Simulating Crimes and Crime Patterns Using Cellular Automata and GISWord格式.docx
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Simulating Crimes and Crime Patterns Using Cellular Automata and GISWord格式.docx
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LinLiu*lin.liu@uc.edu,
JohnEck**eckj@email.uc.edu
*DepartmentofGeography
**DivisionofCriminalJustice
UniversityofCincinnati
Cincinnati,OH45221-0131
1.Introduction
1.1Problemstatement
ThepurposeofthisresearchistodesignandimplementaCellularAutomata(CA)crimesandcrimepatternssimulationmodelandintegrateitwithGeographicalInformationSystems(GIS).CA,adigitalcomputationconceptwhichemergedin1940s,hasbeenappliedtogeographicscienceinrecentdecades,andwasprovenitsvalueformodelingandvisualizingcomplexspatiallydistributedprocesses.MostofCAsimulationmodelshavebeendevelopedinecologicalscience,environmentalscience,andcityplanning(Takeyama,1997;
Wu,2000).
Undercurrentcomputersoftwaredevelopmentconditions,itisratherdifficulttoimplementCA,orotherspatial-temporalbasedcomplexsimulationmodels.Differentapproacheshavebeenexploredtobuildspatial-temporalsimulationmodels.Twomajorapproachesexist,eithermakinguseofcommercialGISsoftware,ornot.Bothapproachesrequireacertaindegreeofsoftwaredevelopmentexperience.Becauseofthistechnicalbarrier,spatial-temporalsimulationmodelershavetospendmoretimeontechnicalissues,whichcomplicatestheapplicationofCAandotherspatialsimulationtheories.Thisresearchdevelopedadynamiccrimepatternsimulationmodelfromastaticcrimemodel,andloose-coupleditwithArcviewGIS.Anexternalcrimesimulationmodulewasfirstdevelopedwithanobject-orienteddesign(OOD)paradigm.Withintheframeworkofthissimulationsystem,customizedGISservesassysteminterface.GISalsosaveseffortsonspatialdataorganization,visualization,andanalysis.Ontheotherhand,thoughOODrequiresprogrammingknowledgebythemodeler,itreducesredundancyforfuturedevelopmentaswellastimeforexpandingexistingsimulationmodels.
Thisresearchhaschosencommercialpropertyrobberysimulationasanexampleforintegratingaspatial-temporalsimulationmodelwithGIS.ThesimulationmodelappliedCAandMonteCarlotheorytothecrimelikelihoodevaluationformulafromroutineactivitytheory(RAT).Thesimulationprocessrunsthroughmanyiterations,eachgeneratingsomeindividualcrimes.Theaccumulationofindividualcrimesrevealscrimepatternsinspaceandtime.
1.2Whychoosingcrimepatternssimulation?
Thecomplexityanduncertaintyofcrimepatternsmakeanidealillustrationofsuchresearch.Crimepatternsdevelopsovertimeperiodasaresultofinteractionsbetweentargetandoffendersoverspace.Acrimeoccurswhenatargethasbeenattackedbyanoffender(oragroupofoffenders).Bothtargetandoffenderhavebeenstudiedextensivelyincriminologyliterature.However,interactionsbetweenthemarerarelyaddressedduetotheircomplexity.In1979,RATwasdevelopedbyFelsonandCohen.RATisamicro-leveltheory.Itdescribesaunitofanalysis,thecriminalevent,andtheminimalelementsrequiredforoccurrence.RATstatedthatifacrimeistooccur,anoffenderandatargetmustcometogetheratthesameplaceandtimewithoutthepresenceofanyonewhocouldandwouldprotectthetarget.AlthoughRATprovidesawaytostudycrimebylookingintotherelationshipsbetweenallrequiredcomponents,itisstillnotapplicableforevaluatingpotentialindividualcrimeeventinthefuture.Eck(1995b)discussedthedifficultyoftestingRAT.ToevaluateifacrimeoccurswithRAT,wemustknowallsixconditions(target,offender,place,management,guardianship,andhandling)atthesamemoment.Collectingspatial-temporaleventdataisnotsufficienttoovercomethisproblem.Thus,testthemodelwithactualdataisratherdifficult.
However,withCAandMonteCarlosimulations,wecanmodeltheinteractionbetweentargetsandoffendersoverspaceandtime.Wehavedevelopedtheconceptoftensiontosimulatetargets’reactiontowardsoffenders.IntheCAmodel,acellhasmultiplevalues,whichincludetension;
andalltargetvariables,suchasdesirability,managereffectiveness,etc.Tensionvaluechangeswhenacrimeoccurs,orwhenspatialinteractionoccursbetweenatargetanditsneighborhood.Atargetpreventionindexvaluecanthenbeevaluated,sincealltargetvariablesdirectlyorindirectlyrelatetotension.Theoffenders'
movementisdeterminedbyaMonteCarlosimulation.MonteCarlosimulationsassumethatoffenderswillmorelikelyvisittargetsclosetothem,andtargetswillmorelikelyattractoffendersclosetothemaswell.Soitisclearthatthiscrimesimulationmodelisacombinationoftwoapproaches-CAandMonteCarlosimulation.Inthismanner,wehaveawaytotraceboththemovementofindividualandtheindividualtargets’reactiontooffenders.
1.3ExpandingCA’sCapability
AnotherreasonforchoosingcrimepatternsimulationistoexpandCA’sapplicationtoinvisiblespatial-temporalprocesses.MostCAapplicationshaveoccurredinecology,urbanplanningandenvironmentstudies.OneoftheCAcoreelementsisstatevariable.Statevariablesrepresentthestatusofcells,whicharethefocusofthemodeling.Landusetypeandnumberofpollutantparticleareexamplesofstatevariable.Comparedwithvisiblephenomena,itismoredifficulttosimulatespatial-temporalchangesofinvisiblephenomenawithCAmodeling.Tosimulationcrimepatterndevelopingprocessfromamicro-level,firstweneedtofindouttheinvisiblephenomenonwhichbroadcastoverspaceandtime,andsetitasstatevariable.Theothervariablescanthenberelatedtothestatevariabledirectlyorindirectly.
2.CAandSpatialSimulation
2.1CellularAutomata
Cellularautomata(CA)couldbetracedbacktotheverybeginningsofdigitalcomputation.In1940s,JohnvonNeumannfirstdevelopedtheideaofCA.TheoriginalideaofCAisself-reproducible.Atthattime,Neumanntriedtofindatheoryofmachinesthatwouldreproducethestructurebyitself.CAdidnotbecomepopularuntil1970,whenamathematicianinCambridge,England,suggestedaparlorgamecalled'
Life'
whichcombinedallthenotionsofCAinamodelwhichsimulatedthekeyelementsofreproductioninthesimplestpossibleway.
CAisamicro-levelmodelingapproach.First,unit(usuallygrid)analysiswillbeperformedonaspatial-temporalbasedprocess.Thenthespatialrelations/ruleswillbesetupforthegridbetweenitanditsneighborhood.Finally,afterinitialconditionsaregiven,theCAsimulationisreadytouse.CAhasbeenusedtosimulatespatial-temporalprocessessincetheearlyof1990s.Almostalltheseapplicationssimulatevisiblephenomena.Intheearlystage,CAwasappliedtowaterquality,ecologyandforestfiremodeling.Clarke(1998)indicatedthattheprogressinecologywasduetotheindividualbasedecologicalmodels,andtheconceptthatcomplexaggregatepatternsoftencomefrommanyinteractingself-motivatedagents.Thesameargumentalsoholdsforwaterqualitystudies.CAwaterqualitymodelsoftendevelopfrommicro-levelpollutantdiffusionequation.Castroetal.(1993)inhisdissertationdevelopedariverBiologicalOxygenDemand(BOD)/DissolvedOxygen(DO)modelbasedoncellularautomata.Costa(2000)’sstudyinwaterqualitymodeling,thedispersionprocessofparticlewassimulatedfollowingarandomwalkapproach.Recently,someland-useCAmodelshavebeendeveloped(TakeyamaandCouclelis,1997;
Clarke,1998;
Wu,1999;
Wu,2000).Landusetypechangingrules,andspatialrelationsbetweenagridanditsneighborsareoftenthefocusoftheseapplications.
CAdescribestheworldbyusingdiscretespaceandtimevariables.Inatwo-dimensionalspace,itcouldbeviewedascellswithsamedimension.Generally,CAconsistsoffourelements,whichcouldbeconsideredasatuple(X,S,N,f).
Xarecellswhichareobjectsinanydimensionalspace,wecancallthiscellarspace(Takeyame,1997).Sisanonemptyfinitesetofautomatonstates.Eachcellcantakeononlyonestateatanyonetimefromasetofstates,sS.Third,thestateofanycelldependsonthestatesandconfigurationsofothercellsintheneighborhoodnofthatcell.Finally,fisstatetransitionfunctionorrule,fF.=f(,).Thetransitionrulewilltaketheprevious(timet)statusofacell,andthestatusofitsneighborhoodasinput,andreturnthestatusattimet+1.
CAisoneofthedynamicspatialsimulationmodelingapproaches.Thecoreissueistofindthestatevariable,orvariables.Cell,orspatialunitinteractswitheachotherbecauseofthedifferenceoftheirstatesand/ortheirlocations.Thestateofacellmayimpactanothercell’sstateoverdistance,afterafewsimulationiterations.Forvisiblespatial-temporalprocesses,statevariablesofspatialunitaremoreunderstandableandeasytofind.Forestfire,pollutantparticles,landusetypesaresomeofthetypicalexamples.Invisiblespatialbroadcastingprocessesareoftenfoundinsocialphenomena.Thoughtheymaybemicro-leveltheory,suchasRAT,mostsocialtheoryarenotcellarbased,andtheyarehardtoquantifyorfilteroutspatialvariablefromothertheoreticalcomponents.ThispaperdesignedaCAcrimepatternsimulationmodel,developedfromcrimelikelihoodevaluationequationfromEck(1995b).Wehavedevelopedtheconceptoftensiontosimulatethecellarbasedbroadcastingofimpactscausedbycrime.Thisapproachprovidesaviablesolutionforapplyingcellularautomatatheorytoinvisiblespatial-temporalprocesses.
2.2Majorapproach
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