On Similarity Methods in Machine Learning

On Similarity Methods in Machine Learning

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时间:2019-07-20

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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

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