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1、OverviewClassificationandregressiontreesWei-YinLohClassificationandregressiontreesaremachine-learningmethodsforconstructingpredictionmodelsfromdata.Themodelsareobtainedbyrecursivelypartitioningthedataspaceandfittingasimplepredictionmodelwithineachpartition.Asaresult,thep
2、artitioningcanberepresentedgraphicallyasadecisiontree.Clas-sificationtreesaredesignedfordependentvariablesthattakeafinitenumberofunorderedvalues,withpredictionerrormeasuredintermsofmisclassifica-tioncost.Regressiontreesarefordependentvariablesthattakecontinuousororderedd
3、iscretevalues,withpredictionerrortypicallymeasuredbythesquareddifferencebetweentheobservedandpredictedvalues.Thisarticlegivesanin-troductiontothesubjectbyreviewingsomewidelyavailablealgorithmsandcomparingtheircapabilities,strengths,andweaknessintwoexamples.C2011JohnW
4、iley&Sons,Inc.WIREsDataMiningKnowlDiscov2011114–23DOI:10.1002/widm.8CLASSIFICATIONTREESXtakesorderedvalues,thesetSisanintervaloftheform(−∞,c].Otherwise,Sisasubsetofthevaluesnaclassificationproblem,wehaveatrainingsam-IpleofnobservationsonaclassvariableYthattakenbyX.Thep
5、rocessisappliedrecursivelyonthedataineachchildnode.Splittingstopsiftherelativetakesvalues1,2,...,k,andppredictorvariables,decreaseinimpurityisbelowaprespecifiedthreshold.X1,...,Xp.Ourgoalistofindamodelforpredict-Algorithm1givesthepseudocodeforthebasicsteps.ingthevalueso
6、fYfromnewXvalues.Intheory,thesolutionissimplyapartitionoftheXspaceintokAlgorithm1Pseudocodefortreeconstructiondisjointsets,A1,A2,...,Ak,suchthatthepredictedbyexhaustivesearchvalueofYisjifXbelongstoAj,forj=1,2,...,k.IftheXvariablestakeorderedvalues,twoclassical1.Starta
7、ttherootnode.solutionsarelineardiscriminantanalysis1andnear-22.ForeachX,findthesetSthatminimizesestneighborclassification.ThesemethodsyieldsetsthesumofthenodeimpuritiesinthetwoAjwithpiecewiselinearandnonlinear,respectively,childnodesandchoosethesplit{X∗∈S∗}boundariestha
8、tarenoteasytointerpretifpislarge.thatgivestheminimumoverallXandS.ClassificationtreemethodsyieldrectangularsetsAjbyrecursively
