美赛数学建模优秀论文

Centroids,Clusters,andCrime129

Centroids,Clusters,andCrime:

AnchoringtheGeographicPro lesofSerialCriminals

AnilS.Damle

ColinG.West

EricJ.Benzel

UniversityofColorado–Boulder

Boulder,CO

Advisor:AnneDougherty

Abstract

Aparticularlychallengingproblemincrimepredictionismodelingthebehaviorofaserialkiller.Since ndingassociationsbetweenthevictimsisdif cult,wepredictwherethecriminalwillstrikenext,insteadofwhom.Suchpredictingofacriminal’sspatialpatternsiscalledgeographicpro ling.Researchshowsthatmostviolentserialcriminalstendtocommitcrimesinaradialbandaroundacentralpoint:home,workplace,orotherareaofsigni cancetothecriminal’sactivities(forexample,apartoftownwhereprostitutesabound).These“anchorpoints”providethebasisforourmodel.Weassumethattheentiredomainofanalysisisapotentialcrimespot,movementofthecriminalisuninhibited,andtheareainquestionislargeenoughtocontainallpossiblestrikepoints.Weconsiderthedomainametricspaceonwhichpredictivealgorithmscreatespatiallikelihoods.Addition-ally,weassumethattheoffenderisa“violent”serialcriminal,sinceresearchsuggeststhatserialburglarsandarsonistsarelesslikelytofollowspatialpatterns.

Therearesubstantialdifferencesbetweenoneanchorpointandseveral.Wetreatthesingle-anchor-pointcase rst,takingthespatialcoordinatesofthecriminal’slaststrikesandthesequenceofthecrimesasinputs.Estimatingthepointtobethecentroidofthepreviouscrimes,wegeneratea“likelihoodcrater,”whereheightcorrespondstothelikelihoodofafuturecrimeatthatlocation.Forthemultiple-anchor-pointcase,weuseacluster- ndingandsortingmethod:Weidentifygroupingsinthedataandbuildalikelihoodcrateraroundthecentroidofeach.Eachclusterisgivenweightaccordingtorecencyandnumberofpoints.Wetestsinglepointvs.multiplepointsby

cCopyright2010byCOMAP,Inc.Allrightsreserved.TheUMAPJournal31(2)(2010)129–148.

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