资源描述:
《2010MCM美国数学建模(2)》由会员上传分享,免费在线阅读,更多相关内容在教育资源-天天文库。
1、Team#7209Page35of35ForofficeuseonlyT1________________T2________________T3________________T4________________TeamControlNumber7209 ProblemChosenBForofficeuseonlyF1________________F2________________F3________________F4________________2010MathematicalContestinModeling(MCM)
2、SummarySheetSummaryInthispaper,wefirstestablishtheOffenceCircleModeltodeterminethepossiblescopeofacrimedetection.Comparedwiththetraditionalmethod,ourmethodismuchmoreaccurate,thecentreis12.67kmclosertotherealanchorpoint.Secondly,wecreateProbabilityModeltolocatetheanchor
3、point,andusetwoattenuationfunctions,oneisexponentialdecayfunctionandtheotherisnormalattenuationfunction.Theresultsobtainedare(53.817390-1.542570),(53.589390-1.918570)respectively.Comparedwiththerealanchorpoint,theexponentialdecayfunctionhasthebettereffect,theresultis9.
4、35kmclosertotherealanchorpoint.Withtheanalysisofseeminglymessycrimetimedata,weusetheGaussiandistribution,log-normaldistributionetc.tofitthedistributionofthecrimetime.Finally,throughcomputerprogrammingwithC++,wepredictthenextcrimetimeisFebruary4,1981withtheconfidencelev
5、elof81.2376%.Topredictingthenextcrimesite,weestablishtheDirectionmodelandBayesianmodel.Ourteamcalculatethetwomodelsrespectivelywiththepreviouscrimedata,thengettheresults:(53.394138,-1.621970)fortheDirectionmodeland(53.379986,-1.578862)forBayesianmodel.Thepredictednextc
6、rimesitethroughDirectionmodelis20.04kmawayfromtherealcrimesite,whilethroughBayesianmodelis9.17km.Thelatteris10.87kmclosertotherealcrimesite.Therealreasonisthattheyapplytodifferenttypesofsamples,inotherwords,theDirectionmodelissuitableforlinearsamples,whiletheBayesianMo
7、delfornon-linear.Attheendofthemodel,weintroducetheDoubleProbabilityModelbasedonBayesianAlgorithm,thismodelcombinethelocationandtimeofthenextcrime.Itcangiveacomprehensiveguidetothepolice.Infuturework,wewilldeveloptheSVMModel,collectsufficientcrime-relateddata.Furthermor
8、e,wecandesignasoftwarewhichwillhelpthepolicetocatchoffender.Keyword:GeographicProfiling;Bayesian;SVMAlgorithm;Probabi