第四屆“認(rèn)證杯”數(shù)學(xué)中參賽隊伍的參賽隊號：（請各個參賽隊提前填寫好競賽統(tǒng)一編號（由競賽送至評委團(tuán)前編號競賽評閱編號（由競賽評委團(tuán)評閱前進(jìn)行編號 ActivitiesontheWeb:Thenumberofterrorattacksisincreasingyearbyyear.OnNovember13,2015,theterroristattackthattookceinPariscausedhundredsofdeaths.Thehazardsofcyberterrorismhave emoreandmoreserious.TheUSAhasenactedanumberoflawsaimedatthepreventionofcyberterrorism,suchas“USAPATRIOTAct”.Itisnecessarytoestablishamodelforthepreventionofterroristnetworkspreadandtomonitorandfindthepeoplewithatendencytoterrorism.TheInternetbehaviorysisandriskassessmentmodel(IBARA)wasestablishedfortheInternettoassesstheinternetbehaviorsofthosepeoplewhoaremonitored.Inthispaper,basedonIBARA,wenotonlyresearchtherelationshipbetweenpeople’sInternetbehaviorandtheirpossibleterroristtendency,butalsoyzeanddiscusstherelativetativeriskindexofindividualterrorismtendencyandtherelevantstrategiestopreventterroristattacks.Firstly,theInternetbehaviorwasdividedintotwoparts:Webtextandimage.Thecomplexvectorspaceofwordfrequencyysisalgorithmwasadoptedtoestablishthe tendencyofterrorismriskindexsubmodule(PTTRISM)whichcanpredictpeople’stendencytoterrorism.InPTTRISM,thispaperyzesthebehaviorofindividualWebtextusingthekeywordextractiontechniqueandfrequencyysistechnique.Accordingtotheysisresults,it’sgiventhevalueoftheriskindexofindividualterrorisminthispaper.UsingthePTTRISMtoyzethedatasample,wehaddrawnaconclusionthatmostpeoplewhohavebeenaccesstotheterrorism-relatedinformationarenotlikelyto epotentialterrorists.ThePTTRISMcouldcalculatepeople’sriskindexaboutthetendencytoterrorismthroughyzingInternetbehavior.Secondly,infact,theobjectofnetworkmonitoringisnota butalargenumberofpeople,whichmakestomonitoringdatatoolargeandcomplex.Inordertofacilitatetherapidandefficientclassificationandysisofbigdata,abigdataclusteringstatisticssubmodule(MDCSSM)isestablishedbasedonthetechniqueofdensity-basedclustering.Atthesametime,inordertoshortenthecomputingtimeoftheMDCSSM,inthispaperisadoptedthestandardparticleswarmoptimization(PSO)withtheweight-shrinkfactor.Itrealizedtheeffective,fastandautomaticclusteringysisofdatasets.Validationofthesubmodelusingthedata，Themodelcanbeusedtoyzealargeamountofdata.Duetosacristyofthemonitoringdata,weutilizesomefrequently-testedpublicdatasets,“Iris”,“Glass”,“Wine”and“Aggregation”torecethemonitoringdataandverifytheclusteringalgorithm.Theclusteringresultsdemonstratethattheclusteringalgorithmcancategorizethemonitoringdatasetsinaneffective,fastandautomaticmanner.Finally,Weproposesomesuggestionsto ObamaaboutfightingagainstterrorismasfollowsbasedonIBARA:Putintomoreresourcesintermsofnetworkagainstterrorism.YoucouldbuildUserOnlineMonitoringSystemofBehaviorandPsychologicaltomonitorandassessthebehavioroftheEstablishInformationsecurityevaluationsystemtoweakenandevenpreventtheterroristpropagandathroughthenetwork.Strengthenpublicanti-terrorismeducation,raisepublicawarenessofanti-Duetothetimeconstraints,themodelstillhassomedefectswhichneedtobeimproved.InthePTTRIsubmodule,factorsofvoiceandimagefilesarenotconsidered.IntheMDCSsubmodule,theselectionofadaptivefunctioninClusteringysiscouldbefurtherimproved.Withthefurtherimprovementofthemodel,wewillgetmoreaccurateresults.:PSO,wordfrequencyysisalgorithm,density-basedclustering,terrorism,Internetbehavior TheDescriptionofthe OurApproximationtheWholeCourseofDataMiningToterroristson TheDifferencesinWeightsandSizesofAvailable Terms,DefinitionsandSymbolsin Assumptionsin TheModelofTerrorism-RelatedWebsiteBrowsingandVectorSpaceModelsofLexical TheModelofRisk SolutionsandResultsfor StrengthandWeaknessin Extra Additional TheFoundationofMDCSSMtoCategorizeBig TheResultsof Strengthand Conclusionsofthe MethodsUsedinour Applicationsofour ProposaltoFighting Inordertoindicatetheoriginofweb-relatedterrorismproblems,thefollowingbackgroundisworthmentioning.TerroristcellsareusingtheInternetinfrastructuretoexchangeinformationandrecruitnewmembersandsupporters[1][2](Lemos2002;Kelley2002).Forexample,high-speedInternetconnectionswereusedintensivelybymembersoftheinfamous‘HamburgCell’thatwaslargelyresponsibleforthepreparationoftheSeptember11attacksagainsttheUnitedStates[3](Corbin2002).ThisisonereasonforthemajoreffortmadebylawenmentagenciesaroundtheworldingatheringinformationfromtheWebaboutterror-relatedactivities.ItisbelievedthatthedetectionofterroristsontheWebmightpreventfurtherterroristattacks[2](Kelley2002).OnewaytodetectterroristactivityontheWebistoeavesdroponalltrafficofWebsitesassociatedwithterroristorganizationsinordertodetecttheaccessingusersbasedontheirIPaddress.Unfortunayitisdifficulttomonitorterroristsites[3](suchas‘AzzamPublications’(Corbin2002)sincetheydonotusefixedIPaddressesandURLs.ThegeographicallocationsofWebservershostingthosesitesalsochangefrequentlyinordertopreventsuccessfuleavesdrop. ethisproblem,lawenmentagenciesaretryingtodetectterroristsbymonitoringallISPstraffic[4](Ingram2001),thoughprivacyissuesraisedstillpreventrelevantlawsfrombeingend.Figure1:theannualnumberofterrorists’attackfrom1968toTheDescriptionoftheOurApproximationtheWholeCourseofDataMiningToterroristsonwebsitesHowoftendoestheinternetuserwhoismonitoredvisitthewebsitethatcontainsterrorizedinformationandpropagandaofterrorism.Thelexicalmeaningofcontentsoftheirs,chats,postviewsandtextfilesbeingdownloaded.Asforotherformatsoffiles,suchass,imagesandaudios,thetechniquesoftheimagedescriptionandvoicerecognitionareusedasatooltodetecttheterrorists.Forcategorizingthemonitoringdata,theclustertechniquesareadoptedtosectdatainaneffective,fastandautomaticmanner.PresentsomeusefulsuggestionstoObamaforfightingTheDifferencesinWeightsandSizesofAvailableDuetodifferencesbetweenthecollecteddatasets,it’squitenecessarytopreprocesstheavailabledata,Suchastextdatasets,numericaldatasets,imagedatasetsandevenvoicedatasets.ThePreprocessofTextData:removenon-alphabeticalcharactersfromthetextdatasetandputtheminto cellstructures.ThePreprocessofImageData:removenon-imageryinformationfromtheimagedatasetsandconverttheRGBimagesintothegray-valueimages.Iftheimagedatasetsarepollutedbynoises,it’squitenecessarytodenoiseimagebeforeyzingtherelevantinformation.ThePreprocessofVoice:iftheaudiodatasetsarepollutedbynoises,it’saneedtoimplementaudio-denoisingstepsbeforediggingouttheauditoryinformation.ThePreprocessofNumericalDataset:Duetoexistenceofdifferencesbetweendatasamplesinunitsandmagnitudes,thenumericaldatasetneedstobenormalizedandInthispaperanewmethodologytodetectusersaccessingterroristrelatedinformationbyFrequency-ysisTechniques,VectorSpaceModelsofLexicalMeaning[5],ImageDescription[6]andVoiceRecognition[7],DataCluster[8].Terms,DefinitionsandSymbolsinThesignsanddefinitionsaremostlygeneratedfromourmodelsinthisRistheriskindex,whichdenotestheriskdegreethattheInternetuser

PtP

isthedegreethatthetextcontentsthattheInternetuserinvolvesrelatedtoterrorismduringthetimeintervalPtimageisthedegreethatimagesthattheInternetuserbrowsesanddownloadarerelatedtoterrorismduringthetimeintervalt.PtaudioisthedegreethataudiosthattheInternetuserlistenstoanddownloadarerelatedtoterrorismduringthetimeintervalt.wi,jistheweightfactorofvectorspaceqAssumptionsinThemaindesigncriteriafortheproposedmethodologyTrainingthedetectionalgorithmshouldbebasedonthecontentofexistingterroristsitesandknownterroristtrafficontheWeb.Detectionshouldbecarriedoutinreal-time.Thisgoalcanbeachievedonlyifterroristinformationinterestsarepresentedinacompactmannerforefficientprocessing.Thedetectionsensitivityshouldbecontrolledbyuser-definedparameterstoenablecalibrationofthedesireddetectionperformance.Allinformationrelatedtoterrorismisnotencryptedbyencipheredalgorithms,suchasRSAAllinformationthatcanbemonitoredispresentedbyimages,audiosandNeglectthesocialattributesofthemonitored andonlyconsiderthenetworkpropertiesSpaceModelsofLexicalMeaningOnemajorissueinthismodelistherepresentationoftextualcontentofWebpages.Morespecifically,thereisaneedtorepresentthecontentofterror-relatedpagesasagainstthecontentofacurrentlyaccessedpageinordertoefficientlycomputethesimilaritybetweenthem[9].Thisstudywillusethevector-spacemodelcommonlyusedinInformationRetrievalapplicationsforrepresentingterrorists’interestsandeachaccessedWebpage.Inthevector-spacemodel,theweightwi,jassociatedwithapair(ki,dj)ispositiveandnon-binary.Further,theindextermsinthequeryqarealsoweighted.Letwi,qbetheweightassociatedwiththepair(ki,q)wherewi,q0.Then,thequeryvectorq(w1,q,w2,q,,wt,q)isdefinedaswheretisthetotalnumberofindex.Thevectorfora djisrepresentedbydj(w1,j,w2,j,,wt,j).Thevectormodelproposestoevaluatethedegreeofsimilarityofthe djwithregardtothequeryqasthecorrelationbetweenthevectorsdjandqThiscanbemeasuredbythecosineoftheanglebetweenthesetwovectorsddqsim

(3-1- Whered and arethenormsofarethenormsof andvectors.Inthevectorspacemodel,thefrequencyofatermkiinside d

i,

N

(3-1-Thenormalizedfrequencyof ki djisgiven freqi, (3-1-i,jmax(freqi,Thebestknownterm-weightingschemesuseweightswhicharegivenwi,jfi,jlog(freqi,j (3-1-InthispapereachWebpageinconsideredasaandisrepresentedasavector.Theterrorists’interestsarerepresentedbyseveralvectorswhereeachvectorrelatestoadifferenttopicofinterest.ThequeryofthemethodologydefinesandrepresentsthetypicalbehaviorofterroristusersbasedonthecontentoftheirWebactivities.ThequeryisbasedonasetofWebpagesthatweredownloadedfromterroristrelatedsitesandisthemaininputofthedetectionalgorithm.ItisassumedthatitispossibletocollectWebpagesfromterror-relatedsites.ThecontentofthecollectedpagesistheinputtotheVectorGeneratormodulethatconvertsthepagesintovectorsofweightedterms[10](eachpageisconvertedtoonevector).Inordertodefinethedegreethattheinternetuserbrowsestheterrorism-relatedwebsitesduringthetimeintervalt,theformulab(m)isdefinedbythefunctiontheinternetuserbehaveslikeapotentialterroristwhenbrowsingthewebsitemaswhere(x)

b(m)simxPtext

(3-1-(3-1-Inthispaper,weadopt0.5asthevalueofthreshold.Thequeryinthispaperislistedinthetablebelow.Detailsof1Bomb2345Attackto6cStateofIraqandalShams789cTheModelofRiskHerewereporttheremarkablefindingthatidenticalpatternsofarecurrentlyemergingwithinthesedifferentinternationalarenas.NotonlyhavethewarsinIraqandColombiaevolvedtoyieldasamepower-lawbehavior,butthisbehavioriscurrentlyofthesametativeformasthewarinAfghanistanandglobalterrorisminnon-G7countries.Notonlyisthemodel’spower-lawbehaviorinexcellentagreementwiththedatafromIraq,Colombiaandnon-G7terrorism,itisalsoconsistentwithdataobtainedfromtherecentwarinAfghanistan.Power-lawdistributionsareknowntoariseinalargenumberofphysical,biological,economicandsocialsystems.Inthepresentcontext,apower-lawdistributionmeansthattheprobabilitythataneventwilloccurwithbehaviorPisgivenby[12]R(P) (3-1-whereP(0,1],PPtextandCandαarepositivecoefficients[13][14],tstudieshaveshownthatthedistributionobtainedfrompastterrorists’attackexhibitsapower-lawwith[15]=1.809.Sincewecan’tgetthecoefficientsCeffectively,wedefinearelativeriskindexramongagroupofpeoplewhoaremonitoredduringthespecifictimeintervalasar aRa

(3-1-SolutionsandResultsforTheSolutionStepstoGenerationofTerm-FrequencyItisterm-frequencymatrixofalluniqueterms dj j1,2,,NTheterm matrixFreqisaMNmatrixwithtiuniquetermsindictionaryi1,2,,Mand stheelementsofFreqarerepresentedas freqi,jwhicheachelementindicatesthefrequencyofitermin TheCranfielddatacollectionispreprocessedtoconvertintoindividual1398textfiles.Also,non-embeddingspecialcharactersandnumeralshavebeenremovedfromthesefiles.79,728wordshavebeencollectedwhicharethenprocessedtofindthefrequencyofuniquewordsineachs.Thedictionaryofuniquewordsisof7805words.Thusthetermfrequencymatrixisofsize78051398.GenerationofQuerymatrixandTerm-weightcalculationsandAfterremovingstop-listwordsandnon-embeddingspecialcharactersisusedasquery,whichcontributestothesetof1398uniquequeriesrepresentedasq.Here,wehavetakenqueriesastitlesoftheinsteadofthedatasetqueriessoastojudgetherelevancymoreprofoundly.Thegeneratedmatrixfor1398queriesisQ .Aterm-frequencymatrixisprocessedtogetthetermweightsconsideringterm-weightingTheResultsofFigure2:IndextermsinaFigure2showsthedistributionofindextermsindictionaryforindividuals.Thedictionaryconsistsof7805uniqueterms.Figure3:FrequencycountofeachuniquetermamongdataFigure3showsfrequencycountofeachuniquetermindictionarydistributedincompletedataset.Someoftheuniquetermssuchas(‘ISIS’,2059),(‘Qaeda’,1245),(‘hijack’,1076),(‘Assassination’,897),withhighfrequencyinentiresisFigure4:thedistributionofthePvalueamongthe Figure5:thedistributionofthervalueamongthe IntheFigure5,wedefine0.1asthethresholdoftheriskindex.Ifaone’sriskindexisbeyond0.1,heorshecan eapotentialterrorist,andotherwisemorelikelytobeanordinaryFromthe1398individualtextfilesthatareobtainedfrom1398individuals,wecaneasilydrawaconclusionthatmostpeoplewhohavebeenaccesstotheterrorism-relatedinformationarenotlikelyto epotentialterrorists.Therearejust12onesofallmonitored swhoarelikelyto epotentialterrorists,besidesalltheirriskindexesarebeyond0.1.StrengthandWeaknessinStrength:Themodelhasprovedthatwecandetectanddiscriminateterroristsfrommanyinternetuserswhoaremonitoredforthepurposeofpreventingterrorism.Moreover,wehavedrawnsomeusefulconclusionsaboutthetendencyofterrorism.Throughthecalculationofthemodel,wecanfindthatmostpeoplewhoaremonitoredandhaveaccesstotheinformationofterrorismwillnotbelikely eapotentialterrorist.Themodelcanbeappliedtosuchthoseactivities,terroristsurveillanceandcriminalactivitymonitoring.Weakness:Thismodeljustappliestoyzethetextinformationofthosepeoplewhoweremonitored.Aswehavestatedinthearticle,thenetworkbehaviorofthemonitored maybeyzedfromthreeaspectsofinformation,thatis,text,imageandwebsite.Inourmodel,weuseonlythefrequencyysisofthetexttoevaluatetheriskindexofthe whoismonitoredonreal-time.Expertsusetheexpressivebigdatatoindicatehugeamountsofinformation.Especiallyinthecontemporaryinformationalworld,bigdatacanrevealalotofinformationthatishiddenbehindthebigdata.Theyticaltechniquesofbigdatacanbeutilizedtofightagainstterrorism.Butunlikethetraditionaldatamining,dataysisofterrorism-relatedinformationneedscategorizingtheminaneffective,fastandautomaticmanner.Inthispaper,wepresentanewclusteringalgorithmtocategorizebigdata.ExtraSignsanddefinitionsindicatedabovearestillvalid.Herearesomeextrasignsandivtisthevelocityofparticleiat tioniixtisthepositionofparticleiat tionirdi,jisthedistancebetweenthesampleiandthesample(x,

istherelativecoordinatepairbasedtherdi,AdditionalThetestdatasetinthepapercanbeequivalenttothemonitoringTheclusteringalgorithmcanobtainhowmanygroupsofthedatasetandhowmanyremaindersineachgroup,butcan’tachievetoobtaintheinformationofeachTheFoundationofMDCSSMtoCategorizeBigIntermsofclustering’sobjectives,theaimsofdataclusteringareminimizesimilarityamonginstanceinoneclusterandizedissimilaritybetweentwoclusters.ParticleSwarmOptimization(PSO)isapopulation-basedsearchalgorithmwhichsimulatesbirdbehaviorinfindingfood[16].InPSO,birdsrepresentedasparticleareemployedtoperformsolutionexploration.Particleatanyinitialpositionmovestootherpositionwithacertainvelocityanddirection.Ineveryitionvelocityisadjustedbasedonparticlebestsolutionandsocialbestsolution.ThevelocityofeachparticleisEquatio（3-updatedusingEquation（3-2-2）.ThisconceptmakesPSO esdifferentwithotherheuristicmethods[17].vt1wvtcr(pbestxt)cr(gbestxt 1 2 xt1vt Wherevt tarevelocityandpositionofparticleiat tiont, Thenotationwisdefinedasinertiaweight.Thisisamechanismtocontroltheexplorationandexploitationabilitiesoftheparticleandalsotoeliminatetheneedforvelocityclam.Inthispaper,PSOalgorithmisextendedsothatitcan automaticclusteringproblem.Generally,therearetwomajorissuesinsolvingautomaticandfastclustering,namelydeterminingclusternumberandfindingclustercentroids.Inorderto modatethesetwoobjectives,theautomaticclusteringalgorithmemploysaparticlewhichcomprisesoftwosections.Thefirstsectionisresponsibleforrepresentingnumberofclusterswhiletheothersectioninformsclustercentroids.Explorationstepisconductedtowardsthesetwosectionsgradually.Afterupdatingasection,infeasibilityconstraintwillbechecked[18].Itcoversfeasiblenumberofclustersandcluster’ssize.Inaddition,k-meansisperformedtoupdatethesecondsectionofeachparticlebasedonactiveclustersobtainedbyitsfirstsection.Figure6:flowchartofthemodelAparticlecomprisesoftwosections.Sectiononerepresentsnumberofclusterswhilesectiontwogivesinformationregardingclustercentroidordatapointsbelongstothecorrespondingcluster.Throughthisscheme,eachparticlehasitsownexplorationpathsothatthesearchspacecanbeexploredwideranddeeper.SupposesdataclusteringisconductedtowardsagivendatasetD{dj|i1,2,,S}whereSisnumberofdatapointsanditconsistsofMattributes.Lettheappropriatenumberclustersisanintegernumberintherange[2,Nmax],whereNmaxispumnumberofclusters.Aparticlepin tiontsymbolizedasXtpof(1M)Nmaxbitsasillustratedasthefollowing pNAllbitsarecontinuousnumberwithin[0,1].The Nmaxbitsrepresentsporinactiveclusters.Clusterkinparticlepisanactiveclusterifthekthbit Xtpgreaterthanorequalto0.5.Otherwise,thecorrespondingclusterisinactive.Furthermore,therestbitscorrespondtoclustercentroid.Theinitialparticleandvelocityaregeneratedrandomly.EachbitiinaparticleisupdatedusingEquationguaranteefeasibilityofthenextparticle.Inthisadditionalprocedure,vt1wtv

cr(yxt)cr

xt

（3-2-

xt1xtvt Inthisadditionalprocedure,ifresultfromEquation（3-2-9）,isoutside[0,1],xt1sigmoid(xpi),ifx

xt ,vt velocityoftheithbitinparticlepfor tiontypt ithbitinparticleypt iz theithbitinglobaliInupdatingthevelocity,twoparametersarerequired.Thereareinertiaweightw,andlearningratec1andc2.Theclusteringalgorithmappliestime-varyinginertiaweight.Herein,theinertiaweightlinearlydecreasesbasedontheEquation（3-2-11）,w

(wmaxwmin)

max heretheTistotali tionandtiscurrentition.1)Procedureforevaluatingnumberofclusters[20].GivenparticleXt{xt,..., },NareactiveclustersinXt,and|N| pNmax numberofactiveIf|NpGeneratetheintegernumberi,j{1,...,Nmax},iIfxtxtxt |Np|=|NpEndIfxtxtxt |Np|=|NpEndifEndif2)Procedureforevaluatingcluster'sGivenparticleXt{xt,..., },NisactiveclustersinXt,and|N|is pNmax numberofactiveclusters,and|xt|issizeofcluster Fori=1toIfxtIf|xt|2and|Npxtxt If|xt|ReassigndatatoanotherclusterwhichhastheshortestdistanceEndif|Np||Np|1ElseifChooseanydatapointsdq,drD,qx betheoriginalclusterofdqandAssigndatad,dtocluster xtxt EndifEndfor

xx xxInthispaper,thefitnessfunctionofPSOclusteringalgorithmisgivenas2

(Npp2

min{cicj1)i,jNp,i

（3-2-

TheResultsofSincethescarcityofthebigmonitoringdata,otherdatasetsareadoptedtotestourclusteringalgorithmofparticleswarmoptimization,suchas“Iris”,“wine”,“Glass”and“Aggregation”fromthepublicdatasetwebsites.Afterfinishingclusteringtodata,thecategorizeddataneedstobevisualizedinadirectmanner.Forone-dimensionalorMtwo-dimensional,eventhreedimensionaldata,thedatasetcanbedirectlyvisualizedintheCartesiancoordinate.Butforhighdimensional,thedatasetcan’tbevisualizedintheCartesiancoordinate,thusatechniqueofdimension-reductionisintroducedinthispaper,themultidimensional-scalingmethodisintroducedasfollows[21]:M )2(M i, jkn

((xx)2(yy)2rd2 i, s.txi0,xjInthedatasetIris,thereare150sampleswith4attributes.Thus,it’saneedtodemonstratetheclustercentersandclusterresultsintwodifferentgraphs.Figure7:ClustercentersIrisdatasetinarelativecoordinateFromtheFigure7itcanbeeasilyconcludedthattherearethreeclusteringcentersinthedatasetIris,whichmeansthedatasetIriscanbegroupedintothreeFigure8:ClusterdistributionofIrisdatautilizingPSOclusteringFromtheFigure8,thedatasetIriscanbeseparatedintothreegroupsastheparticleswarmoptimizationgoesonlikethefourstep-shapedsubgraphsintheFigure7.Figure9:ClustercentersandClusterdistributionof“Wine”FromtheFigure9wecangetthatthe“Wine”datasetwasobviouspointedtotwokindsbythefastclusteringmodelbasedonPSOalgorithmClustercentersandClusterdistributionweregivenintheFigure8Figure10:ClustercentersandClusterdistributionof“glass”FromtheFigure10,Thedataof“glass”datasetwasdividedintotwogroupsastheparticleswarm.Inthegraph,thetwocategoriesofdataareclustered.Figure11:ClustercentersandClusterdistributionof“Aggregation”FromtheFigure11,wecangetthatthe“Aggregation”datawasseparatedintothreegroupsastheparticleswarm.ThefastclusteringmodelbasedonthePSOplishedtheclusterof“Aggregation”StrengthandStrength:Theclusteringmodelcanachievethegoalofcategorizingthedatasetsinaneffective,fastandautomaticmanner.Andthisclusteringmodelalsoaimstomakeupfortheignoranceofthesizeofdatasetswhichisthoughtnothavemuchinfluenceontheaccuracyoftheclusteringresults.Anothergiantadvantageoftheclusteringmodelisthatitdoesnotneedanypriorknowledge.Thisclusteringalgorithmbelongstounsupervisedlearning.Weakness:Theclusteringmodelneedscomparativelygoodinputparameters,suchasthethresholdvalueofclusteringradius.Andalsothefitnessfunctionissensitivetotwopenaltyfactors.ConclusionsoftheForthePTTRISM,thevectorspaceoflexicalmeaningandwordfrequencyysisdemonstratetheirpracticabilityinevaluatingtheriskindexesofpeoplewhoaremonitoredon-lineandreal-time.ThroughCatanfielddatasetsvalidation,andincombinationwiththerealsituation,onlyaveryfewpeoplearelikelytoeapotentialterroristbygiventhesetthresholdvalueoftherelativeriskindex(0.1).TheresultofCatanfielddatasetshowsthatonly12peoplefrom1398individualsshoulddeserveformuchmoreattention,becausetheirriskindexesarethesetthresholdvalueoftherelativeriskindex.FortheMDCSSM,theclusteringtechniqueofparticleswarmoptimizationcanachievethegoalofcategorizingthebigmonitoringdatainaneffective,fastandautomaticmanner.InordertovalidatethepracticabilityoftheFunctionModel1,themodel2mustbetestedbysometough-processingdatasets.Butduetoscarcityofthebigmonitoringdatasets,someotherequivalentdatasets,suchas“Iris”,“Wine”,“Glass”and“Aggregation”arerecedforthebigmonitoringdata.Theexperimentalresultsdodemonstrateagoodperformanceofclusteringdatasetsinaneffective,fastandautomaticmanner.MethodsUsedinourThecombinationofthevector-spaceoflexicalmeaningandword-frequencyysispromotesthereliabilityofwebtextcontenttoevaluatetherelativeriskindex.Theadoptionoftheentropyweightbasedoninformationretrievalenhancestheysisoftheinternetvisitors’typicalbehaviors.Theunsupervisedlearningtechniqueofdensity-basedclusteringisutilizedtoseparatethecategoriesofdatasets,inordertoacceleratethecomputingtime,thestandardparticleswarmoptimizationwiththeweight-shrinkfactorisadoptedinthispaper,andmoresignificantly,basedtheessentialthoughtsofparticleswarmoptimization,theclusteringproceduresresemblestheoptimizationprocedurestoachievethegoalofcategorizingtheinformationaldatasetinaneffective,fastandautomaticmanner.ApplicationsofourThemodel1doesnotonlyhelpevaluatetheinternetvisitors’behaviorsanddetect,evendiscriminatethevisitor’sidentity,butalsoprovidearobusttoolforcommercialpeoplethatcanbeappliedtodigoutpotentialcustomers.Themodel2isapplicabletomanyothersubjects,besidesdatamining.Someacademicresearchershavealreadysuccessfullyappliedk-meansclusteringtoimageprocessing,suchasimagesegmentation,edge-detection.Thisclusteringalgorithmcanrecethek-meansclusteringinimageFromthestatisticsoftheannualnumberofterrorists’attackfrom1968to2009,thenumberofterrorists’attackisincreasingyearbyyears.Theterroristattackshavecausedabadinfluenceonworldpeace.Manycountriesintheworldhavecommittedtocarryouttheactivitiestofightingterroristorganizations.Forexample,RussiandispatchedfighterstobombISIS,arepresentativeofworldterroristorganizations.Thusitisimperativetofightterroristsandprevent.Therearethreestrategiesthatmayhelpfightterrorismasfollows:Putintomoreresourcesintermsofnetworkagainstterrorism.YoucouldbuildUserOnlineMonitoringSystemofBehaviorandPsychologicaltomonitorandassessthebehaviorofthepublic.It’sfoundthatonlyfewpeoplehastendencyofterrorism.Youcouldestablishnetworkinformationsecurityevaluationsystemtoweakenorevenpreventtheterroristpropagandathroughthenetwork.Itisafeasiblewaytounitglobalnetworksystemtomonitoronlineusers’behavior.Becauseterroristsorpeoplewhohaveatendencytoterrorismspreadaroundtheworld,particularlyintheMiddleEastandAfghanistan.Bythisway,wecanmastertheactionofterrorismo