A Gentle Introduction to SVM

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1、AGentleIntroductiontoSupportVectorMachinesinBiomedicineAlexanderStatnikov*,DouglasHardin#,IsabelleGuyon†,ConstantinF.Aliferis*(MaterialsaboutSVMClusteringwerecontributedbyNikitaLytkin*)*NewYorkUniversity,#VanderbiltUniversity,†ClopiNetPartI•Introduction•Necessarymathematicalconcepts•Supportvectorm

2、achinesforbinaryclassification:classicalformulation•Basicprinciplesofstatisticalmachinelearning2Introduction3AboutthistutorialMaingoal:Fullyunderstandsupportvectormachines(andimportantextensions)withamodicumofmathematicsknowledge.•Thistutorialisbothmodest(itdoesnotinventanythingnew)andambitious(su

3、pportvectormachinesaregenerallyconsideredmathematicallyquitedifficulttograsp).•Tutorialapproach:learningproblemmainideaoftheSVMsolutiongeometricalinterpretationmath/theorybasicalgorithmsextensionscasestudies.4Data-analysisproblemsofinterest1.Buildcomputationalclassificationmodels(or“classifi

4、ers”)thatassignpatients/samplesintotwoormoreclasses.-Classifierscanbeusedfordiagnosis,outcomeprediction,andotherclassificationtasks.-E.g.,buildadecision-supportsystemtodiagnoseprimaryandmetastaticcancersfromgeneexpressionprofilesofthepatients:PrimaryCancerClassifiermodelMetastaticCancerPatientBiop

5、syGeneexpressionprofile5Data-analysisproblemsofinterest2.Buildcomputationalregressionmodelstopredictvaluesofsomecontinuousresponsevariableoroutcome.-Regressionmodelscanbeusedtopredictsurvival,lengthofstayinthehospital,laboratorytestvalues,etc.-E.g.,buildadecision-supportsystemtopredictoptimaldosag

6、eofthedrugtobeadministeredtothepatient.Thisdosageisdeterminedbythevaluesofpatientbiomarkers,andclinicalanddemographicsdata:Optimal12.234232392218Regressiondosageis5modelIU/Kg/weekBiomarkers,Patientclinicalanddemographicsdata6Data-analysisproblemsofinterest3.Outofallmeasuredvariablesinthedataset,se

7、lectthesmallestsubsetofvariablesthatisnecessaryforthemostaccurateprediction(classificationorregression)ofsomevariableofinterest(e.g.,phenotypicresponsevariable).-E.g.,findthemostcompactpanelofbreastcancerbiomarke