones,sothat

over-allaccuracyisimprovedandwrongclassificationrateisreduced.

RuedaA.andKrishnanS.[14]usedmachinelearningtodiagnose

Parkinson’sdiseaseinearlystage.Theyidentifiedprominentsetof

parametersthatcanbestrepresentthedisease.Byusingsustained

vowelrecordings,theyfoundMel-FrequencyCepstralCoefficients

andusedthemasdiscriminativefeatures.AichS.etal.[15]

com-paredaccuracyofmachinelearningalgorithmappliedtodifferent

setoffeatures.TheycomparedRandomForestclassification

algo-rithmwithoriginalfeaturesetextractedfromvoicerecordingsand

withtransformedsetof featuresby usingPrincipalComponent

Analysis(PCA).Theyfoundthat RandomForest withPCAbased

featurereduction methodshowed betteraccuracy with96.83%

comparedtooriginaldataset.Theyfurthermorestatedthat

Intrin-sicModeFunctionswerediscriminativefeatures.In[16],VipaniR.

etal.employedMLalgorithmtodevelopanautomaticclassifierfor

Parkinsondisease(PD)andHuntington’s(HD)diseases.Theyused

gaitdataextractedfrom63subjectsandappliedHilberttransform

forfeatureextraction.UsingLogisticRegression,theyclassifiedthe

subjects.Theytested theclassifier accuracy using MATLABand

foundtheaccuracyofthemodeltoidentifyPDandHDas85.22%.

Theaccuracyofthealgorithmtodetecthealthysubjectswasfound

tobe87.79%.BabyM.etal.[17]proposedamethodtodistinguish

healthypeoplefromtheonesdiagnosedwithPDbasedon

statisti-calfeaturesextractedfrompre-processedgaitanalysisdatausing

WaveletTransform.Afterthat,ArtificialNeuralNetwork(ANN)was

usedasclassificationalgorithmanditsperformancewascompared

withSVMandNaiveBayesclassifier.

MLtogetherwithfeaturetransformation(FT)andfeature

selec-tion (FS) techniques is also used as classification method for

diabetes,kidneydiseaseandheartdiseases.In[18],Vaishali,R.etal.

madeuseofMLtoincreasetheaccuracyofmodelsusedtopredict

Type-2Diabetes.ByusingGoldberg’sGeneticalgorithmappliedto

pre-processedfeatures,theydecreasedthenumberoffeaturesby

50%andusedMultiObjectiveEvolutionaryFuzzyClassifieronthe

newdataset.Theyfoundtheaccuracyaround83%byseparating

thedatasetas70%trainingand30%testsets.WibawaM.etal.[19]

developedmachinelearningbaseddiseaseidentificationtoolfor

earlydiagnosingofchronickidneydisease(CKD).Theyused

cor-relationbasedfeatureselectionmethodtoidentifydiscriminative

featuresamong24parametersincludingsigns,symptomsandrisk

factorsthatmightberelatedtoCKD.TheyusedUCIMLrepository

containing400instances.TheycomparedthreedifferentML

mod-els,namely,SVM,k-NearestNeighbour(kNN)andNaiveBayesand

foundthatkNNwithfeatureselectionmethodshowedthehighest

accuracywith98.1%.ZhaoT.T.etal.[20]appliedmachine

learn-ingtoclassifyheartdisease,whichisoneofthemostimportant

researchareasinclinicaldecisionsupportsystems.Theyproposed

discriminantminimumclasslocalitypreservingcanonical

correla-tionanalysis(DMPCCA)toextractdiscriminativefeaturesfromthe

datasetformedby1579patients.Theycomparedthreedifferent

featureextractiontechniques,namely,PCA,DMPCCAand

Canon-icalCorrelation Analysis(CCA). They appliedSVM toprocessed

featuresetsandfoundDMPCCAtogivethebestresult.YekkalaI.

etal.[21]alsousedMLforheartdiseaseprediction.Theyanalysed

threedifferentmodels:BaggedTree,RandomForestandAdaBoost

withParticleSwarmOptimization(PSO)asfeaturesubset-selection

methodtopredictwithhighaccuracy. Theyfoundthat Bagged

Tree,whenusedwithPSO,gavethebestexperimentalresult.

Sub-anyaB.andRajalaxmiR.R.[22]studiedmetaheuristicalgorithm

todeterminetheoptimalfeaturesubsetthatimproves

classifica-tionaccuracyandremovesredundantparameterscausingwrong

classifications.TheyusedSwarmIntelligencebasedArtificialBee

Colony(ABC)tofinddiscriminativefeaturesandfoundthatSVM,

usedtogetherwithABC,showedhighaccuracywithjustonlyseven

features.

Althoughthereislotsofworkdoneondiseaseidentification

usingML,almostnostudyhasbeencarriedoutonMLapplication

toVSdisorders.OneoftheveryfewstudiesistheonefromYehS.C.

etal.[23],wheretheauthorsusedSVMasMLtooltoanalyse

quanti-fiedbalanceindicesofthepatientswhohadgonethroughdesigned

interactivevirtualrealityrehabilitationprogram.Thefocusofthe

studywastoseetheeffectofvirtualrealityasrehabilitation

pro-gramonquantifiedbalanceindicesparameter.Machinelearning

wasnotusedasadiseaseidentificationtoolinthatstudy.

Table1showstherelevanceoftheresearchitemsusedinthe

LiteratureReviewparttoourcurrentresearch.

Inthewholeofourproject,wearedevelopingaMLalgorithm

Fig.1.Avisualforascensionmadebyfootduringwalking.

wesearchedforthemethodtogivethehighestaccuracywherewe

examinedthreeMLmethods[1].SVMwithGaussianKernelwas

foundtoperformbestwithanaccuracyof83.3%.Whenapplying

thelearningmodel,oneofthemostimportantstepstoimprove

thedatasetqualityisthedimensionalityreductionprocess.Inthis

paper,wecomparetheaccuraciesoftwodifferent

dimensionality-reductiontechniques,theFeatureSelection(FS)andtheFeature

Transformation(FT)methods andsearchfor theonetopresent

thehighestaccuracyasdimensionalityreductiontool.Inthis

con-text,therestofthepaperisarrangedasfollows:InSection2,we

describethedatasetformationandfeaturesusedtotrainthe

mod-els.InSection3,wegivebriefbackgroundinformationaboutthe

featurereductiontechniques.Thissectionisfollowedby

introduc-tionofexperimentalresultsandtheset-updescription.Finally,we

submitconclusionandstatethefutureworkweplantodo.

2. Backgroundinformatıon

2.1. Datasetformation

Datasetwasformedbyusingsensoryinformationtakenfrom37

people,outofwhich21werehealthyand16peoplewerediagnosed

tohaveVSimperfections.Amongallthesubjects,11peoplefromVS

groupand10peoplefromhealthygroupwerefemale.Themeanage

ofhealthyparticipantsandpeoplewithVSimperfectionswas48.4

and55.6,respectively.PeoplewithVSimperfectionsweresuffering

fromdifferenttypesofbalancedisorderssuchasBenign

Paroxys-malPositionalVertigo(BPPV),MultipleSclerosis(MS),Vestibular

Neuritis(VN) etc.The patientswere primarilydiagnosed using

DynamicPosturography.ComputerizedDynamicPosturographyis

aclinicalmethodtodeterminetheproblembehindthebalance

disorderofthepatientthatdifferentiatesbetweensensory,motor

andcentraladaptivefunctionalimpairments[24].Itmakesuseofa

movableplatformonwhichthepatienttriestocontrolthebalance

usinginformationfromthevestibular,visualandproprioceptive

systems.Sensorswereplaced onsubjects’feet,kneeandwaist,

consistentwithliteratureaboutmotiontrackingandgaitanalysis

[25,26].Weaskedpeopletowalkan11.5mlongstraightpathand

duringthisperiod,sensorydatawerecollectedforfurtherdata

pro-cessingandfeatureextraction.The22featuresweusedtotrainour

modelswerehighlyconsistentwiththeoneswidelyusedin

litera-tureaboutgaitanalysis[27–30].Asdatasetdimensionwasnottoo

bigandtherewerenotenoughsamplesforeachVS-disordergroup,

onlybinaryclassificationwasperformed,wheresubjectswere

clas-sifiedasbelongingeitherto‘healthy’orto‘VS-disorder’group.The

22featuresusedtotrainthelearningmodelsanddefinitionsfor

someofthemaregiveninTables2and3,respectively.Figs.1–3

visualizesomeofthefeaturesused.

2.2. Dimensionalityreduction

Dimensionality reduction is a pre-processing tool for high

dimensionaldataanalysis,especially forthedatasetwithsmall

numberofsamplesandlargenumberoffeatures.Inthecasewhere

Table1

SummaryoftheLiteratureReviewpart.

Literaturereview Therelevancetothecurrentresearch

[1] Herewepresentedourpreviousstudy.Theresultof thisstudy(SVMwithGaussiankernel)wasusedto comparetheeffectivenessoffeatureextraction methods.

[2] GeneraloverviewonhowVSdisordersarenormally diagnosedispresented.

[3–9] Thesepapersshowsomefields(heartdisease,PD,AD, diabetes)whereMLiswidelyusedasdisease identificationtool.Weshowedwhatmethodsthey usedandwhatweretheresults.Ouraimwastogive someoverviewtothereaderaboutMLapplicationin medicaldecisionmaking.

[10–13] HerewepresentedMLapplicationinthegaitanalysis field.Weinvestigatedwhichsensoryinformationare used(IMU,forceplates,mobilephonesaswearable sensorsetc.),howthemodelaccuraciesareincreased. Inourresearch,weanalysedgaitparametersto diagnoseVSimperfection,soweaimedtomakethe readerfamiliarwithcurrentgaitanalysismethods. [14–17] Aimofthispaperistofindfeatureextractionmethod

thatcanincreaseaccuracyanddecreasecomputation timewhichwillbeevenmoreimportantasdataset dimensionincreases.Therefore,inthesereviews,we showedwhyfeatureextractionisused,whatwerethe MLmodelaccuraciesappliedtooriginaldatasetandto thedatasetformedbyfeatureextractionmethods. [18–22] HerewepresentedgeneralpipelineonhowFTandFS

areusedtoincreaseaccuracyofthemodel.The pipelinecanbesummarizedas;

• applydifferentFTandFSmethodstoformnew featureset

• applytheMLmodeltothefeatureset • iftheaccuracyisincreased,usethatmethodto

extractdiscriminativefeatures. Weusedsimilarpipelineinourresearch. [24] Hereweshowedoneofthefewresearchesthatwe

wereabletofindwhereMLwasappliedinVSfield. OuraimwastoshowthatMLisrarelyusedinVSfield, andalso,inthesestudiesMLisnotusedasdisease identificationtool,ratheritisusedfordifferent purposes.

Table2

Featuresusedtotraınmlmodels.

Featureno Featuredefinition

1 Rightfootaveragesteplength 2 Leftfootaveragesteplength

3 Averagespeed

4 Totaltravelleddistance-leftfoot 5 Totaltravelleddistance-rightfoot

6 Stepsymmetry1(totaltravelleddistance-rightfoot/total travelleddistance-leftfoot)

7 Stepsymmetry2(totaltravellingtime-rightfoot/total travellingtime-leftfoot)

8 Leftkneebendingangle 9 Averagebendingangle-leftknee 10 Rightkneebendingangle 11 Averagebendingangle-rightknee 12 Maximumlateralwaistswingtoleft 13 Maximumlateralwaistswingtoright 14 Leftkneemaximumswing

15 Rightkneemaximumswing 16 Averageswing-rightknee 17 Averageswing-leftknee 18 Averageascension-rightfoot 19 Averageascension-leftfoot 20 Waist-maximumposteriorswing 21 Waist-maximumanteriorswing 22 Waistinclinationangleduringwalking

Fig.2.Avisualforsteplength.

Fig.3.Asampleillustrationforwaistinclinationangleduringwalking.

datasetis small,usingmanyfeatures mayleadtothelearning

algorithmtoover-fitthedata;also,itmaycausehighalgorithm

complexity.Therearetwomajorkindsofdimensionality

reduc-tionmethods,FSandFT,wheretheformerchoosessmallestfeature

subsetfromoriginalfeaturesleadingtohighestlearningalgorithm

accuracy;thelattertransformsfeaturestoanewreducedspace

bypreservingmostoftherelevantinformationrelatedto

previ-oussubset[31].Featureselectionmethodselectsthesubsetfrom

theinitialfeaturesettohaveleastnumberoffeaturesbyremoving

redundant,irrelevantornoisydataandthusimprovingthedata

setquality[32].Ontheotherhand,FTperformssome

transforma-tiondependingonthelearningmodelandtransformscorrelated

featurestoanewsubspace[33].

2.2.1. Featureselectionmethod

Generally,highdimensionaldatacanincludefeaturesthatmay

beirrelevant,thusincreasefeature-setdimension,whichresultsin

increasingthesearchspaceandalgorithmcomputationtime.

Fea-tureselectionprocessisamethodusedtoselectsubsetoffeatures

fromoriginalspacethatcontainsleastnumberoffeaturesgiving

highestaccuracy[34].Advantagesoffeatureselectionmethodcan

besummarizedasfollows[32]:

• Reduces featurespace dimension and decreasescomputation

time.

• Increasesdatasetqualitybyremovingirrelevantfeatures.

• Theresultingmodelhashigheraccuracy.

• Makesdatavisualizationeasierduetoreducednumberof

fea-tures.

Featureselectioncanbecategorizedintothreeclassesasfilter,

wrapperandhybridmethod.Filtermethodisthesimplestoneand

doesnotconsidertheclassificationalgorithm.Itjustperforms

sta-tisticalanalysisondatasettochoosefeaturesubsetyieldinghighest

accuracy[35].Wrappermethod,ontheotherhand,performs

selec-tionbyconsideringthelearningalgorithm,whichslowsdownthe

featureselectionprocess[36].Filtermethodshaveless

computa-tiontime comparedtowrappermethodsastheydonotinvolve

anylearningmodel,butit resultsin lessreliability[34]. Hybrid

methodusesadvantagesofboththefilterandwrappermethods.It

usesindependentmethodtochoosefeaturesubsetandevaluates

itsperformanceonmodelaccuracybyapplyingittothelearning

modelused[37].

Widelyusedfilter methodin bioinformatics istoapply

uni-variatecriteriononeachfeaturewhileassumingthereisnotany

interactionbetweenthem.Weusedthet-testandcomparedp

val-ues,thatis,absolutevalueoftstatisticstoseehoweffectiveitisin

distinguishingpeoplewithVSdisorderfromhealthyindividuals.

Thet-test,alsoknownasStudent’stest, isawidelyused

statis-ticalmethodincomparingtwogroups.It isamethodoftesting

hypothesisaboutthemeanofsamplesdrawnfromnormally

dis-tributedpopulationwhenthestandarddeviationofthepopulation

isunknown.Ithastwo types,namely, theindependentandthe

pairedt-test.Inindependentt-test,onesamplefromtwo

inde-pendentnormallydistributedpopulationsarecompared,whilein

pairedt-testthesamplesarenotrandomlyselected;thesecond

sampleisobtainedbydoingcertainchangesonthefirstsample

[38].Forthegivenbinaryclassificationproblem,tvalueofsample

canbecalculatedas[39];

t(xi₎₌ |

_

n22_i1+n1_i22

(1)

where␮i1andi1denotesthemeanandstandarddeviationofthe

i-thfeatureofthefirstclass,while␮i2andi2arethemeanand

standarddeviationofthesecondclass.n1 andn2arenumberof

samplesofthefirstandsecondclass,respectively.

Sequential backward selection (SBS) was used as wrapper

methodtofindthefeaturesubsetthatincreasesmodelaccuracy.

Unlikethefiltermethod,in thewrappertype featureselection,

thelearningmodelisalsotakenintoaccount.SBSalgorithmstarts

trainingbyusingallfeaturesandcontinuesbyremovingfeatures

untilthereisnochangeinthemodelaccuracy.

2.2.2. Featuretransformationmethod

PCAisastatisticalmethodthatreducesdimensionalityofthe

rawmatrix.It usesanorthogonaltransformationtoconvertset

ofobservations ofvariables that mayhavecorrelation between

themtonewuncorrelatedvariables,wherethenewsubspacehas

adimensionlessthanorequaltopreviousfeaturespace.These

newvariables arecalledprinciplecomponentsandtheproblem

formulationisbasedonchoosingthepropernumberofprinciple

componentsforthedimensionalityreduction.

Before running the PCA algorithm, raw feature data set is

normalizedwithzero-meanandunit-variance[40].Thus,each

nor-malizedfeaturevectorx(i)

N willbeoftheform

x(i)_N =x(i)_− (2)

whereisthemeanvalueofthei-thfeaturevectorx(i)_andis

thestandarddeviationof_x(i)_.

Theproblemdefinitiontofindtheoptimalhyper-planecanbe

Fig.4.PCAalgorithmtofindtherightvalueofk.

projectionsofsamplesareminimum.PCAalgorithm,asexplained

above,reducesthedimensionoffeaturematrixfromntokandthe

maindesignparameterforthismethodinvolveschoosingtheright

kvalue.Theproceduretofindtheproperkvaluecanbesummarized

asfollows[40].

a)Calculatecovariancematrix,



b)CalculateSmatrix(diagonalmatrix)usingsingularvalue

decom-posingappliedon



c)Setk=1

d)Using99%varianceretentionasruleofthumb,calculatetheratio

usingexpression(3);





whereSisdiagonalmatrixfoundbySVDandmisnumberof

fea-tures

e) Ifinequalityisviolated,stop

f)Else,increasek&gotostep(d)

Fig.4showstheflowdiagramforthePCAmethodbasedonS

matrix.

InstandardPCAmethod,thedataisassumedtobeinlow

dimen-sionallinearsubspace.Whenthedataislowdimensionalnonlinear

subspacekernelmodifiedPCA(KPCA)isused[41].Themainidea

ofKPCAistoincreasetheoriginaldatasettohigherdimensional

space,wherelinearseparationispossible.Thestepstofollowto

applyKPCAmethodcanbegivenasfollows[42];

• Transformoriginaldatasettonewhighdimensionalspaceusing

chosennonlinearkernelfunction

• ComputethecovarianceofthenewdatasetandapplySVDtofind

matrixU,whichcontainsprincipalcomponents

• ChosefirstkprincipalcomponentsfrommatrixU

• Useprincipalcomponentstofindnewtransformedfeatures

• Usenewfeaturesandapplythelearningmodeltofindthe

accu-racy

PolynomialandGaussiankernelfunctionswereusedto

trans-formtheoriginaldatasettonewhighdimensionalspace.

Fig.5. Illustrationforsensorplacementonthebody.

Table3

Someımportantfeaturesandtheırdefınıtıons.

Parameter Definition

Waistposterior oscillation[deg]

Waistangleasaresultofoscillationdone duringwalking

Lateraloscillation[deg] Oscillationdonetotherightorleftwrt stationarypositionofhumanbody Ascensionmadeby

foot[m]

Distancebetweenfootandgroundduringtoe off

Speed[cm/s] Ratiooflengthofwalkingpathtotimespent onwalking

3. Experımentalsetupandresults

3.1. Datacollection

Sensoryinformationfromhumansubjectswascollectedusing

MATLABandMTW2Wireless3DOFMotionTrackerIMUsensors

fromXsens,whichinclude3Daccelerometer,gyroscopeand

mag-netometer [43]. IMU sensorsprovide acceleration data for gait

analysis.Nevertheless,thesesensorssufferfrombiaserrorswhich

resultinhighpositionerrorsifnotcorrected.Thus,wehave

devel-opedalgorithmstocorrectpositiondataforboththefeetandthe

knees[44].Duringthedataacquisitionprocess,attentionwaspaid

thattheXsenssensorswerewithinthecommunicationrangeof

Bluetoothtoavoidpacketlossdue tothecommunication

inter-ruption.Also,XsensusesproprietaryradioprotocolcalledAwinda,

basedonlow-cost2.4GHzISMchipsets,whichdetectsandhandles

occasionalpacketlossinreal-timeprocessing.Whenthe

commu-nicationis lost, theXsens sensorsstore datain the bufferand

retransmititwhenthecommunicationisback.After

retransmis-sion,thedataisremovedfrombuffer.Thesebufferscanstoreup

to1000datapackets.Takingintoaccountthatthesamplingrateof

oursensorswas100Hz,10sofmisseddatacanberetransmitted

whenwirelesscommunicationisback[45].Thesensorsareplaced

onwaist,kneesandfeetofthesubjectsasshowninFigs.5and6

[25,26].TechnicalspecificationsofthesensorarelistedinTable4.

Byexaminingsomeofthespecificationslikeroll,pitchandstatic

accuracygiveninTable4,itcanbeseenthatthesensorsareaccurate

enoughtouseforgaitanalysis.ThedatawascollectedinCerrahpasa

MedicalSchool-Istanbulandattentionwasgiventothefactthat

IMUsensorswouldnotbeaffectedbyenvironmentalconditions

suchasmagneticfieldscreatedbynearbydevices[44].Therefore,

wecollecteddatamainlyonweekendswithelectronicdevicesin

Fig.6. Humansubjectwithwearablemotionsensors.

Fig.7.Theblockdiagramoftheoverallmethodology.

interference.Thesubjectswereaskedtomoveonaflatpathtobe

surehavingzerochangeinz-axisdata(Fig.6).Furthermore,Ethical

Committeeapprovalwastakentoconducttheexperiments.

Exper-imentalprocedurewasexplainedtosubjectsbeforethetestsand

theywereaskedtosignconsentform.

3.2. Results

TheblockdiagramoftheoverallmethodologyisgiveninFig.7.

Theinitial22features weresupposed tocorrelate moreor less

withinthemselves,sothatthenumberofdiscriminativefeatures

wouldbesignificantlylessthanthisnumber.Figs.8and9show3D

histogramplotsofsomeimportantfeaturesforVSgroup.Observing

thesefiguresprovidesthepre-understandingthat‘leftknee

bend-ingangle’issomewhatcorrelatedwith‘averagevelocity’,whereas

‘leftkneelateraloscillations’and‘stepsymmetry’areindependent

features.

WeusedMATLABClassificationAppLearnertoolboxfordata

processing,model training and testing performancesof feature

selectionandtransformationalgorithms.

Fig.8.3Dhistogramplotforleftkneebendinganglevsaveragevelocity.

Fig.9. 3Dhistogramplotforleftkneelateraloscillationsvsstepsymmetry.

Fig.10. CDFplotforp-values.

T-testfiltermethodandSBSaswrappermethodwereusedfor

featureselection,whilestandardPCAandKPCAwereappliedas

featuretransformationmethodtogetherwithSVMwithGaussian

Kerneltothetrainingdataset.Bothmethodswereappliedtothe

featuresetconsistingof37people.Inordertogetbetter

Fig.11.Recognizingthenumberofmostsignificantfeaturesthatleadtomaximum trainingaccuracy.

Table4

Technicalspecificationsofthesensorsused.

Parameter Value Unit

Roll,pitch,accuracy <0.5 degree

Staticaccuracy <1 degree

Dynamicaccuracy 2 degreeRMS

Angularresolution 0.05 degree

Internalsamplingrate 1800 Hz

Maximumacceleration 16 g

Maximumupdaterate 75 Hz

Table5

Somekeymodelparametersbeforeandaftert-test.

Parameters Beforet-test Aftert-test

Trainingtime 6.18seconds 0.75seconds

Predictionspeed 610observations/second 1200observation/second

eachfeature,CumulativeDistributionFunction(CDF)ofp-values

areplottedinFig.10.Consideringp<0.05,werecognizethatabout

65%ofthefeaturesfulfilthisnullhypothesis,inotherwords,around

14features(65%*22≈14)canbediscriminativeaccordingtot-test.

Tofindoutthediscriminativefeatures,weusedmisclassification

error(MCE)parameter,whichisdefinedastheratioofmisclassified

observationstototalobservations[46].

MATLABwasusedtoevaluateMCE.Wefoundthatfourfeatures

ledtominimumMCE.Theresultwasintuitive,asbyexamining

thegraphinFig.10,onecanrecognizethattherearefourmost

significantfeatures(Fig.11).

InFig.11,theredarrowsindicatethefeaturesthat increase

themodelaccuracyaround15–20%each.Thoughthereareeven

someotherfeaturesontheCDFplot(pointedwithblackarrows)

thatincreasetheaccuracyaround5–10%each,wecancomment

thatthosefeaturesareeffectivetorisetheaccuracy-for

example-from75%to80%,whiletheycannotincreaseitfrom60%to65%

etc.

UsingMATLAB,themostsignificantfourfeaturesfoundwere

averagevelocity,leftkneelateralswing,averageascentbyright

footandaveragesteplength’.Thesefourfeatureswereusedtoform

atrainingsetforMLandtodeterminetheaccuracyofSVMwith

GaussianKernel.Accuracywasfoundtobe72.2%.Togetherwith

theaccuracy,trainingtimeandpredictionspeedareother

impor-tantparameterstopointtooverallperformance ofthemethod.

Fig.12.ROCcurveforthelearningmodelwithSBSmethod.

Table6

SomekeymodelparametersbeforeandafterSBS.

Parameters BeforeSBS AfterSBS

Trainingtime 6.18seconds 0.85seconds

Predictionspeed 610observations/second 800observation/second

Table7

SomekeymodelparametersbeforeandafterPCA.

Parameters BeforePCA AfterPCA

Trainingtime 6.18seconds 0.9seconds

Predictionspeed 610observations/second 240observation/second

Table8

SomekeymodelparametersbeforeandafterKPCAwithpolynomialkernel. Parameters BeforeKPCAWith

PolynomialKernel

AfterKPCAWith PolynomialKernel

Trainingtime 6.18seconds 1.05seconds

Predictionspeed 610observations/second 220observation/second

Table5showsnumericalvaluesfortrainingtimeandprediction

speedparametersbeforeandaftert-testapplication.

TotesttheSBSmethod,MATLABbuilt-in“sequentialfs”

func-tionhasbeenusedandsearchandperformancecriteriawereset

as“backward”andclassifierperformance,respectively.By

apply-ingSBSmethod,16features,werefoundtobediscriminative.The

mostdiscriminative16features wereusedtotrainthelearning

model.Theaccuracywasfoundtobe81.1%.ReceiverOperating

Characteristicswasusedtovisualizetheperformanceofthe

learn-ingmodeltrained withfeaturesfoundbySBSmethod(Fig.12).

Table6showsperformancemetricofthemodelbeforeandafter

SBSmethodapplication.

On theotherside, weappliedthePCAprocedurewhere we

firstnormalizedthefeaturematrixusingzeromean-unitvariance

method.Next,SVDwasperformedusingMATLABand22×22U

andSmatriceswerefound.ThediagonalSmatrixwasusedtofind

theproperkvaluewithpredefined99%variancespecification.The

kvaluewasdeterminedtobe13;thatis,theoriginalfeaturespace

consistingof22featureswastransformedtoanewspacewith13

features.Usingthese13features,whichareinfactalinear

combi-nationoftheoriginal22features,wetrainedSVMwithGaussian

Fig.13.ROCcurveforthelearningmodelforKPCAwithpolynomialkernel.

Fig.14. ROCcurveforthelearningmodelforKPCAwithGaussiankernel.

Table9

SomekeymodelparametersbeforeandafterKPCAwithGaussıankernel.

Parameters BeforeKPCAWith GaussianKernel

AfterKPCAWith GaussianKernel

Trainingtime 6.18seconds 1.2seconds

Predictionspeed 610observations/second 170observations/second

trainingtimeandpredictionspeedparametersbeforeandafterPCA

application.

Next,weappliedKPCAalgorithmwherepolynomialand

Gaus-siankernel function were usedfor nonlinear transformation of

dataset to newhigh dimensional space.By applyingstandard

PCA in new space and setting k = 13, we found transformed

featuresforbothkernelfunctions.Afterthefeature

transforma-tionprocess,SVMwithGaussiankernelwasusedasthelearning

modeltotesttheaccuracy.TheaccuracyforKPCAwith

polyno-mialkernelfunctionandGaussiankernelfunctionwasfoundto

be81%and89.2%,respectively.Figs.13and14showsROCcurves

forKPCAwithpolynomialandgaussiankernelfunctions,

respec-tively.

Tables8and9showperformancevaluesintermsoftraining

timeandpredictionspeedforKPCAwithpolynomialandGaussian

kernels,respectively.

Asanextstep,weincreasedthenumberoffeaturesfoundas

aresultoffeatureselectionmethodtoequateto13,numberof

features used in PCAmethod, toseewhether themodel

accu-racywouldcapturethefeaturetransformationmethodfromthe

perspectiveof classificationresult.Thus, we added9more

fea-turestoequateto13 andfoundthelearningmodelaccuracyto

be77.8%. Theresult wasasexpected, asthefeatures foundby

FSmethods are subsets oforiginal features, while the features

foundFTmethods arelinear/nonlinearcombinationsoforiginal

features.

4. Conclusion

Thisstudyisanimportantpartofaproject,whereourgoalin

thewholeoftheprojectistodevelopaMLalgorithmtobeusedto

identifythevestibularsystemdisorderforindividualswhosuffer

fromimbalancewhenwalking.Theaimofthisstudywastoapply

dimensionalityreductiontechniquesandfindoutorobtain

dis-criminativefeaturesthatcanincreasetheaccuracyofthealgorithm

and decreasethetraining time. Weanalysed 22 initialfeatures

collectedfrom37peopleconsistingof21healthyonesand16

indi-vidualswithVSdisorders.Weappliedt-testand SBSasfeature

selectionmethodandstandardPCAandKPCAwithpolynomialand

Gaussiankernelsasfeaturetransformationmethodstodecrease

thesamplematrixdimension.Wedetermined4discriminative

fea-turesas‘ascensionofrightfoot,averagevelocity,leftkneelateral

swingandaveragesteplength’byusingt-testmethod,while16

featureswerefoundtobediscriminativebyapplyingSBSmethod.

ByusingMATLABClassificationAppLearner,wetrainedSVMwith

GaussianKernelwithamatrixformedbyfeaturesfoundwith

t-testandSBSmethodfrom37peopleandtheresultingaccuracy

was72.2%and81.1%fort-testandSBSmethods,respectivelyOn

theotherhand,applicationofPCAandKPCAmethodsdecreased

thenumberoffeaturesfrom22to13.StandardPCAmethod

pro-videdan accuracyof 82.6%,which wasslightly below thanthe

model accuracy (83.3%), while applying KPCA withpolynomial

andgaussiankernelfunctionsresultedinanaccuracyof81%and

89.2%,respectively.Thehighaccuracyresultedwithgaussian

ker-nelfunction,impliedthatthereisnonlinearcorrelationbetween

features.Besidesitsperformanceregardingtheaccuracy,theFT

methodalsodecreasedthetrainingtimedramatically,around6

times.

The importance of dimensionalityreduction process willbe

evenmoreobviouswhenthesamplematrixsizewillincrease.In

thenearfuture,weplantoincludenewfeaturesobtainedfrom

insolepressuresensors.Ontheotherhand,inthisstudywedid

notperformsub-classificationbetweendiseasesinorderto

pre-ventover-fittingofthetrainingmodel,asmostofthepatients(11

outof16)hadthesamediagnosisasBPPV.Asanextstep,wealso

aimtoincreasedatasetundereachVSdisorderlabelthatwill

obvi-ouslyraisetheoverallperformanceoftheMLalgorithmandwill

furtherhelptosub-classifybetweenreasonsofimbalance.Weare

alsosearchingfornewfeaturestoincreasetheoverallaccuracy

inthediagnosis.Inthiscontext,weconsidertoanalysethetime

domaincharacteristicsofthefeaturesusingchaoticapproach,

com-plexnetworkanalysis,fractality/multi-fractalityetc.Itisobvious

thatforthesetypesofanalysesweneedlargerdatasets,sothatthe

statisticalfeatureextractionwillbemeaningful.

CRediTauthorshipcontributionstatement

Acknowledgments

Thisresearchisapartoftheproject‘Developmentofadynamic

vestibularsystemanalysisalgorithm&Designofabalance

mon-itoringinstrument’ (ID:115E258)supported by the Scientific &

TechnologicalResearchCouncilofTurkey(TUBITAK).

DeclarationofCompetingInterest

Theauthorsdeclarethattheyhavenoknowncompeting

finan-cialinterestsorpersonalrelationshipsthatcouldhaveappearedto

influencetheworkreportedinthispaper.

AppendixA. Supplementarydata

Supplementarymaterialrelatedtothisarticlecanbefound,in

theonlineversion,athttps://doi.org/10.1016/j.bspc.2020.101963.

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S. ˙Ikizo˘glu graduated from Istanbul Technical Uni-versity (ITU)- Control and Computer Engineering. He completedhisdoctorateatthesameinstitutein1992. HeiscurrentlyAssociateProfessor atITU-Controland Automation Engineering Dept. His area of interest mainly covers:Measurement, Instrumentation, Control andMechatronics.

S.HeydarovgraduatedfromElectricalandElectronics EngineeringDepartmentwithControlEngineering con-centrationfromMiddleEastTechnicalUniversity-Turkey. Heis currentlyPh.D studentinControl and Automa-tion Eng.Dept.atIstanbulTechnical University.Heis alsolectureratIstanbulGelisimUniversity,Electronics Technologies department. His research areaof inter-estincludesdataanalysis,modelingandsimulationof biomedicalsystems.