A Review of Dimension Reduction Techniques微数约检研究综述

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1、AReviewofDimensionReductionTechniquesMiguelA.Carreira-Perpin~anTechnicalReportCS{96{09Dept.ofComputerScienceUniversityofSheeldM.Carreira@dcs.shef.ac.ukJanuary27,1997AbstractTheproblemofdimensionreductionisintroducedasawaytoovercomethecurseofthedimen-sionalitywhendealingwithvectordatain

2、high-dimensionalspacesandasamodellingtoolforsuchdata.Itisdenedasthesearchforalow-dimensionalmanifoldthatembedsthehigh-dimensionaldata.Aclassicationofdimensionreductionproblemsisproposed.Asurveyofseveraltechniquesfordimensionreductionisgiven,includingprincipalcomponentanalysis,projectionp

3、ursuitandprojectionpursuitregression,principalcurvesandmethodsbasedontopologicallycontinuousmaps,suchasKohonen'smapsorthegeneralisedtopographicmapping.Neuralnetworkimplementationsforseveralofthesetechniquesarealsoreviewed,suchastheprojec-tionpursuitlearningnetworkandtheBCMneuronwithanobjec

4、tivefunction.Severalappendicescomplementthemathematicaltreatmentofthemaintext.Contents1IntroductiontotheProblemofDimensionReduction51.1Motivation............................................51.2Denitionoftheproblem....................................61.3Whyisdimensionreductionpossible?....

5、.........................61.4Thecurseofthedimensionalityandtheemptyspacephenomenon.............71.5Theintrinsicdimensionofasample..............................71.6Viewsoftheproblemofdimensionreduction.........................81.7Classesofdimensionreductionproblems..........................

6、..81.8Methodsfordimensionreduction.Overviewofthereport..................92PrincipalComponentAnalysis103ProjectionPursuit123.1Introduction............................................123.1.1Whatisaninterestingprojection?...........................123.2Theprojectionindex......................

7、.................133.2.1Denition.........................................133.2.2Classication.......................................133.2.3Desirableproperties...................................143.2.4Outliers..........................................143.2.5In