2024年3月15日发(作者：高中数学试卷每题分)

Abstract

Thispaperpresentsonecasestudytoillustratehowprobabilitydistributionand

geneticalgorithmandgeographicalanalysisofserialcrimeconductedwithina

quesare

illustratedforpredictingthelocationoffuturecrimesandfordeterminingthepossible

residenceofoffendersbasedonthegeographicalpatternoftheexistingcrimesand

quantitativemethod,undthatsuchmethodsarerelativelyeasyto

implementwithinGISgivenappropriatedatabutrelyonmanyassumptionsregarding

offenders’omesuccesshasbeenachievedinapplyingthe

techniquesitisconcludedthatthemethodsareessentiallytheory-lessandlack

researchintotheevaluationofsuchmethodsandinthegeographic

behaviourofserialoffendersisrequiredinordertoapplysuchmethodsto

investigationswithconfidenceintheirreliability.

uction

ThisseriesofarmedrobberiesoccurredinPhoenix,Arizonabetween13September

and5December1999andincluded35robberiesoffastfoodrestaurants,hotelsand

enderswerenamedthe“Supersonics”bythePhoenixPolice

DepartmentRobberyDetailasthefirsttworobberieswereofSonicDrive-In

he35

th

robbery,theoffendersappeartohavedesistedfromtheir

asfortheoffendersto

targetbusinesseswheretheycouldeasilygainentry,pullonaskimaskorbandanna,

confrontemployeeswithaweapon,orderthemtotheground,emptythecashfroma

safeorcashregisterintoabagandfleeonfootmostlikelytoavehiclewaitingnearby.

Whileitappearsthattheoffendersoccasionallyworkedaloneorinpairs,theMO,

weaponsandwitnessdescriptionstendtosuggestagroupofatleastthreeoffenders.

Theobjectiveoftheanalysiswastousethegeographicdistributionofthecrimesto

predictthelocationofthenextcrimeinanareathatwassmallenoughtobesuitable

orkingwitha

popularcrimeanalysismanual(Gottleib,ArenbergandSingh,1994)itwasfoundthat

theprescribedmethodproducedtargetareassolargethattheywerenotoperationally

r,theapproachwasattractiveasitrequiredonlybasicinformationand

tifyareasthatweremoreusefulfor

the

RobberyDetail,itwasdecidedtouseasimilarapproachcombinedwithother

wasa“live”case,

newcrimesandinformationwereintegratedintotheanalysisasitcametohand.

tion

Inordertomodifythemodelexisted,weapplyserialnewassumptionstotheprinciple

retheassumptions:

alsprefersomethingaboutthelocationswherepreviouscrimeswere

.

Wesupposedthecriminalshaveagreateropportunitytoranawayiftheycommittedcommitted.

tion,thecriminalsprobably

choosepreviouskillsiteswheretheirtargetpotentialvictimsliveandwork.

2.

Offendersregarditsafertocrimeintheirpreviouskillsiteastimewent

truethatthesitewouldbeseverelymonitoredbypolicewhenashortterm

crimehappenedandconsequentlythecriminalwouldsufferariskofbeingarrestedin

entionedabove,thepolicewouldreducethefrequencyof

examiningthepreviouskillsitesastimewentby.

a

reasonableassumptionsinceitisprobablyinsecuretocrimeinthesitethatstaysfar

awayandthatcostsanamountofenergytoescapeandaddstheopportunitytobe

salsoimpossibletocrimeinthesite

near

result,wecanmeasureaoptimaldistanceinseriesperpetrations.

methatallthecaseinthemodelare

waythecriminalis

subjecttotheassumptionsmentionedaboveduetohisinsufficientpreparation.

\'

movementsunconstrained.

Becauseofthedifficultyoffindingreal-world5.

CriminalsCriminals\'

distancedata,weinvokethe“Manhattanassumption”:Thereareenoughstreetsandsidewalksina

sufficientlygrid-likepatternthatmovementsalongreal-worldmovementroutesisthesameas

“straight-line”monstratedthatacross

severaltypesofserialcrime,theEuclideanandManhattandistancesareessentially

interchangeableinpredictinganchorpoints.

dictionofthenextcrimesite

3.1Themeasureoftheoptimaldistance

Duetothefactthatthementaloptimaldistanceofthecriminalisrelatedtowhetherheisacareful

personornot,s,theoptimaldistancewill

r,suchdistanceshouldbereflectedonthedistancesofthe

ethatthecoordinatesofthencrimesitesisrespectively

(

x

1

,

y

1

)

、

(

x

2

,

y

2

)

、……、

(

x

n

,

y

n

)

,anddefinethedistancebetweenthe

i

th

crimesiteandthe

j

th

one

as

D

i,

j

.ThedistanceabovewefirstconsideritasEucliddistance,whichis:

D

i

,

j

=(

x

i

−

x

j

)

2

+(

y

i

−

y

j

)

2

Withthat,weareabletomeasurethedistancebetweenthe

n

th

crimesiteandthe

n-1

th

one

respectively.

Accordingtotheassumption2,thecriminalbelievesthattheearliercrimesiteshavebecamesafer

forhimtocommitacrimeagain,sowecandefinehismentaloptimaldistance,givingthesitesthe

weightsfromlittletomuchaccordingtowhentheoffenseshappenedintimesequence,as:

SD

=

∑

w

i

D

i

,

n

i

=1

n

−1

Satisfying

w

1

<

w

2

<......<

w

n

−1

，

w

i

=1

.Presumingthe

∑

i

=1

n

−1

i

th

crimehappensin

t

i

,which

ismeasuredbyweek,wecanhave

w

k

=

t

k

t

i

∑

i

=1

n

−1

.

SDcanreflectthecriminal\'smentalconditiontosomeextent,sowecanuseittopredictthe

mentaloptimaldistanceofthecriminalinthe

n

+1

th

eferringtothe

n

th

crimesite,

thecriminalisabletouseSDtoestimatetheoptimaldistanceinthenexttime,andwhilereferring

totherestcrimesites,,theoptimalsecurity

ofthe

i

th

crimesitecanbemeasuredasthefollowing:

SD

i

=

t

i

*

SD

n

t

n

3.2Themeasureoftheprobabilitydistribution

Giventhecrimesitesandlocation,wecanestimatetentativelytheprobabilitydensitydistribution

ofthefuturecrimes,whichequalstothatweaddsomesmallnormaldistributiontoeverysceneof

llnormaldistributionuses

theSDmentionedaboveasthemean,whichis:

(

r

i

−

SD

i

)

2

1

n

1

f

(

x

,

y

)=

∑

exp(−)

2

n

i

=1

2

πσ

2

σ

r

i

isdefinedastheEucliddistancebetweenthesitetothe

i

th

crimesite,andthestandard

differenceofthedeviationofthecriminal\'smentaloptimaldistanceisdefinedas

σ

,whichalso

reflectstheuncertaintyofthedeviationofthecriminal\'smentaloptimaldistance,involvesthe

cussionofthestandard

differenceisasfollowing:

3.3Thequantizationofthestandarddifference

Thestandarddifferenceisidentifiedaccordingtothefollowinggoal,whichis,everypredictionof

thenextcrimesiteaccordingtothecrimesiteswherethecrimeswerecommittedbeforeshould

vingtosatisfyingsuchoptimizationobjective,itis

d,wehavetousetheoptimized

solutionssearchingalgorithm,whichisgeneticalgorithm.

Figure1:TheDistributionofthePopulationoftheLastGeneration

Accordingtothefigure,thepopulationofthelastgenerationismostlyconcentratednear80,

whichisusedasthestandarddistanceandsubstitutedtothe*e*formula,weare

abletopredicttheprobabilitydensityofWhetherthezoneswillbethenextcrimesite.

Caseanalysis:

Figure2:Thepredictionofthe

5

th

crimesiteaccordingtothe4oneshappenedbefore


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