Featureextractio_省略_lassifiedobjects_9ae
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Vol.15 Special1 Trans.NonferrousMet.Soc.China Mar.2005Featureextractionandclassificationofhyperspectralremotesensingimageorientedtoeasymixed-classifiedobjects¹
ZHANGLian-peng1,LIUGuo-lin2,JIANGTao2(1.DepartmentofTerritoryInformationandSurveyingEngineering,XuzhouNormalUniversity,Xuzhou221009,China;2.ShandongUniversityofScienceandTechnology,Tai.an271019,China)
Abstract:Theclassificationofhyperspectralremotesensingdataisanimportantproblemtheoreticallyandpract-i
cally.Withtheincreaseofspectralbands,theseparabilityofobjectsonremotesensingimageshouldbeimproved.Buttheeffectsoftraditionalalgorithmonfeatureextractionsuchasprincipalcomponentanalysis(PCA)isnotsogoodforhyperspectralimage.ThekeyproblemisthatPCAcanonlyrepresentthelinearstructureofdataset;whilethedatacloudsofdifferentobjectsonhyperspectralimageusuallydistributeonanonlinearmanifold.Thispaperes-tablishedanalgorithmofnonlinearfeatureextractionnamedasnonlinearprincipalpolylines,basedonthealgo-rithm,aclassifierisconstructedandtheclassificationaccuracyofhyperspectralimagecanbeimproved.Keywords:hyperspectralremotesensing;featureextraction;classification
1 INTRODUCTIONWiththedevelopmentofremotesensingtech-nologyfromaircraftandspacecraft,theresearchandapplicationofhyperspectralremotesensingarebecomingahotpotofremotesensing[1].Foritsseveralhundredspectralbands,hyperspectralre-motesensingcanderivemoredetailedandmoreac-curateinformation.Butfortheanalysisofhyper-spectralremotesensingdata,theeffectsoftrad-itionalalgorithmoffeatureextractionsuchasprin-cipalcomponentanalysis(PCA)isnotsogood.ThemainlimitationofPCAisthatitcanonlyre-presentthelinearstructureofdataset;whilethedatacloudsofdifferentobjectsonhyperspectralimageusuallydistributeonanonlinearman-ifold[2-5].Forthisreason,whichisnecessarytode-velopanonlinearfeatureextractionalgorithmtoreducethenonlinearrelationsofhyperspectralbands.ItcanbeakindofexpansionofPCA[6-10].ThispaperfirstlyintroducestheconceptofPrincipalCurves(PC),whichisproposedbyHastieandStuetzle(1989)[1],thebasicideaofPCistocalculateasmoothcurvepassingthroughthemiddleofdataset,PCAisaspe-cialcaseofPC,thefirstdirectionofPCAisaprincipalline.ForitscomplicatedalgorithmofPC,thispaperproposesasimplifiedalgorithmcallednonlinearprinc-ipalpolylines,thealgorithmcalculateapolylinepass-ingthroughthemiddleofdataset.Basedontheprin-cipalpolyline,thepaperconstructsaclassifierforclassifyingthehyperspectralremotesensingimage,theaccuracyofclassificationcanbeimproved.2 NONLINEARPRINCIPALCURVESTheprincipalcurvesproposedbyHastieandStuetzle(1989)isdefinedasfollows:f(t)isasmoothcurveinn-dimensionalspaceRd,ifitfollowsthenextthreeconditions,itisnamedasprincipalcurve:1)f(t)doesnotintersectitself2)f(t)hasfinitelengthinsideanyboundedsubsetofRd3)f(t)isself-consistent,i.e.,f(t)=E[X|tf(X)=t].Intuitively,self-consistencymeansthateachpointoff(t)istheaverageofallpointsthatpro-jectsthere.Thus,theprincipalcurvesaresmoothsel-fconsistentcurveswhichpassthroughthemid-dleofdatasetandprovideagoodone-dimensionalnonlinearsummaryofdataset.Theexistenceofprincipalcurvesdefinedbytheself-consistencyhasnotbeenprovedtheoret-icallyexceptforsomespecialdistributionssuchasnormaldistribution.Butnomatterwhetherornottheexistenceofprincipalcurves,HastieandStuet-zlehavedevelopedanalgorithmforconstructingprincipalcurvesasfollows:Step1:Letf(0)(t)bethefirstlineofPCAfordatasetX,j=0Step2:ProjectXonf(j)(t),calculatetheprojectionindex,tf(i)(X)tf(i)(X)=maxt:+X-f(j)(t)+=minS+X-fi(S)+
Step3:Constructnewcurve,f(j+1)(t)f(j+1)(t)=E[X|tf(i)(X)=t]
Step4:Stopif1-$(f(j+1)$(f(j))principalcurves,otherwise,letj=j+1andgotoStep2,where$(f(j+1))istheexpectedsquareddistance
¹Project(40174003)supportedbytheNationalNaturalScienceFoundationofChinabetweendatasetXandsmoothcurvef(j+1).Fromtheabovealgorithm,wecanimaginethatitisverycomplicatedandtimeconsumingforhyperspectralremotesensingdatabecauseofthehighdimensionalspace.Thus,thispaperestabl-ishesasimplifiedalgorithmforprincipalcurvesnextsection.3 ALGORITHMOFNONLINEARPRINCIPALPOLYLINESTheprincipalcurvesalgorithmofHastieandStuetzlearefromthebackgroundofmachinelearn-ingespeciallyfromthescriptrecognition.Inthealgorithmofscriptrecognition,thescriptcanbetreatedasanimage,andthepixelsareveryclosedsothatthedatasetisverydenselydistributed.Therefore,thealgorithmofHastieandStuetzleisfeasibleforscriptrecognition.Butforthehyper-spectralremotesensingdata,becauseofthehighdimensionalproblem,thepointsofdatasetareverysparselydistributedinhighdimensionalspace(Kendall,1961,Hughes,1968,Scott,1992),thus,thetinyadjacentareaofapointinhighd-imensionalspaceareusuallyempty,itmeansthatitisdifficulttocalculatetheaverageofprojectionpoints.Therefore,itishardtoconstructasmoothcurvepassingthroughthemiddleofdatasetofhy-perspectralremotesensingimage.Thepaperes-tablishesanalgorithmtoconstructaprincipalpolylinepassingthroughthemiddleofdatasetofhy-perspectralremotesensingimageasfollows:LetX1,,,XmarepointvectorsinRdcorre-spondingtopixelsofahyperspectralremotesens-ingimage.Step1:LetuIRdisthefirstPCAdirectionvector,s(0)(t)=tuisthefirstPCAlineinRd,j=0Step2:ProjectX1,,,Xmtos(j)(t),j=1,2,3,,,m,projectionindexists(Xi)=XTiu(1)Sortts(Xj)inascendingorder,supposets(X1)[ts(X2)[,[ts(Xm),letD>0isapriorde-finedtinyconstant,divideallts(Xj)(j=1,2,3,,,m)intoNsubgroups,whereNPPm,thatis,if|ts(Xi)-ts(Xj)|i=1,2,3,,,N.