这是一篇来自science杂志的论文,极其典型!介绍了测地距离在流行降维中的使用。
Scientistsworkingwithlargevolumesofhigh-dimensionaldata,suchasglobalclimatepatterns,stellarspectra,orhumangenedistributions,regularlyconfronttheproblemofdimensionalityreduction:Þndingmeaningfullow-dimensionalstructureshiddenintheirhigh-dimensionalobservations.Thehumanbrainconfrontsthesameproblemineverydayperception,extractingfromitshigh-dimensionalsensoryinputsÑ30,000auditorynerveÞbersor106opticnerveÞbersÑamanageablysmallnumberofperceptuallyrelevantfeatures.Herewedescribeanapproachtosolvingdimensionalityreductionproblemsthatuseseasilymeasuredlocalmetricinformationtolearntheunderlyingglobalgeometryofadataset.Unlikeclassicaltechniquessuchasprincipalcomponentanalysis(PCA)andmultidimensionalscaling(MDS),ourapproachiscapableofdiscoveringthenonlineardegreesoffreedomthatunderliecomplexnaturalobservations,suchashumanhandwritingorimagesofafaceunderdifferentviewingconditions.Incontrasttopreviousalgorithmsfornonlineardimensionalityreduction,oursefÞcientlycomputesagloballyoptimalsolution,and,foranimportantclassofdatamanifolds,isguaranteedtoconvergeasymptoticallytothetruestructure.
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