B Centroids Clusters and CrimeWord文件下载.docx

B Centroids Clusters and CrimeWord文件下载.docx

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Boulder,CO

Advisor:

AnneDougherty

Abstract

Aparticularlychallengingproblemincrimepredictionismodelingthebehaviorofaserialkiller.Sincefindingassociationsbetweenthevictimsisdifficult,wepredictwherethecriminalwillstrikenext,insteadofwhom.Suchpredictingofacriminal’sspatialpatternsiscalledgeographicprofiling.

Researchshowsthatmostviolentserialcriminalstendtocommitcrimesinaradialbandaroundacentralpoint:

home,workplace,orotherareaofsignificancetothecriminal’sactivities（forexample,apartoftownwhereprostitutesabound）.These“anchorpoints”providethebasisforourmodel.

Weassumethattheentiredomainofanalysisisapotentialcrimespot,movementofthecriminalisuninhibited,andtheareainquestionislargeenoughtocontainallpossiblestrikepoints.Weconsiderthedomainametricspaceonwhichpredictivealgorithmscreatespatiallikelihoods.Addition-ally,weassumethattheoffenderisa“violent”serialcriminal,sinceresearchsuggeststhatserialburglarsandarsonistsarelesslikelytofollowspatialpatterns.

Therearesubstantialdifferencesbetweenoneanchorpointandseveral.Wetreatthesingle-anchor-pointcasefirst,takingthespatialcoordinatesofthecriminal’slaststrikesandthesequenceofthecrimesasinputs.Estimatingthepointtobethecentroidofthepreviouscrimes,wegeneratea“likelihoodcrater,”whereheightcorrespondstothelikelihoodofafuturecrimeatthatlocation.Forthemultiple-anchor-pointcase,weuseacluster-findingandsortingmethod:

Weidentifygroupingsinthedataandbuildalikelihoodcrateraroundthecentroidofeach.Eachclusterisgivenweightaccordingtorecencyandnumberofpoints.Wetestsinglepointvs.multiplepointsby

TheUMAPJournal31

（2）（2010）129–148.§

cCopyright2010byCOMAP,Inc.Allrightsreserved.Permissiontomakedigitalorhardcopiesofpartorallofthisworkforpersonalorclassroomuseisgrantedwithoutfeeprovidedthatcopiesarenotmadeordistributedforprofitorcommercialadvantageandthatcopiesbearthisnotice.Abstractingwithcreditispermitted,butcopyrightsforcomponentsofthisworkownedbyothersthanCOMAPmustbehonored.Tocopyotherwise,torepublish,topostonservers,ortoredistributetolistsrequirespriorpermissionfromCOMAP.

usingthepreviouscrimestopredictthemostrecentoneandcomparingwithitsactuallocation.

Weextractsevendatasetsfrompublishedresearch.Weusefourofthedatasetsindevelopingourmodelandexaminingitsresponsetochangesinsequence,geographicconcentration,andtotalnumberofpoints.Thenweevaluateourmodelsbyrunningblindontheremainingthreedatasets.

Theresultsshowaclearsuperiorityformultipleanchorpoints.

Introduction

Theliteratureongeographicpatternsinserialcrimesshowsastrongpatterningaroundananchorpoint—alocationofdailyfamiliarityforthecriminal.Webuildpredictionschemesbasedonthisunderlyingtheoryandproduceasurfaceoflikelihoodvaluesandarobustmetric.

Thefirstschemefindsasingleanchorpointusingacenter-of-massmethod;

thesecondschemeassumestwotofouranchorpointsandusesacluster-findingalgorithmtosortandgrouppoints.Bothschemesuseastatisticaltechniquethatwecallcrateringtopredictfuturecrimelocations.

Background

Thearrestin1981（andsubsequentconviction）ofPeterSutcliffeasthe“YorkshireRipper”markedavictoryforStuartKind,aforensicbiologistwhoseapplicationofmathematicalprincipleshadsuccessfullypredictedwheretheYorkshireRipperlived.

Today,information-intensivemodelscanbeconstructedusingheat-maptechniquestoidentifythehotspotsforaspecifictypeofcrime,ortoderiveassociationsbetweentherateofcriminalactivityandattributesofalocation（suchaslighting,urbanization,etc.）[Boba2005].

“Geographicallyprofiling”thecrimesofasinglecriminalhasfocusedonlocatingthecriminal’sanchorpoints—locations（suchasahome,work-place,orarelative’shouse）atwhichhespendssubstantialamountsoftimeandtowhichhereturnsregularlybetweencrimes.

CanterandLarkin[1993]proposedthataserialcriminal’shome（orotheranchorpoint）tendstobecontainedwithinacirclewhosediameteristhelinesegmentbetweenthetwofarthest-apartcrimelocations;

andthisistrueinthevastmajorityofcases[KocsisandIrwin1997].Canteretal.[2000]foundthatforserialmurders,generalizationsofsuchtechniquesonaveragereducetheareatobesearchedbynearlyafactorof10.

Bycontrast,forecastingwhereacriminalwillstrikenexthasnotbeen

exploreddeeply[Rossmo1999].PaulsenandRobinson[2009]observethatformanyU.S.policedepartmentstherearesubstantialpractical,ethical,andlegalissuesinvolvedincollectingthedataforadetailedmapping

ofcriminaltendencies,withtheresultthatonly16%ofthememployacomputerizedmappingtechnique.

Ourtreatmentoftheproblemwillemployanchor-point-findingalgo-rithm.Wegeneratelikelihoodsurfacesthatactasaprioritizationschemeforregionstomonitor,patrol,orsearch.

Assumptions

DomainisApproximatelyUrban

Weusetheword“urban”todenotefeaturesofanurbanizedareathatsimplifyourtreatment:

Theentiredomainisapotentialcrimespot,themovementofthecriminaliscompletelyunconstrained,andtheareaislargeenoughtocontainallpossiblestrikepoints.Itisimportanttonote,however,thatevenforserialcrimecommittedinsuburbs,villages,orspreadbetweentowns,theurbanizationconditionholdsonthesubsetofthemapinwhichcrimesareregularlycommitted.Toseethis,considerthethreeurbanizationconditionsseparately:

•Entiredomainisapotentialcrimespot.Everyneighborhoodcontainsapossiblecrimelocation.Suchanassumptionismadebynearlyallgeographicprofilingtechniques[Canteretal.2000;

Rossmo1999]

Itisobviousthateverydomainwillviolatetheseconditionstosomeextent:

Allbutthemostinventiveserialkillers,forexample,willnotcommitacrimeinthemiddleofalake,orintheuninhabitedfarmlandbetweensmalltowns.Nevertheless,thisobservationsimplyrequiresthattheoutputofthemodelbeinterpretedintelligently.Inotherwords,whileweassumeforsimplicitythattheentiremapisapotentialtarget,policeofficersinterpretingtheresultscaneasilyignoreanypredictionswemakewhichfallintoanobvious“deadzone.”

•Criminal’smovementisunconstrained.Becauseofthedifficultyoffind-ingreal-worlddistancedata,weinvokethe“Manhattanassumption”:

Thereareenoughstreetsandsidewalksinasufficientlygrid-likepat-ternthatmovementsalongreal-worldmovementroutesisthesameas“straight-line”movementinaspacediscretizedintocityblocks[Rossmo

1999].Kent[2006]demonstratedthatacrossseveraltypesofserialcrime,theEuclideanandManhattandistancesareessentiallyinterchangeableinpredictinganchorpoints.

•Domaincontainsallpossiblestrikepoints.Thisconditionsaysthatthetwoconditionsaboveholdonasufficientlylargearea.

Takentogether,thesethreeconditionsdescribetheregionofinterestasametricspaceinwhich

•Thesubsetofpotentialtargetsisdense,

•themetricistheL2norm,and

•thespaceis“complete”:

Sequencesofcrimesdonotleadtopredictionsofcrimesoutsidethespace.

ViolentSerialCrimesbyaSingleOffender

•Focusonviolentcrimes.Geographicprofilingismostsuccessfulformurdersandrapes,withtheaverageanchor-pointpredictionalgorithmbeing30%lesseffectiveforcriminalswhoareserialburglarsorarsonists[Canteretal.2000;

Rossmo1999].

•Serialcrimes.Wetakeserialkilling（orviolentcrime）asinvolving“threeormorepeopleoveraperiodof30ormoredays,withasignificantcooling-offperiodbetween”[HolmesandHolmes1998].

•Singleoffender.

SpatialFocus

Useoftemporaldataisproblematic.Timedatacanbeinaccurate.Also,whileresearchhasfoundcyclicalpatternswithinthetimebetweencrimes,thesepatternsdon’tassociatedirectlytopredictingthenextgeographiclocation.Whatisusefulisgeneraltrendsinspatialmovementoveranorderingofthelocations.Wehenceignorespecifictimedataincrimesetsexceptfororderingofthecrimesequence.

DevelopingaSerialCrimeTestSet

ExistingCrimeSets

Researchershavecompileddatabasesofserialcrimesfortheirownuse:

Rossmo’sFBIandSFUdatabases[Rossmo1999],LeBeau’sSanDiegoRapeCasedataset[LeBeau1992],andCanter’sBaltimorecrimeset[Canteretal.

2000].Eachofthesedatabaseswasdevelopedwithspecificmethodsofintegrityandspecificsourcelocations.Theseproprietarydatabasesarenotavailabletous,sowearefacedwithtwooptions:

simulateserialcriminaldataorfindanindirectwayofusingtheprivatedata.

TheProblemwithSimulation

Simulationmightseemlikeanattractivesolutiontothelackofdata.However,utterlyrandomcrime-sitegenerationwouldcontradicttheun-derlyingassumptionofaspatialpatterntoserialcrimes,whilegeneratingsitesaccordingtoanunderlyingdistributionwouldprejudgethepattern!

Actualdatamustbeusedifthereistobeanyconfidenceinthemodel.

AnAlternative:

PixelPointAnalysis

Instead,we“mine”theavailabledata,inRossmo[1995]andinthespatialanalysisofjourney-to-crimepatternsinserialrapecasesinLeBeau[1992].LeBeaudepictsthedat