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BroilerGrowthPerformanceAnalysisfromCorrelationAnalysis,MultipleLinearRegression,toNeuralNetworkMeiyanXiao,PeijieHuang,PiyuanLin,ShangweiYanCollegeofInformaticsSouthChinaAgriculturalUniversityGuangzhou,ChinaCorrespondingAuthorpjhuangscau.edu.cnAbstractThepurposeofthisstudyistoinvestigatethedataWeusethebroilergrowthdatasetofthemostfamousfittingforbroilergrowthperformanceparameters.Inthispaper,poultryraisingcompanyinChinatoevaluateourapproachandthegradualadvancinganalysismethods,fromcorrelationtheresultsshowtheeffectivenessofourapproach.analysis,multiplelinearregression,toneuralnetwork,areproposed.Themeantechnologyroadmapisfirstly,correlationTherestofthispaperisorganizedasfollows.Inthenextanalysisisusedtodetectthedegreeofcorrelationbetweenthesection,wepresentthegradualadvancinganalysismethods.broilergrowthperformanceparameterandthecandidateinputExperimentsarepresentedanddiscussedinSection3.Finally,variables.AndthenchoosethepredictorvariablesthathavegoodSection4listssomeconclusions.correlationwiththedependentvariabletobuildthemultiplelinearregressionorneuralnetworkpredictionmodel,orboth,II.GRADUALADVANCINGANALYSISMETHODSaccordingtothelineardegreeofcorrelations.CombinedpredictionmaybechoseoncebothmodelshavegoodpredictionTheexploremethodsinourstudyofdatafittingforbroilerperformances.Weusethebroilergrowthdatasetofthemostgrowthperformanceparametersisdevelopedstepbystep,fromfamouspoultryraisingcompanyinChinatoevaluateourcorrelationanalysistoMLR,andthentononlinearfittingapproachandtheresultsshowtheeffectivenessofourapproach.meansbyneuralnetwork.KeywordsgrowthperformancecorrelationanalysismultipleA.TechnologyRoadmaplinearregressionneuralnetworkbroilerbreedingThetechnologyroadmapofourgradualadvancinganalysismethodsisshowninFig.1.I.INTRODUCTIONBioinformatics1isapromisingyoungfieldthatappliescomputertechnologyinbiologyanddevelopsalgorithmsandmethodstomanageandanalyzebiologicaldata2.Forthemodernpoultrybreedingcompanies,itisdeservedtopredictthepoultrygrowthperformanceparameters,suchasrateforsale,feedintake,dailygainandfeedconversionratio,basedonthemassivehistoricaldatagraduallycumulatedinproduction.However,becauseofthecomplexityanduncertaintybringbytheinfluenceofenvironmentalandphysiologicalfactors,informationintegrationofbiologicaldataisachallenge.Inthispaper,thegradualadvancinganalysismethods,fromcorrelationanalysis,multiplelinearregressionMLR3,toneuralnetwork4,areproposedtostudythedatafittingforbroilergrowthperformanceparameters.Inbroilerbreeding,seasonalfactorplaysanimportantpart.Ontheeffectofseasonalfactors,broilergrowthperformanceFigure1.Technologyroadmapoftheproposedmethodscanbeobviouslydifferent.SobroilergrowthperformanceTheassociationbetweenvariablescanbelinearorparametershaveobviousseasonalvariation.Seasonalfactorsnonlinear.Correlationanalysisismostlyusedtoevaluatelinearincludeairtemperature,precipitation,windspeed,pressure,relationships.Associationsbetweentwovariablescanberelativehumidity,etc.Thispapertakestheinfluenceoftheairanalyzedwithabivariatecorrelationanalysis.Whiletemperaturetotherateforsaleforexampletointroducetheassociationsbetweenonedependentvariableandasetoftwobroilergrowthperformanceanalysismethods.ormoreindependentvariables,whichhavestrongThisworkissupportedbytheSciTechResearchProjectofGuangdongProvinceunderGrantNo.2007A020300010,theNational863HighTechResearchDevelopmentPlanofChinaunderGrantNo.2006AA10Z246,andtheNewDisciplineSupportingFundofSouthChinaAgriculturalUniversityunderGrantNo.2007X022.NotlinearenoughDependentvariableIndependentvariablesCorrelationAnalysisComparisonCombinedpredictionwhenbothhavegoodpredictresponsesMultipleLinearRegressionNeuralNetworkStronglinercorrelation9781424447138/10/25.00©2010IEEEcorrelationswiththedependentvariable,canbestudiedusingmultiplecorrelationregressionanalysis,suchasMLR.Alternatively,ifthedegreeofcorrelationsisnotlinearenoughbetweenthedependentvariableandtheindependentvariables,somenonlinearfittingsprovidegoodchoose.Inthenonlinearfittingmethods,comparingtoGompertzthatusingleastsquaresinnonlinearregression,neuralnetworkisprovedtohasgoodabilitytopredictresponses5.Finally,inpracticalapplication,ifbothMLRandneuralnetworkhavegoodpredictionperformances,wecanconsiderthecombinedprediction.B.CorrelationAnalysisAcorrelationanalysisisastatisticalprocedurethatevaluatestheassociationbetweenthedependentvariableandtheindependentvariablesrespectively.Thesimplestwaytofindoutqualitativelythecorrelationistoplotthedata.AndwecanquantifythedegreeofcorrelationbyspecifyingthecorrelationcoefficientR,definedasyyinixxiyxnRσµσµ−−−∑1111wherexµandxσdenotethesamplemeanandthesamplestandarddeviationrespectivelyforthevariablexandyµandyσdenotethesamplemeanandthesamplestandarddeviationrespectivelyforthevariabley.Assumethataperfectlinearrelationshipexistsbetweenthevariablesxandy,i.e.,baxyiifori1,2,...,nwith0≠a.Nowverifyusingthedefinitionsofthemeanandthevariancethatbaxyµµandxyaσσ.Thisimpliesfrom1thatRa/|a|.Orinotherwords,R1ifa0andR1ifa0.ThecaseR1correspondstothemaximumpossiblelinearpositiveassociationbetweenxandy,meaningthatallthedatapointswilllieexactlyonastraightlineofpositiveslope.Similarly,R1correspondstothemaximumpossiblenegativeassociationbetweenthestatisticalvariablesxandy.Ingeneral,1≤R≤1withthemagnitudeandthesignofRrepresentingthestrengthanddirectionrespectivelyoftheassociationbetweenthetwovariables.C.MultipleLinearRegressionOncewehaveestablishedthatastrongcorrelationexistsbetweenthedependentvariableandmorethanoneindependentvariable,wewilluseMLR.AlinearregressionmodelthatcontainsmorethanonepredictorvariableiscalledaMLRmodel.ThefollowingmodelisaMLRmodelwithtwopredictorvariables,1xand2xuxxy2210βββ2Themodelislinearbecauseitislinearintheparameters,0β,1βand2β.Themodeldescribesaplaneinthethreedimensionalspaceofy,1xand2x.Theparameter0βistheinterceptofthisplane.Parameters1βand2βarereferredtoaspartialregressioncoefficients.Parameter1βrepresentsthechangeinthemeanresponsecorrespondingtoaunitchangein1xwhen2xisheldconstant.Parameter2βrepresentsthechangeinthemeanresponsecorrespondingtoaunitchangein2xwhen1xisheldconstant.uistherandomerror.D.NeuralNetworkNeuralnetwork4offeranalternativetoregressionanalysisforbiologicalmodeling.Inrelationtosystemmodeling,thedifferencebetweenartificialneuralnetworksandregressionanalysisisthatanequationisnotassumed,tighterfitsofdataarepossible,anditispossibletoworkwithnoisydata.Verylittleresearchhasbeenconductedtomodelanimalgrowthusingartificialneuralnetworks5,6.Inourstudy,wechoosetheBackPropagationBPneuralnetwork,whichisafeedforwardmultilayernetworkbasedontheBackPropagationalgorithmdevelopedbyRumelhartandMcCelland7andhasbecomeoneofthemostwidelyusedneuralnetworkinpractice.TheActivationTransferFunctionATFofaBPnetwork,usually,isadifferentiableSigmoidSshapefunction,whichhelpstoapplynonlinearmappingfrominputstooutputs.AtwolayerBPnetworkwasusedinourmodel.ThegoodnessoffitsfortheobtainedneuralnetworkmodelwascalculatedbymeansquareerrorMSEandmeanpercentageerrorMPE.TheMPEandMSEarecomputedas∑−nttttyyynMPE1ˆ13nyyMSEnttt∑−12ˆ4wheretyequalstheobservedvalueattimet,tyˆequalstheestimatedvalue,andnequalsthenumberofobservations.III.EXPERIMENTALRESULTSA.ExperimentSetupWetakethebreedingareaofGuangdongprovinceofChinaforexampletoevaluateourapproach.ThedatasetoftendaymeanairtemperatureisprovidedbyGuangdongProvincialClimateandAgrometeorologicalCente.AndthebroilergrowthdatasetisprovidedbyGuangdongWensFoodGroupLimitedCompany,whichisthemostfamouspoultryraisingcompanyinChina.AndwetakehenofshortfeetbuffBforexampletoevaluatetheinfluenceoftheairtemperaturetotherateforsale.Weselecthengrowthdataof2007,whichconsistsof5714data,andremain4209dataafterdatapreprocessing,whichistoeliminateabnormaldata,suchasabnormalrateforsale,nulldayage,andnullweight.FortheMLRandneuralnetworkmodels,weselect70samplesrandomlyfortraining,andtherestfortesting.B.CorrelationAnalysisConsideringthatthefullgrowingstageofbroilercanbedividedintochicklingstagethefirst4weeksandadultchickenstage.Differentstageshavedifferentphysiologicalcharacteristic.So,inourstudy,firstly,weusescatterplotstoshowtherelationshipbetweentherateforsaleandthetendaymeanairtemperatureofhen,chicklingstage,andadultchickenstagerespectively,whichareshowninFig.2toFig.4.Andthen,thedegreesofcorrelationsarequantifiedbycorrelationcoefficientR,whichisshowninTable1.0.920.930.940.950.960.970.9871217222732Tendaymeanairtemperature℃RateforsaleFigure2.TendaymeanairtemperatureofhenVSrateforsale0.940.950.960.970.9871217222732Tendaymeanairtemperature℃RateforsaleFigure3.TendaymeanairtemperatureofchicklingstageVSrateforsale0.940.950.960.970.9871217222732Tendaymeanairtemperature℃RateforsaleFigure4.TendaymeanairtemperatureofadultchickenstageVSrateforsaleTABLEI.CORRELATIONCOEFFICIENTCaseRTendaymeanairtemperatureofhenandrateforsale0.8506Tendaymeanairtemperatureofchicklingstageandrateforsale0.8932Tendaymeanairtemperatureofadultchickenstageandrateforsale0.8594AswecanseefromTable1,correlationcoefficientRoftherateforsaleandthetendaymeanairtemperatureofchicklingstageandadultchickenstageisbiggerthanthatoftherateforsaleandthetendaymeanairtemperatureofhen,whichindicatesthedivisionofchicklingstageandadultchickenstagetodofurtherresearchisarightchoose.C.MultipleLinearRegressionThefollowingMLRequationisfitforthetrainingdata21057.00755.0367.93xxy5whereyistherateforsale,and1xand2xarethetendaymeanairtemperatureofchicklingstageandadultchickenstagerespectively.D.NeuralNetworkSimilartotheMLRmodel,weusethetendaymeanairtemperatureofchicklingstageandadultchickenstageasinputs,andsettherateforsaleasoutput.Fig.5showstherealobservedvaluesandpredictedrateforsaleforbothMLRandneuralnetworklabeledasNNinFig.5methods,usingthetestingdata.Figure5.ComparsionofMLRandneuralnetworkinpredictionTable2showsthestatisticsfortheMLRandneuralnetworkforpredictingbroilerrateforsale.TABLEII.MODELSTATISTICSFORMLRANDNEURALNETWORKFORPREDICTINGRATEFORSALEModelStatisticMPEMSEMLR0.524.328E05Neuralnetwork0.473.538E05AswecanseefromTable2,neuralnetworkmodeloutperformsMLRmodelinbothMPEandMSE.Butfromtheresult,wecanseetheMLRmodelalsohasgoodpredictionperformances.IV.CONCLUSIONSInthispaper,wehavedealtwiththeresearchofthedatafittingforbroilergrowthperformanceparameters.Gradualadvancinganalysismethods,fromcorrelationanalysis,MLR,toneuralnetwork,areproposed.WeusethebroilergrowthdatasetofthemostfamouspoultryraisingcompanyinChina,andtakestheinfluenceoftheairtemperaturetotherateforsaleforexampletoevaluateourapproach.Aswecanseefromexperiment,correlationanalysisisusedtodetectthatthedivisionofchicklingstageandadultchickenstageisgoodforfurtherresearch,sincethetendaymeanairtemperatureofthesetwostageshavebiggercorrelationcoefficientRwithrateforsalethanthatofthetendaymeanairtemperatureofhen.Neuralnetworkmodelhasbetterabilitytopredictresponses.ButwecanseetheMLRmodelalsohasgoodpredictionperformance.So,wecanconcludethattheMLRandneuralnetworkmodelsbuiltbythetendaymeanairtemperatureofchicklingstageandadultchickenstagebothhavegoodpredictionperformancesandaresuitforcombinedpredictionforrateforsaleinpracticalapplication.REFERENCES1J.Cohen,BioinformaticsAnintroductionforcomputerscientists,ACMComputingSurveys,362,122158,2004.2J.HanandM.Kamber,DataMiningConceptsandTechniques,2ndedition,MorganKaufmann,2006.3S.Weisberg,AppliedLinearRegression,3rdedition.NewYorkWiley,2005.4M.T.Hagan,H.B.Demuth,M.H.Beale,Neuralnetworkdesign,PWSPublishedcompany,1996.5W.B.Roush,W.A.DozierIII,S.L.Branton,Comparisonofgompertzandneuralnetworkmodelsofbroilerchickens,PoultryScience.85794797,2006.6D.Yee,M.G.Prior,andL.Z.Florence,Developmentofpredictivemodelsoflaboratoryanimalgrowthusingartificialneuralnetworks,Comput.Appl.Biosci.9517–522,1993.7D.E.Rumelhart,J.L.McCelland,Learningrepresentationsbybackpropagatingerrors,Nature,3236188533536,1986.
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