资源描述:
《On Similarity Methods in Machine Learning》由会员上传分享,免费在线阅读,更多相关内容在学术论文-天天文库。
1、OnSimilarityMethodsinMachineLearningMieczyslawM.KokarDepartmentofElectricalandComputerEngineeringNortheasternUniversity360HuntingtonAvenueBoston,MA02115,USAAbstractThispaperreviewsanumberofusesofsimilaritytheoryinthecontextofmachinelearning.First,itsho
2、wshowsimilaritytheorycanbeusedtouncoverthefactthatsomeoftherelevantvariablesaremissinginagivenmodel.Then,itshowshowthesameideacangivehintsonwhichvariablesshouldbeconsideredasrelevant.Thisisfollowedbyanideaofhowdimensionalanalysiscanhelpinfindingphysical
3、lawsbaseduponmeasurementsofaphysicalphenomenon.Finally,thepaperintroducesthenotionof“criticalhypersurface”andshowshowthisnotioncanbeutilizedinmonitoringtime-varyingdynamicalsystems.1IntroductionSimilaritymethodshavebeenproventobeveryusefulinmanyapplica
4、tions.Themainpowerofthesemethodsistheirpredictiveability,i.e.,theabilitytocomputethevalueofavariablecharacterizingagivensystemwithoutevenknowingthecompletesystemmodel.However,whileinordertopredictwedonotneedtoknowthemodel’sequations,westillneedtoknowat
5、leastacompletesetofthevariablesthatcharacterizethesystem.Thecompletenessrequirementiscrucialsinceonlyacompletesetofvariablesgivesusthesimilarityinvariantsthat,inturn,giveusthepredictionability.Unfortunately,thesearchforacompletesetofvariablesisanilldefi
6、nedtask-thesearchspaceistoolargeandthusitisnotpossibletocarryoutsuchataskinanyreasonabletime.Todothis,onewouldneedtoidentifya“suspect”variable,buildanexperimentalsetting,andthentestwhetherthisvariableinfluencesthesystemunderconsiderationornot.Evenworse,
7、somevariablesareconstantintypicalsituations;buthowcanwetellforsurewhetheroursystemwillstaywithinthetypicalregimeofoperation?Fortunately,similaritytheorymayprovideuswithsomeusefulhintsonwhichofthevariablesshouldorshouldnotbeconsideredascandidatesforthei
8、nclusionintothecompletesetofvariables.Theideaistofirstuseavariableasacomponentinasimilarityinvariant(similaritynumber)andthentestwhetherthisinvariantinfluencesthesystemornot.Suchtestsarenotstraightforwardandsometimesarenoteasytorealize,bu