测地距离—来自science杂志

测地距离—来自science杂志
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. 本软件ID:1894928