支持向量回归机及其应用研究

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1、中国农业大学博士学位论文支持向量回归机及其应用研究姓名：田英杰申请学位级别：博士专业：管理科学与工程指导教师：邓乃扬20050601AbstractSupportVectorMachines(SVMs)arenewdataminingmethodsdevelopedinrecentyeambasedonthefoundationsofStatisticalLearningTheory(SLT)，andtheyhavebeenproventobemorepowerfulandrobustthanexistingmethodsinmostaspects．SVMsaredevelo

2、pingpromisinglyeitherintheoryorapplications．Suppoavectormachinesforclassificationproblemarecalledsupportvectorclassification(SVC)，whileforregressionproblemaresupportvectorregression(SVR)．ThispaperfocusesonSVRinseveralaspects，includingtheoryfoundationandapplication．1．TheSuccessofSVMsdependsh

3、eavilyonthemodelselection．OneofthemostpopularapproachesistoselectthekernelandtheparametersbyminimizingtheboundofLeave-One-Out(too)error．ForSVCsomefamousboundshavebeenproposed，wederivethreeLOOboundsforthreealgorithmsofSVR，andanewSVRalgorithm(LOO--SVR)isproposed．2．AgeneralizedmodelofSVRisprop

4、osed，intheoptimizationproblemofwhichaselectablefunctionisincluded．DifferentselectionsofthisfunctionwillderivesomekindsofexistingalgorithmsofSVR，andthekernelfunctioninthismodelmaynotbenecessarilydefinite；UnconstrainedSVRisconstructedaftertransformingtheprimalconvexquadraticprogrammingintounc

5、onstrainedprob!em，sothatsomeefficientunconstrainedoptimizationmethodscanbeappliedtoSVR．3．Forstandarde-SVR，weproposetwowaystoderiveit．OneisthataftertransformingregressionproblemtoclassificationproblemandapplyingSVCtothisproblem，wededucetheprimalproblemofstandarde-SVR．Theotheristhataftergivin

6、gouttheconceptofmargininregressionproblem，theprimalproblemofe-SVRcanalsobederivedbyimplyingtheideaofmaximizingn]argin．4．ExistingresearchesofSVP．arebasedonoptimizationtheoryoffinitedimensionspace．Thispaperprovestherelationbe“veenthesolutionsofprimalproblemanddualprobleminHilbertspace，whichma

7、ybeinfinitedimension，thereforemakesuptheoptimizationtheoryfoundation．5．Fortheproblemofsoilerosionprediction，weconstructsupportvectorregressionpredictmodel，andchooseoptimalparametersbyminimizingtheboundofLOOellorweproposed．Thecomparisonresultswithtraditio