Clustering fMRI data with a robust unsupervised learning algorithm for neuroscience data mining

(1)

ContentslistsavailableatScienceDirect

Journal

of

Neuroscience

Methods

j ou rn a l h om epa g e : w w w . e l s e v i e r . c o m / l o c a t e / j n e u m e t h

Clustering

fMRI

data

with

a

robust

unsupervised

learning

algorithm

for

neuroscience

data

mining

Hadeel

K. Aljobouri

a,b,∗

_,

_Hussain

_A.

_Jaber

a

_,

_Orhan

_M.

_Koc¸

_ak

c

_,

_Oktay

_Algin

d,e

_,

Ilyas

C¸

ankaya

a

a_Electrical_and_Electronics_Engineering_Department,_Graduate_School_of_Natural_Science,_Ankara_Yıldırım_Beyazıt_University,_Ankara,_Turkey b_Biomedical_Engineering_Department,_College_of_Engineering,_Al-Nahrain_University,_Baghdad,_Iraq

c_Psychiatry_Department,_School_of_Medicine,_Kırıkkale_University,_Kırıkkale,_Turkey

d_Department_of_Radiology,_Ataturk_Training_and_Research_Hospital,_Ankara_Yıldırım_Beyazıt_University,_Ankara,_Turkey e_National_MR_Research_Center,_Bilkent_University,_Ankara,_Turkey

h

i

g

h

l

i

g

h

t

s

•Anovelapplicationoftherobustunsupervisedlearningapproachisproposedinthecurrentstudy.Robustgrowingneuralgas(RGNG)algorithmwas fedintofMRIdataandcomparedwithgrowingneuralgas(GNG)algorithm,whichhasnotbeenusedforthispurposeoranyothermedicalapplication.

•LearningalgorithmsproposedinthecurrentstudyarefedwithrealandfreeauditoryfMRIdatasets.

•Anothercomparisonwasconductedwiththemodel-based(hypothesis)dataanalysisapproachusingthestatisticalparametricmapping(SPM)package, whichisbasedonthegenerallinearmodel.

•ThefMRIresultobtainedbyrunningRGNGwaswithintheexpectedoutcomeandissimilartothosefoundwiththehypothesismethodindetecting activeareaswithintheexpectedauditorycortices.

•ResultsshowthatthefMRIapplicationofthepresentedRGNGapproachisclearlysuperiortootherapproachesintermsofitsinsensitivitytodifferent initializationsandthepresenceofoutliers,aswellasitsabilitytodeterminetheactualnumberofclusterssuccessfully,asindicatedbyitsperformance measuredbyminimumdescriptionlength(MDL)andreceiveroperatingcharacteristic(ROC)analysis.

a

r

t

i

c

l

e

i

n

f

o

Articlehistory:

Received17December2017

Receivedinrevisedform13February2018 Accepted14February2018

Availableonline20February2018 Keywords:

Clusteringtechnique Datamining

Growingneuralgas(GNG) Robustgrowingneuralgas(RGNG)

a

b

s

t

r

a

c

t

Background:Clusteringapproachesusedinfunctionalmagneticresonanceimaging(fMRI)researchuse brainactivitytodividethebrainintovariousparcelswithsomedegreeofhomogeneouscharacteristics, butchoosingtheappropriateclusteringalgorithmsremainsaproblem.

Newmethod:Anovelapplicationoftherobustunsupervisedlearningapproachisproposedinthecurrent study.Robustgrowingneuralgas(RGNG)algorithmwasfedintofMRIdataandcomparedwithgrowing neuralgas(GNG)algorithm,whichhasnotbeenusedforthispurposeoranyothermedicalapplication. LearningalgorithmsproposedinthecurrentstudyarefedwithrealandfreeauditoryfMRIdatasets. Results:ThefMRIresultobtainedbyrunningRGNGwaswithintheexpectedoutcomeandissimilarto thosefoundwiththehypothesismethodindetectingactiveareaswithintheexpectedauditorycortices. Comparisonwithexistingmethod(s):ThefMRIapplicationofthepresentedRGNGapproachisclearly superiortootherapproachesintermsofitsinsensitivitytodifferentinitializationsandthepresenceof outliers,aswellasitsabilitytodeterminetheactualnumberofclusterssuccessfully,asindicatedby itsperformancemeasuredbyminimumdescriptionlength(MDL)andreceiveroperatingcharacteristic (ROC)analysis.

Conclusions:TheRGNGcandetecttheactivezonesinthebrain,analyzebrainfunction,anddetermine theoptimalnumberofunderlyingclustersinfMRIdatasets.Thisalgorithmcandeﬁnethepositionsof thecenterofanoutputclustercorrespondingtotheminimalMDLvalue.

∗ Correspondingauthorat:BiomedicalEngineeringDepartment,Collegeof Engi-neering,Al-NahrainUniversity,Baghdad,Iraq.

E-mailaddress:hadeelbme77@eng.nahrainuniv.edu.iq(H.K.Aljobouri).

1. Introduction

Functionalmagneticresonanceimaging(fMRI)isapowerfultool

usedbyneuroscientiststoexaminebrainactivitybycalculatingthe

levelsofoxygenintheblood.Bloodoxygenationleveldependent

(2)

(BOLD)signalrepresentstheratioofoxygenatedtodeoxygenated

hemoglobinmeasurementsinthebloodandiscloselyrelatedto

neuralactivity.FMRIconsiders metabolicfunctioninmeasuring

neuralactivitybecauseitdeterminesthehemodynamicresponse

function(HRF)ormetabolicdemands(oxygenconsumption)inthe

brainorspinalcord(Aljobourietal.,2015).

FMRIisusedtounderstandneuronalmechanismsbehindmany

disorders,suchasbipolardisorder,schizophrenia,Parkinson’s

dis-ease,autismspectrumdisorders,andAlzheimer’sdisease.

ThefMRIdatasetis acquiredfromascannermachine inthe

form of raw data as sequences of 3D images because of the

variations of voxel intensitiesover time. With different

exper-imental conditions, the acquired fMRI data are formed as a

combinationofBOLDsignalchangesandnoisesorartifacts.These

artifacts are attributed to hardware systems (the MRI scanner

itself),individualsthemselves(e.g.,headmotion),orphysiological

effects.

ClusteringtechniquesinfMRIresearchareconsidered

model-free or exploratorydata analysis approaches. These techniques

candeﬁnetheactivezonesandﬁndstructuresinthebrainand

fMRI data competently without the need for prior knowledge

aboutactivationpatternsorexperiments.However,choosingthe

appropriateclusteringalgorithmsremainsaproblem.Independent

componentanalysis(ICA)andprincipalcomponentanalysis(PCA)

algorithmsareregardedasﬁnemethodstoseparatefMRIsignals

intoagroupofdeﬁnedcomponents.Thesealgorithmscannot

eas-ilypredictoccurrencesduringacquisitionandhavelimitationsin

termsofindependenceandorthogonality,respectively(Korczak,

2012).VariousclusteringalgorithmsareappliedinfMRIfordata

mininginsteadofthepreviousclassicalmethods,whichcannot

eas-ilypredictoccurrencesduringacquisition.Theclassicalmethods

includeK-means,fuzzyclassiﬁcation,hierarchicalclassiﬁcations,

Linde–Buzo–Gray(LBG),clusteringusingrepresentatives(CURE),

neuralmodelsKohonen’sself-organizingmap(SOM),neuralgas

(NG),andFritzke’sgrowingneuralgas(GNG)algorithms.However,

oneofthemainproblemsoffMRIclusteringalgorithmsis

decid-ingthenumberofclustersasaninput(Dimitriadouetal.,2004;

Wismulleretal.,2004).Resultswithahighlevelofinterpretation

wereobtainedusingclusteringapproaches,buttheseapproaches

areassociatedwithhighcostintermsofcomputingtimeand

mem-oryspace(BockandDiday,2000;Lindquist,2008;Goutteetal.,

1999; Baumgartneretal.,1998; Liaoetal.,2008;Katwal,2011;

Pereiraetal.,2009).

TheGNGalgorithmexhibitsthebestclustering performance

andproducerobustness;however,thisalgorithmhaslimitations

associatedwiththesensitivityforinitialization(choosingasetof

neuronvectors),theorderofinputvectors,andtheexistenceof

manyoutliers(QinandSuganthan,2004).Therefore,anovel

appli-cation,whichreliesonusingtherobustgrowingneuralgas(RGNG)

algorithmwithfMRIdatasets,isproposedtodetecttheactivezones

inthebrain.ThisalgorithmwascomparedwiththeGNGalgorithm,

whichhasnotyetbeenusedforthispurpose.

RGNGwasproposedtoidentifyactivatedregionsinthebrain

of various fMRI datasets with differentand important features

unlikeotherclusteringapproaches.Differentrobustness

proper-tiesareassociatedwiththeRGNGnetworkbecauseitisinsensitive

toinitialization,inputsequenceordering,andoutliers,determines

theoptimalnumberofunderlyingclustersduringdifferentgrowth

stages,anddealswithmultimodaldatasetseffectively.

The approach of using RGNG with fMRI dataset is the ﬁrst

attemptintheliterature.Thecurrentstudyis organizedas

fol-lows:Section2providesthemostimportantpackagesusedwith

fMRIdataanalysisincomparisonwiththeclusteringandespecially

theproposedRGNGapproach.Section3describestheproposed

workandalgorithmsusingsimpleﬂowchartsandtables.Section

4describesthepreprocessingandperformancemeasures.Section

5presentstheexperimentaloutputresults.Finally,Section6

con-cludesthepaperandintroducesfutureresearchdirections.

2. fMRIdataanalysistechniques

FMRIdataanalysismethodscanbedividedmainlyintotwo

cat-egories,namely,model-driven ormodel-based(hypothesis)and

data-drivenormodel-free(exploratory)approaches.The

model-drivenmethodsdeal withdeﬁniteactivationpatterns,response

functions,orexperiments.Thesemodelsrequireprevious

knowl-edgeand statisticallytest theanalyzeddataonthepresenceor

absenceofaresponse.Themethodsrelatedtothiscategory

dif-fereitherbystatisticalmethodorsignalestimationprocedurein

performingtheactivation.Anexampleisthecommonlyused

gen-erallinearmodel(GLM),whichisthemostfundamentalandbasic

approachusedforfMRIdataanalysiswithstatisticalparametric

mapping(SPM)(SPM,1991).

Data-drivenmethods,incontrast,havetheabilitytocountallof

thevoxelssimultaneously,deﬁnetheactivezonesandﬁnd

struc-turesin thebrainandfMRI datacompetently withoutprevious

knowledgeaboutactivationpatternsorexperimentalparadigms.

Thesemethodscanbedividedmainlyintotwo groups,namely,

blindsourceseparation(BSS)andclusteringapproach.

BSSattemptstoﬁndunobservedsignalsor“sources”from

sev-eralobservedmixturesandgenerateamodelofthedata.Various

methodsareusedforBSS:PCA(Fristonetal.,1993;Fristonetal.,

1996),ICA(Hyvarinenetal.,2001;McKeownetal.,1998;Calhoun etal.,2001;Mckeown,2000),andcanonicalcorrelationanalysis

(CCA)(Frimanetal.,2002)methodsareusedtoseparatethese

mix-turestoobtainsourcesignals.TheFMRIBSoftwareLibrary(FSL)

package (TheAnalysisGroup,2012)usesmelodicICA, which is

adata-driven(model-free)approach,butisinsufﬁcientformost

fMRIdatasetsbecauseICAhassomelimitations.ICAattemptsto

ﬁndmaximallyindependentmapsandsplitthewideactivation

areas into a number of maps, which have a strongcorrelation

betweentimecourses(TCs)ofdifferentcomponents.The

indepen-dentcomponents(ICs)fromICAdecompositionareunordered,that

is,thisfeatureisassociatedwiththemodelorderselectionforlinear

model-basedregionextraction,whichremainsanopenproblem.

Thus,determiningwhetherornotICsarecorrelatedwithnonlinear

activationisdifﬁcult.

Clustering(Chenetal.,2006; Seghieretal.,2007)analysisis

basedongroupvoxelsaccordingtotheirTCsignalsinasimilarHDR

(Hemodynamic response) over time. The advantages presented

for theproposed clustering RGNG algorithm will beexplained.

Thisapproachismainlyadata-drivenormodel-free(exploratory)

approach.Table1comparesstatistical,transformationand

cluster-ingmethods.

ClusteringanalysisiswidelyusedforfMRIdataprocessingto

detectthebrainactiveareaeffectively.Inthefollowingparagraph,

thedataminingideaisidentiﬁedbasedontheGNGnetwork.

Lachicheetal.(2005)introducedanewinteractivedatamining

approachtofMRIimages,whichhasnotbeenusedforthepurpose

of thecurrent study,and showedthat GNGsuccessfully

recog-nizedtheactiveareasinthefMRIimagesofthebrain(Lachiche

etal.,2005).TheideaofdeﬁningadistancebetweenvoxelsoffMRI

imageswasargued,andthisdistanceisproposedtobebasedon

thesignalonly.

Korczak(2007)introducedanewinteractivedatamining

tech-niquetofMRIimagestoobservecerebralactivity;thistechniqueis

basedonadata-drivenapproach(Korczak,2007).Different

unsu-pervised clustering algorithms were presented, developed, and

tested onsequencesof fMRI images. Five clusteringalgorithms

(GNG,SOM,LBG,K-means,andCURE)wereappliedtosynthetic

(3)

perfor-Table1

Comparisonamongstatistical,transformationandclustering.

BasedApproach fMRIAnalysisMethods ApproachProperties Statisticalmethod Model-Driven/Model-Based/Hypothesis

UsedwithSPMpackageandbasedonGLM

Themostfundamental,basicandcommonlyusedapproachforfMRI dataanalysis,butitneedspreviousknowledgeaboutactivation patternsorexperiments.

Transformationmethod Data-Driven/ModelFree/Exploratory

UsedwithFSLpackageandbasedonmelodicICanalysis

Itisbasedonlinearmixingandisunordered.Thus,itmustdealwith independentdata.

Clusteringmethod Data-Driven/ModelFree/Exploratory

RGNGisanexamplewhichwereusedinthisstudy

ItcandeﬁneactivezonesandidentifystructuresinthebrainandfMRI datacompetentlywithouttheneedforpreviousknowledgeabout activationpatternsorexperiments.

manceoftheGNGalgorithmwasthebestamongallotherclustering methods,withacceptablerobustness.

Heydaretal.(2009)developedthealgorithmoftheGNG

net-work,whichcanruntheoptimalnumberofclustersautomatically

(Heydaretal.,2009).Theexperimentalresultsusedartiﬁcialand

real fMRI datasets with the proposed algorithm, which is an

improvedversionoftheGNGalgorithm.TheycomparedtheJaccard

coefﬁcientoftheproposedalgorithmwithsomewell-known

clus-teringalgorithms,suchasK-means,NG,GNG,andfuzzyC-means

(FCM);theresultsshowedthat theproposedalgorithm

outper-formedtheotheralgorithms.

TheGNGoriginatesfromtheNGalgorithmbyFritzke(Fritzke,

1995;Fritzke,1997),andtheRGNGalgorithmwasintroducedby

QinandSuganthan(2004)withintheGNGstructure.Thework

pre-sentedinthispaperusingRGNGwithfMRIdatawillbetheﬁrst

attemptintheliterature.Thecurrentstudypresentedhowtofeed

RGNGwithrealandfreeauditoryfMRIdatasets.

GNGandRGNG,bothartiﬁcialneuralnetworkapproachesbased

on unsupervised clustering for fMRI analysis, are compared in

Table2.Thistablepresentstheresearcherswhointroducedthese

approaches,theresearcherswhousedtheseapproachesinfMRI

research,and the advantages and limitations of each approach

(AlJobourietal.,2017).

3. Methodologyandproposedwork

The GNGalgorithm is reviewed beforeintroducing the

pro-posedRGNGalgorithmforfeedingwithfMRIdata.TheGNGand

RGNGalgorithmsareextensiveandcomplex.Thus,ﬂowchartsand

amathematicalmodelweredevelopedforconvenienceandeasier

writingoftherelatedcodes.

3.1. GNGalgorithm

TheGNGalgorithmwasdevelopedbyFritzke(1995,1997);he

proposedchangingtheunitnumbers(mostlyincreased)inaSOM

networkwithavariabletopologicalstructure.TheGNGisagrowing

softcompetitivelearningalgorithm,whichcombinesthetopology

formationrulesofthecompetitiveHebbianlearning(Martinetzand

Schulten,1991)withthegrowingcellstructures(Fritzke,1994)into

anewmodel.

BeforefeedingtheGNGalgorithm,thefollowing parameters

mustbedeﬁned:

Inthesubsequentexperiments,theparametersettingsareﬁxed

foreachalgorithm,withtypicalvaluesproposedintheliterature.

TheGNGalgorithmwassetwithtypicalvaluesasin(Fritzke,1997):

εb=0.05,εn=0.006,␣max=100,ˇ=0.0005,and=300.

Fig.1presentstheﬂowchartoftheGNGalgorithmandshows

thattheinactiveneuronsthatdonotwinduringalongtime

inter-valmaybedetectedthroughtheGNGalgorithm bytracingthe

(4)

changesofanagevariableassociatedwitheachedge.Theproposed

ﬂowchartcanbesummarizedinthefollowingsteps:

TheGNGstartswithaminimalnetworksize,andafew

num-bersofnewneuronsandconnectionsareinsertedintoagrowing

structureusingvectorquantizationuntilthedesiredqualityofthe

modelisachieved(e.g.,netsize,timelimit,predeﬁnednumbersof

neuronsinserted,orsomeperformancemeasure).

3.2. Robustgrowingneuralgas(RGNG)algorithm

The“deadnode”problemoccursintheGNGalgorithmbecause

ofthegrowthschemeassociatedwiththeGNGalgorithm.Dead

node problems occur because of inappropriate initializations,

whichcausesomeprototypestoneverwinthroughthetraining

process.Evenwiththeinitializationinsensitiveclustering

meth-ods,goodclusteringresultsmaynotbeobtainediftheorderofthe

inputsequenceisnotchosenproperly.

Asidefromproblemsrelatedtothesensitivityforinitialization

andtheorderofinputvectorsorting,otherproblemsrelatedtothe

presenceandpositionofvariousoutliersoccur.Thus,theGNG

net-workmayfailtodifferentiatetheoutliersfromtheinliersthrough

theoriginalprototypeupdatingrulewhenvariousoutliersexistin

adataset.

AnovelRGNGwaspresentedbecauseofthelimitationsofthe

GNGalgorithm(QinandSuganthan,2004)withintheGNG

struc-ture.TherobustnessofRGNGtowardinitialization,inputvector

sorting,andtheexistenceandpositionofvariousoutliersimproved,

aswellasitsabilitytoﬁndtheoptimalnumberofneuronsduring

runtimedynamically.

Fig.2presentstheﬂowchartoftheRGNGalgorithm.The

pro-posedﬂowchartcanbesummarizedinthefollowingsteps:

BeforefeedingtheRGNGalgorithm,thefollowingparameters

mustbedeﬁned:

Table2

ComparisonbetweenTwoArtiﬁcialNeuralNetworkApproachesbasedontheUnsupervisedClusteringforfMRIAnalysis.

Methods GNG RGNG

Introducedby • Fritzke(1995) • Lachicheetal.(2005)

• Korczak(2007) • Heydaretal.(2009) UsedwithfMRI • QinandSuganthan(2004) Itwasnotpreviouslyproposed Advantages • Itsabilitytomodifythenetworktopologybyremoving

edgeswithitsagevariable

• Theneighborhoodsortingstepisunnecessary • Itcanﬁndanetworksizeandstructureautomatically,

continuelearning,andaddunitsandconnectionsuntila performancecriterionisfulﬁlled

• Thenumberofclassesisnotﬁxedinadvanceasinmost clusteringalgorithms

• Insensitivetoinitialization,inputsequenceordering,and thepresenceofoutliersduringdifferentgrowthstages • Canautomaticallydeterminetheoptimalnumberofclusters • Dealswithmultimodaldatasetseffectively

Limitations Itssensitivityfor: • Initialization

• Theorderofinputvectors • Existenceofmanyoutliers

(5)

Fig.2.FlowchartdesignoftheRGNGalgorithm.

In thesubsequentexperiments, theparametersettings were

ﬁxedforeachalgorithm,withtypicalvaluesproposedinthe

lit-erature.TheRGNGalgorithmwassetwithtypicalvaluesasin[12]:

εbi=0.1,εbf=0.01,εni=0.005,εnf=0.0005,␣max=100,k=1.3,and

=1×10−4.

For eachreference vectorwi,i=1,2, ..., c,a seriesof edges

emerged from itslocation toa jointwithits direct topological

neighbors.SimilartotheGNG,theRGNGalgorithmstartsinstep

1withtheinitializationofafewprototypevectors(usuallytwo),

W= {w1,w2}.

InfMRI,WrepresentstheTCofthefMRIdataset(seeFig.3),

widenotestheTCofexemplari,andwc istheTCoftheclosest

exemplarc.Prototypevectorsw1,w2arerandomlychosenwith

referencevectorsfromtheTCofallvoxelsP (x),andadatavoxel

xisgeneratedasaninputsignalfromthefMRIdatasetusedfor

training,X= {x1,x2,...,xN}.

The maximum number of neurons to grow is deﬁned as

prenumnodeandthemaximumpredeﬁnedtrainingepochisdeﬁned

asMax iterduringeach growthstage withacertain prototype

number.Theinitialorcurrenttrainingepochnumberissetasm=0.

Theiterationpointinthetrainingepoch(taskperiods)m,t=0.

Thus,thefulliterationstepiterovereachgrowthstepisexpressed

as:

iter=m·N+t, ,(1)

whereNisthelengthofthefMRITC.

ClusteringalgorithmsattempttoclassifytheTCsignalsofthe

voxelsintodifferentgroupsaccordingtothesimilarityamongthe

groups.Thetemporalinformationisorderedinclustersandis

inde-pendentofitsspatialneighborhood.Theseclustersaredescribed

byanaverageTCoraclustercenterobtainedbyaveragingallofthe

TCsofthecluster.ThefMRIdataaretransformedintoaTCofvoxel

intensityvariationsproportionaltoitsaverage,asfollows:

Ixav= 1 N

I_ix, (2) where Ix

av is theaverageintensityof voxelaof aseriesof N

images;

Wi=Iaxv−Iix. (3)

Thedistancesbetweentwo fMRIsignalsWaand Wb maybe

computedasaEuclidiandistance:

dE=

(Wai−Wbi)2. (4)

Theactivitylevelofthedatasetisgenerallybasedonthedistance

betweeninputvectorsxcomparedwithalloftheexemplarTCsWi.

InRGNG,thesmallestEuclideandistancex−wi canbemadeto

deﬁnethebestmatchingnode.

TheRGNGalgorithmusedtheprincipleoftheMDLvalueasthe

clusteringvalidityindex(toﬁndtheoptimalnumberofclustersand

theircenterpositions)correspondingtothesmallestMDLvalue.

Thus,theoptimalnumberofclustersisdeterminedautomatically

bysearching theextrememinimumvalue oftheMDLmeasure

throughthenetwork-growingprocess.TheRGNGapproachhasthe

smallestMDLvaluerecordedwithrespecttotheGNGcombined

(6)

Fig.3.Proposeddataminingsystemarchitecture.(a)Mainblockdiagram.(b) Exper-imentalparadigm“silence”and“talk”.

approachcanﬁndtheoptimalnumberofclustersandtheircenter

positionscorrespondingtothesmallestMDLvalue.

4. Simulationdesign

Theblockdiagram showstheprocess ofbrain functiondata

analysis,whichisperformedinthecurrentstudy.Theprocessis

composedofﬁvestages(seeFig.3B):

• preprocessingoftherawdata;

• clusteringvoxelstogetherbasedonthesimilarityoftheir

inten-sityproﬁleintheTCsoftheimage;

• overlaywiththestructuralimage;

• visualfMRIimage;

• validation.

4.1. Imagespatialpreprocessing

Theexperimentsinthepresentworkwereperformedin

MAT-LAB2016aandSPM12packageforthepreprocessingstage.Various

noisefactorsinterferewiththefMRIsignalsofinterest.Thesubject

istypicallynevercompletelymotionless.Thus,thepreprocessing

stepsmustbeadaptedtoeachidentiﬁedartifactbeforethe

cluster-ingphase.ThepresentworkusedSPMfortheauditoryfMRIdata

spatialpreprocessingstages.ThefMRIdatasetispreprocessedby

applyingthefollowingsteps:

• Realignment; • Coregistration; • Segmentation; • Normalize;

• SmoothingusingFWHM=6.

Thefunctional imageswerereoriented toMNIspace, which

isstandardbrainformedbyusingalargeseriesofMRIscanson

normalcontrolsdevelopedattheMontrealNeurologicalInstitute.

Thenthefunctionalrawdatawererealignedtocorrectforthehead

movements.Thehigh-resolutionanatomicalT1imageswere

coreg-isteredwiththerealignedfunctionalimagestoenableanatomical

localizationoftheactivations.Segmentationprocessisnot

manda-tory.SPM12usesMNItemplateimage,whicharethemostcommon

templatesused for fMRIspatial normalization.In this step,the

anatomicalandfunctionalimageswerespatiallynormalizedinto

MNIspace.Finally,thefunctionalrawdatawerespatiallysmoothed

withaGaussiansmoothingkernelof6.

4.2. FMRIdataset

Quantitative performance assessment uses an auditoryfMRI

dataset.AuditorydataiscomposedofentirebrainBOLD/EPIimages

acquiredona modiﬁed 2T SiemensMAGNETOM Vision system

(Johnetal.,2013).Eachacquisitionconsistsof64contiguousslices

(64×64×643×3×3mmvoxels).Acquisitiontook6.05s,witha

scantoscanrepetitiontime(TR)setarbitrarilyto7s.Atotalof96

acquisitionsweremadefromasinglesubjectinblocksof6scans

(acquiredduringthesameconditionasastimulantorrest),yielding

16blocksandeachblockfor42s.

The experimentalparadigm for successive blocks alternated

between rest and auditory stimulation, starting with rest (see

Fig.3B).Thefunctionaldatastartatacquisition4,functionalimage

(fM4).Auditorystimulationwascomposedofbisyllabicwords(e.g.,

“mother,”“house,”“weather,”and“movie”)presentedbinaurallyat

arateof60/min.Theﬁrstfewscansmustbediscarded(“dummy”

leaddidnotexistinscans)becauseofT1effects.

4.3. Performancemeasure

AnovelapplicationoftheRGNGalgorithmwascomparedwith

GNGandSPMusingtwoperformancemeasures,namely,theMDL

valueandreceiveroperatingcharacteristic(ROC)analysis.

IntheRGNGalgorithm,theMDLvalueisoneofthewell-known

informationtheoryevaluationmeasures,whichhasbeenusedas

theclusteringvalidityindex(Rissanen,1983).TheaverageMDL

val-uesduringthegrowthstageshavebeenplottedversusthelength

(7)

Fig.4.MDLvaluesversusN.

Fig.5.ROCcurvesanalysesoftheauditoryfMRIdataset.

approachescombinedwiththeMDLcriterion;thelengthofthe

fMRITCisselectedrandomlyasN=16.Eachdetectedcluster

num-bercorrespondedtotheMDLvalue.TheRGNGapproachhasthe

smallestMDLvaluerecordedwithrespecttoGNGcombinedwith

theMDLprinciple;thus,itcansuccessfullydeterminetheactual

numberofclusters.

TheROCanalysisisanotherindexoftheperformanceofRGNG

incomparisonwithSPM(Skudlarskietal.,1999).TheROCis

well-knowninmedicalimagingandmachinelearningapplications;the

ROCspaceconsistsofthefalsepositiveratio(FPR)onthex-axis

andthetruepositiveratio(TPR)onthey-axis(SunandXu,2014).

ThegoodclassiﬁerspaceisindicatedbyahighTPRandalowFPR,

whereasthebadclassiﬁerspaceisindicatedbyalowTPRanda

highFPR.

ThecurvesinFig.5,generallyindicatedthatthetwomethods

workasgoodclassiﬁerswithahighTPRandalowFPR.TheRGNG

methodcandetectrealactivationsunderthesameFPRratio.

InfMRI,theFPRiscalculatedbydividingthenumberof

misclas-siﬁedinactivatedvoxelsbythetotalnumberofvoxelsconsidered,

whereastheTPRiscalculatedbydividingthenumberofcorrect

classiﬁcationsofactivatedvoxelsbythetotalnumberofvoxels

con-Fig.6. ActiveareasinthebrainauditorycortexareawithintheSPMpackage.

sidered(Langeetal.,1999).Inthesamesituation,theROCcurves

fortheRGNGandSPMmethodsarecompared,asshowninFig.5.

5. fMRIresults

The principles behind the prototype-based clustering

algo-rithms were introduced in this work. The validity of the

performance oftheRGNG wasanalyzed andveriﬁedwithfMRI

experiments.FMRIanalysisinvolvesknownareasand functions

ofthebrain.Thus,thecommonandexpectedresultsmustbeused

intheexperiments.Oneoftheseareasistheauditorycortex.Real

auditoryfMRIdata,whicharefreelyavailableforeducationand

evaluationpurposes,wereusedintheexperiments[http://www.

ﬁl.ion.ucl.ac.uk/spm/data/auditory/].Thesedatawereutilizedby

previousworks(Lachicheetal.,2005;Korczak,2007;Heydaretal.,

2009).

OneofthedecisiveadvantagesoffMRIisthatfMRIstudiesdo

notrequiretheanalysisofagroupofvolunteers,butcanproduce

valuableresultsatthelevelofsingleindividuals.Theanalysisof

singlevolunteersis crucialinanalyzing smallstructures,which

exhibit stronginterindividual variation (Campain andMinckler,

1976; Francesco etal., 2003), similar totheauditorycortex,as

showninFig.6.

5.1. ComparingauditorydatarunningRGNGwiththatofGNG

Ablockdesignexperimentwasconductedusingauditory

stim-ulus.Figs.7and8AandBshowtheactiveareasintheauditory

cortexoftheentirebrainwhenrunningtheGNG,andRGNG

algo-rithms.AlthoughauditorycortexregionswerefoundbyGNGand

RGNGalgorithms,inGNGotherareasarealsoactivatedoutsidethis

cortex.InRGNG,theseareasarelessorapproximatelydisappeared

underthesameexperimentandtheauditorystimulusofthewhole

brain.

Fig.7showstheclustersinatransparentorglassbrainimage

whichisamoreﬂexibleapproachbyspecifyingarealRGB

(red-green-blue)colorvalueforeveryvoxelintheimage.Fig.8AandB

showthealignmentoftheobtainedclustersintoastructuralspace

ofthebrainwhenrunningtheGNGandRGNG,respectively.With

regardtotheoutputresultsobtainedbyrunningthethree

unsuper-visedclusteringalgorithms,spatialinformationisvisualizedasﬁne

clustersintheauditorycortexarea.TheGNGalgorithmwasusedin

(8)

Fig.7. Clustersinatransparentbrainimagewhenrunningthe(a)GNGand(b) RGNGclusteringtechniques.

Fig.8. Clustersoverlaidontotheanatomicalimagewhenrunningthe(a)GNG(b) RGNGand(c)SPM.

2009).TheROIobtainedwithintheauditorycortexwhenrunning

theGNGalgorithm(Fig.8A)issimilartothatobtainedbythesame

approachintheliterature.Ingeneral,aclustercorrespondstoa

groupofvoxelswithasimilarHDRoveraTC.

Theblockdesignexperimentwasconductedbyrunningthe

pro-posedRGNGapproachusingauditorydata.Theactivationshown

inFig.8Bislocatedinthetemporallobe.Thespatialinformation

showsthattheareasofactivationobtainedaresimilartothose

expectedfromtheauditorycortexexperiments,whicharedetected

asvariationsofvoxelintensityovertime.Inthecurrentstudy,the

dataobtainedbytheRGNGapproachwasseparatedaccordingto

theTCsignalsofvoxelintensityvariationsrelativetoitsaverage.

Similartoallclusteringalgorithms,theRGNGattemptedtoportion

homogeneousareasofactivationinthebrainthatwere

compara-bletothoseareaslocatedusingotherapproachesandfoundinthe

recognizedcorticesrelatedtotheexperiment.Theseareasor

clus-tersaredescribedbyanaverageTCoraclustercenterobtainedby

averagingalloftheTCsofthecluster.

ThenovelapplicationofRGNGoutputclusteringresultscanbe

recognizedasthebestwithrespecttotheGNGapproachbecause

theclusterresultsdeﬁnedthespeciﬁcauditorycortexarea.

More-over,thefMRIoutputresultsobtainedbyrunningtheRGNGwas

thesameastheoutcomeobtainedbyrunningtheSPMusingthe

samedatasetandthesameparadigm,aswillbediscussedinthe

nextsubsection.

5.2. ComparingauditorydatarunningRGNGwiththatofSPM

Theparadigmof theblockdesignexperiment alternatestwo

conditions,namely,withoutthestimulusandwithauditory

stim-uli,which consist of repetitions of two-syllable words,suchas

“mother,”“house,”“weather,”and“movie”.Fig.8Bshowstheability

oftheRGNGclusteringtechniquetoidentifywinnernodes,

deter-minetheoptimalnumberofunderlyingclusters,andproducea

TCforactivationdetectioninanauditorydataset.Fig.8Cshowsthe

areaofactivationintheauditorycortexofwholebrainrunningSPM

withf-contrasttestresultswithfamily-wiseerror(FWE)threshold,

withnomasking,theFWE-correctedpvalue=0.05.

TheresultsofSPMbasedonGLMusingtheparadigmasa

ref-erencesignalintroducedbiasintheexperiment.Bycontrast,the

RGNGapproachdidnotusetheparadigmasthereferencesignal

becauseitworksasamodel-freemethod.Insummary,theRGNG

resultswerewithintheexpectedoutputsandhavesimilarresultsto

thosefoundwiththehypothesismethodindetectingactiveareas

withintheexpectedauditorycortices.TheRGNG signalchanges

overaTCinauditoryfMRIdatasetswhichcanbecalculatedby

label-ingthepixelsofthesamecluster(membershipTC)orbyplotting

thedistanceoftheTCstoagivenclustercenter(distanceTC).

NovelandextensivesimulationstudiesonrealfMRIdatasets

were conductedusing the RGNG unsupervised clustering

algo-rithm. A potential problem associated withGLM model is the

requirementofanaccurateestimateofthefMRIparadigmdesign.

Indifferentcases,itisdifﬁculttoprovideprecisemodeldesigns;

eithertheproblemfromthesubjectswhodidthetaskincorrectly

(alsothesamesubjectmaygiveadifferentresponseforthesame

paradigmatadifferenttime)ordifferentsubjectsmaystillgive

dif-ferentBOLDsignalsduringthesameparadigm.TheresultinFig.8B

showsthatthismethodcancomplementthemodel-basedmethod

tocopewiththedifﬁcultiesandchallengesinfMRIdataanalysis.

TheﬁndingscanimprovetherecognitionofthenatureofthefMRI

dataandtheunderlyingmechanisms.

6. Conclusions

Themajorobjectiveofthisstudyistodetectandclassifythe

activatedareasofthebrainusingarobustandefﬁcientalgorithm.

Thistypeofstudyhasnotyetbeenconducted,andthecurrent

study,whichusesRGNGwithfMRI,istheﬁrstattempttodoso.

In conclusion, the RGNG can detect the activezones in the

brain,analyzebrainfunction,anddeterminetheoptimalnumber

ofunderlyingclustersinfMRIdatasets.Thisalgorithmcandeﬁne

thepositionsofthecenterofanoutputclustercorrespondingtothe

minimalMDLvalue.ThevalidityoftheperformanceoftheRGNG

algorithmwastestedusingrealauditoryfMRIdata,whicharebased

(9)

Somedifﬁcultieswereaddressedbyusingtheconventional

clus-teringalgorithms.For example,thenumber ofclustersmustbe

deﬁned earlier and thecluster detection problemhasdifferent

dimensionswithinthesamedataset.TheRGNGmergestheGNG

structurewithrobustpropertiesandusesMDLtodeﬁnethe

prob-lemsofoptimalnetworkrepresentationsandparameters,which

madetheRGNGinsensitivetotheinitializations,inputsequence

ordering,andoutliersandmorerobusttowardnoisyinputdata.

During thenetwork-growing process, theRGNG can effectively

determinetheoptimalnumberofclustersandtheir

correspond-ingpositions,whichareclosertotheactualclustercenters(with

thesmallestMDLvalue)withminimalinﬂuencefromtheoutliers.

Theexperimentaloutputresultsshowedthesuperior

perfor-manceoftheRGNGovermodel-basedapproachesandoneofthe

prototype-based clusteringalgorithms on realfMRI datasets as

revealedbytheirperformancemeasuredbyMDLandROC

anal-ysis.Thisworkproposednoveland powerfulmethodsfor fMRI

dataanalysis,whichintegratetheadvantagesofthehypothesisand

exploratoryanalysismethods.

TwotypesoffMRIanalysismethodswerecompared,namely,

GLManddata-drivenanalysesusingmachinelearningclassiﬁers.

TheGLMisthemostcommonmethodforfMRIdataanalysisbut

isbased heavilyona prioriBOLDmodeldesign. Insomecases,

theGLMcannotbeusedforbrainactivationdetectionwhen

pre-viousinformation aboutthedata is unavailable.Anexample is

aresearchinvolvingmentalsubjectorduringdaydreamingand

mind-wandering(defaultmodeofbrainfunction)(Yongnan,2010).

Thus,effectivealternativeapproachesusingdata-drivenanalysis

wereintroducedtodetectbrainactivitybasedonthedata

struc-ture.TheproposedapplicationofRGNGonarealfMRIdatasetwas

reviewedonasingle-subjectauditoryfMRIdata.Thismethodcan

bealsoextendedtomulti-subjectdata-drivenanalysis(multiple

subjectdata)offMRIdataset.RGNGapproachmaybepreferable

formultiplesubjectstudiesinsteadofanalysesdatafrom

single-subjectastheusedauditorydata.

Theparadigmoftheauditorydatasetusedintheexperiment

wasablock-typedatadesign.Forfuture,thisworkcanbeextended

towardexperimentswithevent-relateddatadesign.

TheRGNGcandealwellwithfMRI,whichiscomposedof

mul-timodaldatasets.Thus,theapproachcanbeappliedtootherreal

multimodaldatasets,suchasMRIimagesegmentationinthebrain

and otherregionsof thebody.Thus, clustersofdifferentorgan

shapesinthebodycanbedetectedusingotherdistancemetrics

becausetheEuclideandistancemetricusedwiththeRGNGcan

detecttheclustersofthebrain,whichisanapproximately

spher-icalorellipsoidalregionwithminimaldifferencesinthevariance

ineachdimension(FriguiandKrishnapuram,1999).

In future studies, cluster validity measures other than the

MDLcriterioncanbeusedwithRGNG.Minimummessagelength,

Bayesianinformationcriterion,andAkaike’sinformationcriterion

canbeappliedtotackletheuseofthecommonMDLvalidityindex

usedinthiswork.Theﬁndingsfromthisworkcanhelpaddressthe

variousdifﬁcultiesthatneurologistsandpsychologistsencounter

duringanalysistoimprovetheinterpretationoffMRIdata.

Acknowledgment

Theauthorswouldliketothankthereviewerswhosecomments

greatlyimprovedthequalityofthemanuscript.

References

AlJobouri,H.K.,Jaber,H.A.,C¸ankaya,I.,2017.Performanceevaluationof prototype-BasedclusteringalgorithmscombinedMDLindex.Comput.Appl. Eng.Educ.25(4),642–654(WileyInc.).

Aljobouri,H.K.,C¸ankaya,I.,Karal,O.,2015.Frombiomedicalsignalprocessing techniquestofMRIparcellation.Biosci.Biotechnol.Res.Asia12,1115–1138.

Baumgartner,R.,Windischberger,C.,Moser,E.,1998.Quantiﬁcationinfunctional magneticresonanceimaging:fuzzyclusteringvscorrelationanalysis.Magn. Reson.Imaging16,115–125.

Bock,H.H.,Diday,E.,2000.AnalysisofSymbolicData,ExploratoryMethodsfor ExtractingStatisticalInformationfromComplexDataStudiesinClassiﬁcation. DataAnalysisandKnowledgeOrganization,Springer-Verlag.

Calhoun,V.,Adali,T.,Pearlson,G.,Pekar,J.,2001.Spatialandtemporal independentcomponentanalysisoffunctionalMRIdatacontainingapairof task-relatedwaveforms.Hum.BrainMapp.13,43–53.

Campain,R.,Minckler,J.,1976.Anoteonthegrossconﬁgurationsofthehuman auditorycortex.BrainLang.3,318–323.

Chen,H.,Yuan,H.,Yao,D.,Chen,L.,Chen,W.,2006.Anintegratedneighborhood correlationandhierarchicalclusteringapproachoffunctionalMRI.IEEETrans. Biomed.Eng.53,452–458.

Dimitriadou,E.,Barth,M.,Windischberger,C.,Hornika,K.,Moser,E.,2004.A quantitativecomparisonoffunctionalclusteranalysis.Artif.Intell.Med.31, 57–71.

Francesco,D.S.,Fabrizio,E.,Tommaso,S.,Elia,F.,Elio,M.,Claudio,S.,Sossio,C., Raffaele,E.,Klaus,S.,Erich,S.,2003.fMRIoftheauditorysystem:

understandingtheneuralbasisofauditorygestalt.Magn.Reson.Imaging21, 1213–1224.

Frigui,H.,Krishnapuram,R.,1999.Arobustcompetitiveclusteringalgorithmwith applicationsincomputervision.IEEETrans.Patt.Anal.Mach.Intell.21, 450–465.

Friman,O.,Borga,M.,Lundberg,P.,Knutsson,H.,2002.ExploratoryfMRIanalysis byautocorrelationmaximization.Neuroimage16,454–464.

Friston,K.J.,Frith,C.D.,Liddle,P.F.,Frackowiak,R.S.,1993.Functionalconnectivity: theprincipalcomponentanalysisoflargePETdatasets.J.Cereb.BloodFlow Metab.13,5–14.

Friston,K.J.,Poline,J.B.,Strother,S.,Holmes,A.P.,Frith,C.D.,Frackowiak,R.S.,1996. AmultivariateanalysisofPETactivationstudies.Hum.BrainMapp.4,140–151. Fritzke,B.,1994.Growingcellsstructures—aself-organizingnetworkfor

unsupervisedandsupervisedlearning.NeuralNetw.7,1441–1460. Fritzke,B.,1995.AGrowingNeuralGasNetworkLearnsTopologies,Advancesin

NeuralInformationProcessingSystems7.MITPress,Cambridge,pp.625–632. Fritzke,B.,1997.SomeCompetitiveLearningMethods(draft),TechniqueReport.

InstituteforNeuralComputation,Ruhr-University,Bochum.

Goutte,C.,Toft,P.,Rostrup,E.,Nielsen,E.F.,Hansen,L.,1999.OnclusteringfMRI timeseries.Neuroimage9,298–310.

Heydar,D.,Ali,T.,Emad,F.,2009.ExtractingactivatedregionsoffMRIdatausing unsupervisedlearning.In:ProceedingsofInternationalJointConferenceon NeuralNetworks,Atlanta,GeorgiaUSA,pp.641–645.

Hyvarinen,A.,Karhunen,J.,Oja,E.,2001.IndependentComponentAnalysis.John Wiley&Sons.

John,A.,Gareth,B.,Chun-Chuan,C.,Jean,D.,Guillaume,F.,Karl,F.,Stefan,K.,James, K.,Vladimir,L.,Rosalyn,M.,Will,P.,Maria,R.,Klaas,S.,Darren,G.,Rik,H., Chloe,H.,Volkmar,G.,Jeremie,M.,Christophe,P.,2013.SPM8Manual, FunctionalImagingLaboratory,TrustCentreforNeuroimaging.Instituteof Neurology,LondonUK.

Katwal,S.B.,2011.AnalyzingfMRIdatawithgraph-basedvisualizationsof self-Organizingmaps.In:IEEEInternationalSymposiumonBiomedical Imaging,Chicago,pp.1577–1580.

Korczak,J.,2007.InteractiveMiningofFunctionalMRIData,Signal-Image TechnologiesandInternet-BasedSystem,(SITIS‘07).IEEEComputerSociety, Washington,DCUSA,pp.912–917.

Korczak,J.,2012.VisualexplorationoffunctionalMRIdata.In:Karahoca,A., INTECH(Eds.),DataMiningApplicationsinEngineeringandMedicine.,pp. 249–264.

Lachiche,N.,Hommet,J.,Korczak,J.,Braud,A.,2005.Neuronalclusteringofbrain fMRIimages.ProceedingofPatternRecognitionandMachineInference, 300–305.

Lange,N.,Strother,S.C.,Anderson,J.R.,Nielsen,F.A.,Holmes,A.P.,Kolenda,T., Savoy,R.,Hansen,L.K.,1999.PluralityandresemblanceinfMRIdataanalysis. Neuroimage10,1999.

Liao,W.,Chen,H.,Yang,Q.,Lei,X.,2008.AnalysisoffMRIdatausingimproved self-Organizingmappingandspatio-temporalmetrichierarchicalclustering. IEEETrans.Med.Imaging27,1472–1483.

Lindquist,M.A.,2008.ThestatisticalanalysisoffMRIdata.Stat.Sci.23,439–464. Martinetz,T.,Schulten,K.,1991.A.NeuralGasNetworkLearnsTopologies,

ArtiﬁcialNeuralNetworks.Elsevier,pp.397–402.

McKeown,M.,Makeig,S.,Brown,G.,Jung,T.,Kindermann,S.,Bell,A.,Sejnowski,T., 1998.AnalysisoffMRIdatabyblindseparationintoindependentspatial components.Hum.BrainMapp.6,160–188.

Mckeown,M.J.,2000.Detectionofconsistentlytask-relatedactivationsinfMRI datawithhybridindependentcomponentanalysis.Neuroimage11,24–35. Pereira,F.,Mitchell,T.,Botvinick,M.,2009.MachinelearningclassiﬁersandfMRI:a

tutorialoverview.Neuroimage45.

Qin,A.K.,Suganthan,P.N.,2004.Robustgrowingneuralgasalgorithmwith applicationinclusteranalysis.NeuralNetw.17,1135–1148.

Rissanen,J.,1983.Auniversalpriorforintegersandestimationbyminimum descriptionlength.Ann.Stat.11,416–431.

SPM,1991.StatisticalParametricMapping.http://www.ﬁl.ion.ucl.ac.uk/spm/. Seghier,M.L.,Friston,K.J.,Price,C.J.,2007.Detectingsubject-Speciﬁcactivations

usingfuzzyclustering.Neuroimage36,594–605.

Skudlarski,P.,Constable,R.T.,Gore,J.C.,1999.ROCanalysisofstatisticalmethods usedinfunctionalMRI:Individualsubjects.Neuroimage9,311–329.

(10)

Sun,X.,Xu,W.,2014.FastimplementationofDeLong’salgorithmforcomparing theareasundercorrelatedreceiveroperatingcharacteristiccurves.IEEESignal ProcessLett.21,1389–1393.

TheAnalysisGroup,2012.FMRIB(Oxford,UK)http://fsl.fmrib.ox.ac.uk/fsl/fslwiki/. Wismuller,A.,Meyer-Base,A.,Lange,O.,Auer,D.,Reiser,M.F.,Sumners,D.,2004.

Model-freefunctionalMRIanalysisbasedonunsupervisedclustering.J. Biomed.Inform.37,10–18.

Yongnan,J.,2010.Data-drivenfMRIDataAnalysisBasedonParcellation,Ph.D Thesis.UniversityofNottingham(October).