Simulating Crimes and Crime Patterns Using Cellular Automata and GIS.docx

Simulating Crimes and Crime Patterns Using Cellular Automata and GIS.docx

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SimulatingCrimesandCrimePatternsUsingCellularAutomataandGIS

SimulatingCrimesandCrimePatternsUsingCellularAutomataandGIS

JunLiang*liangjn@email.uc.edu,

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