一種基于SVD的交通流量數據補全算法

一種基于SVD的交通流量數據補全算法Title:ASVD-basedTrafficFlowDataCompletionAlgorithmAbstract:Trafficflowdataplaysacrucialroleinmaintainingtransportationnetworkefficiencyandensuringthesmoothflowofvehicles.However,duetovariousreasonssuchassensorfailuresandlimitedsensorcoverage,trafficflowdatacanoftenbeincompleteormissing.ThispaperpresentsaSingularValueDecomposition(SVD)-basedalgorithmfortrafficflowdatacompletion.Theproposedalgorithmutilizesthecorrelationandpatternswithinthetrafficflowdatatoestimatemissingvaluesaccurately.Experimentalresultsdemonstratetheeffectivenessandefficiencyoftheproposedalgorithmincompletingtrafficflowdata.1.Introduction:Trafficcongestionhasbecomeaprevalentissueinurbanareas,leadingtodelays,increasedfuelconsumption,andenvironmentalpollution.Accurateandreliabletrafficflowdataiscrucialfortransportationmanagementsystemstoaddresstheseproblems.However,collectingreal-timetrafficflowdatafromvarioussensorsisacomplexandcostlytask.Thus,theavailabilityofcompleteandaccuratetrafficflowdataisfrequentlycompromised.Incompleteormissingtrafficflowdatahamperstheefficiencyoftrafficmanagementsystemsanddecision-makingprocesses.2.RelatedWork:Varioustechniqueshavebeendevelopedtoaddresstheproblemofmissingtrafficflowdata.Thesetechniquescanbebroadlycategorizedintoclassicalstatisticalmethods,machinelearning-basedapproaches,andmatrixcompletionmethods.However,thesemethodsoftensufferfromlimitationssuchasassuminglinearity,ignoringthenon-linearcharacteristicsoftrafficflow,ordependenceonlarge-scaletrainingdata.Inthispaper,weproposeanSVD-basedtrafficflowdatacompletionalgorithmtoovercometheselimitations.3.SingularValueDecomposition(SVD):SVDisawidelyusedmatrixfactorizationtechniquethatdecomposesamatrixintothreecomponentmatrices:U,Σ,andV^T.UandVareorthogonalmatrices,whileΣisadiagonalmatrix.SVDallowsfortheidentificationoflow-rankstructuresinamatrix.Inthecontextoftrafficflowdatacompletion,SVDcancapturetheunderlyingcorrelationandpatternswithinthedata.4.ProposedAlgorithm:4.1DataPreprocessing:BeforeapplyingSVD,thetrafficflowdataispreprocessedtohandlemissingvaluesandoutliers.Missingvaluesareassumedtobemaskedaszerosandwillbetreatedasunknownsduringthecompletionprocess.Outliersaredetectedandeliminatedusingstatisticaltechniques.4.2DataCompletionusingSVD:ThetrafficflowdatamatrixisdecomposedusingSVD,resultinginU,Σ,andV^T.TherankofthematrixisdeterminedbyanalyzingtheeigenvaluesinΣ.Thehighertheeigenvalues,themoreimportantthecorrespondingfeatures.Weretainthetopkeigenvaluestoapproximatetheoriginaldatamatrix.4.3Low-rankApproximation:Low-rankapproximationisperformedbysettingtheremainingeigenvaluesinΣtozero.ThereducedU,Σ,andV^Tmatricesarethenmultipliedtoreconstructthecompletedtrafficflowdatamatrix.4.4DataRefinement:Tofurtherimprovetheaccuracyofthecompletedtrafficflowdata,arefinementstepisperformed.Thisstepleveragesthetemporalandspatialcharacteristicsofthedatatocorrectanydiscrepanciesbetweenadjacenttimeintervalsorsensorlocations.Techniquessuchasinterpolationorregressionanalysiscanbeemployed.5.ExperimentalEvaluation:Theproposedalgorithmisevaluatedusingreal-worldtrafficflowdatasetsfromamajorcity.Theperformanceofthealgorithmiscomparedwithexistingmethods.Evaluationcriteriaincludetherootmeansquareerror(RMSE),meanabsoluteerror(MAE),andcomputationtime.6.ResultsandDiscussion:ExperimentalresultsdemonstratethattheproposedSVD-basedalgorithmoutperformsexistingmethodsintermsofcompletionaccuracyandcomputationefficiency.Thealgorithmeffectivelycapturestheunderlyingpatternsinthetrafficflowdata,resultinginaccuratecompletionofmissingvalues.Thedatarefinementstepfurtherenhancesthecompleteddataquality.7.Conclusion:ThispaperpresentsanovelSVD-basedalgorithmforcompletingtrafficflowdata.Byleveragingthecorrelationandpatternswithinthedata,theproposedalgorithmaccuratelyestimatesmissingvaluesintrafficflowdatasets.Experimentalresultsdemonstratetheeffectivenessandefficiencyofthealgorithminhandlingmissingtrafficflowdata.Futureresearchdirectionsmayincludeinvestigatingthealgorithm'sperformanceonlarger-scaledatasetsandintegratingothermachinelearningtechniquestofurtherenhancecompletionaccuracy.Acknowledgments:Theauthorsacknowledgethesupportandresourcesprovidedby[organizationname].References:[Listofrelevantreferences]Note:Th