美赛数学建模优秀论文

美赛数学建模优秀论文

WhyCrimeDoesn’tPay:LocatingCriminals

ThroughGeographicPro ling

ControlNumber:#7272

February22,2010

Abstract

Geographicpro ling,theapplicationofmathematicstocriminology,hasgreatlyimprovedpolicee ortstocatchserialcriminalsby ndingtheirresidence.However,manygeographicpro leseithergenerateanextremelylargeareaforpolicetocoverorgeneratesregionsthatareunstablewithrespecttointernalparametersofthemodel.Wepropose,formulate,andtesttheGaussianRossmooth(GRS)Method,whichtakesthestrongestelementsfrommultipleexistingmethodsandcombinesthemintoamorestableandrobustmodel.Wealsoproposeandtestamodeltopredictthelocationofthenextcrime.WetestedourmodelsontheYorkshireRippercase.OurresultsshowthattheGRSMethodaccuratelypredictsthelocationofthekiller’sresidence.Additionally,theGRSMethodismorestablewithrespecttointernalparametersandmorerobustwithrespecttooutliersthantheexistingmethods.Themodelforpredictingthelocationofthenextcrimegeneratesalogicalandreasonableregionwherethenextcrimemayoccur.WeconcludethattheGRSMethodisarobustandstablemodelforcreatingastrongande ectivemodel.

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美赛数学建模优秀论文

Controlnumber:#72722Contents1Introduction2PlanofAttack3De nitions4ExistingMethods

4.1GreatCircleMethod.........................

4.2Centrography.............................

4.3Rossmo’sFormula..........................5Assumptions

6GaussianRossmooth

6.1PropertiesofaGoodModel

6.2OutlineofOurModel...

6.3OurMethod.........

6.3.1RossmoothMethod.

6.3.2GaussianRossmooth....................Method................................................................................44455688101011111114

15

15

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197GaussianRossmoothinAction7.1FourCorners:ASimpleTestCase.........7.2YorkshireRipper:AReal-WorldApplicationofthe7.3SensitivityAnalysisofGaussianRossmooth....7.4Self-ConsistencyofGaussianRossmooth.........GRS...........Method..........

8PredictingtheNextCrime20

8.1MatrixMethod............................20

8.2BoundaryMethod..........................219BoundaryMethodinAction

10Limitations

11ExecutiveSummary

11.1OutlineofOurModel.

11.2RunningtheModel...

11.3InterpretingtheResults

11.4Limitations.......

12Conclusions

Appendices

AStabilityAnalysisImages............................................................................................21222323232424252525

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美赛数学建模优秀论文

Controlnumber:#72723ListofFigures1Thee ectofoutliersuponcentrography.Thecurrentspatial

meanisatthereddiamond.Ifthetwooutliersinthelowerleft

cornerwereremoved,thenthecenterofmasswouldbelocated

attheyellowtriangle.........................

Crimesscenesthatarelocatedveryclosetogethercanyieldillog-

icalresultsforthespatialmean.Inthisimage,thespatialmean

islocatedatthesamepointasoneofthecrimescenesat(1,1)..

ThesummandinRossmo’sformula(2B=6).Notethatthe

functionisessentially0atallpointsexceptforthesceneofthe

crimeandatthebu erzoneandisunde nedatthosepoints..

ThesummandinsmoothedRossmo’sformula(2B=6,φ=0.5,

andEPSILON=0.5).Notethatthereisnowaregionaround

thebu erzonewherethevalueofthefunctionnolongerchanges

veryrapidly...............................

TheFourCornersTestCase.Notethatthehighesthotspotis

locatedatthecenterofthegrid,justasthemathematicsindicates.

CrimesandresidencesoftheYorkshireRipper.Therearetwo

residencesastheRippermovedinthemiddleofthecase.Some

ofthecrimelocationsareassaultsandothersaremurders.....

GRSoutputfortheYorkshireRippercase(B=2.846).Black

dotsindicatethetworesidencesofthekiller............

GRSmethodrunonYorkshireRipperdata(B=2).Notethat

themajordi erencebetweenthismodelandFigure7isthatthe

hotzonesinthis gurearesmallerthanintheoriginalrun....

GRSmethodrunonYorkshireRipperdata(B=4).Notethat

themajordi erencebetweenthismodelandFigure7isthatthe

hotzonesinthis gurearelargerthanintheoriginalrun.....

TheboundaryregiongeneratedbyourBoundaryMethod.Note

thatboundaryregioncoversmanyofthecrimescommittedby

theSutcli e..............................

GRSMethodon rstelevenmurdersintheYorkshireRipperCase

GRSMethodon rsttwelvemurdersintheYorkshireRipperCase62739413155616177818919101112222526

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美赛数学建模优秀论文

Controlnumber:#727241Introduction

Catchingserialcriminalsisadauntingproblemforlawenforcemento cersaroundtheworld.Ontheonehand,alimitedamountofdataisavailabletothepoliceintermsofcrimesscenesandwitnesses.However,acquiringmoredataequatestowaitingforanothercrimetobecommitted,whichisanunacceptabletrade-o .Inthispaper,wepresentarobustandstablegeographicpro letopredicttheresidenceofthecriminalandthepossiblelocationsofthenextcrime.Ourmodeldrawselementsfrommultipleexistingmodelsandsynthesizesthemintoauni edmodelthatmakesbetteruseofcertainempiricalfactsofcriminology.

2PlanofAttack

Ourobjectiveistocreateageographicpro lingmodelthataccuratelydescribestheresidenceofthecriminalandpredictspossiblelocationsforthenextattack.Inordertogenerateusefulresults,ourmodelmustincorporatetwodi erentschemesandmustalsodescribepossiblelocationsofthenextcrime.Addi-tionally,wemustincludeassumptionsandlimitationsofthemodelinordertoensurethatitisusedformaximume ectiveness.

Toachievethisobjective,wewillproceedasfollows:

1.De neTerms-Thisensuresthatthereaderunderstandswhatwearetalkingaboutandhelpsexplainsomeoftheassumptionsandlimitationsofthemodel.

2.ExplainExistingModels-Thisallowsustoseehowothershaveat-tackedtheproblem.Additionally,itprovidesalogicalstartingpointforourmodel.

3.DescribePropertiesofaGoodModel-Thisclari esourobjectiveandwillgenerateasketelonforourmodel.

Withthisunderlyingframework,wewillpresentour …… 此处隐藏：17586字，全部文档内容请下载后查看。喜欢就下载吧 ……