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HyperspectralremotesensingdataclassificationClass:StudentID:Name:AbstractCurrently,hyperspectralremotesensing(HRS)hasbecomeacutting-edgefieldofremotesensing(RS)area.Hyperspectralimageclassificationhasbecomeoneofthehottestresearchfieldsoftheremotesensingarea.Thehyperspectralclassificationtechnologyhasveryhighvaluebothinapplicationandtheoryresearch.However,hyperspectralimageprocessingalsointroducedmanyproblems.Theproblemsare:howtosolvetheproblemofhigh-dimensionalwithsmallamoutofsamples,howtousetheinformationignoredincurrentresearch,suchasstructuralinformation,howtousethevastamountsofunlabeledsamplesthatcontaininformation,howtochoosethefittestclassifier.InHRSapplications,therequirementsofhyperspectralclassifiersperformanceareincreasingly.Thecorrespondinghyperspectralclassificationtechnologyresearchshouldfocusonthetopic,connectingwiththespecificapplicationofhyperspectralremotesensing.IntroductionHyperspectralimagingspectrometer,alsoknownasremotesensing,whichusesalotofverynarrowbandofelectromagneticwavesreflectedfromtheobjectofinteresttoobtaintherelevantdatatoachieveabreakthroughinremotesensingtechnologytoimprovespectralresolution.Hyperspectralremotesensingandgeneraldifferenceisthattheformerthanthelatterhasmorefinelyspectralbands,youcanformacompletespectraldata.Technicalstaffthroughthespectralanalysisofthedata,thefeaturecanbealotofinformation,soastoachievelong-range,non-contactdetectionofobjectsconductedresearch.Fromtheperspectiveoftechnologicalinnovation,hyperspectraltechnologycombinesmodernhigh-techinaseriesofimportantprogress,theuseofthespectralcharacteristicsofthesurfacefeaturesfineandtheintrinsiclinkbetweenthefeaturedetection,resultinginremotesensingimageseachpixelcorrespondingtothespectralcurveofasmooth.Hyperspectralremotesensingimageprocessingusingthereflectionspectrumoffeaturerecognitionfeaturedistinguishitstype,canbeeffectivelyquantifiedfeatureattributerecognitionandinformationextraction.Hyperspectralremotesensingspectralresolutionreferstothedirectionofthedetectoratawavelengthofrecordingwidth,alsoknownasbandwidth.Hyperspectralbandsquantity,thenumberofspectralchannelsuptotensorevenhundreds,andoftenbetweeneachspectralchanneliscontinuous.Improvespectralresolutionremotesensingdirectionofdevelopment,thenarrowerbandofthemorelikelytoaccuratelyidentifyasinglesurfacematerialcomposition.ImagingSpectrometerimaginginspace,whileatthesamespatialresolutioncanberecordedintoonehundredspectralchanneldata,thuscontainsawealthofinformationandimagespacegeometricspectralinformation,theyarestackedtogethertoformahyperspectralcube.Hyperspectralcubeintwo-dimensionalspacebasedontheincreaseofone-dimensionalspectralinformation,thusformingathree-dimensionalspacecoordinates.Imagingspectrometerthatisgeneratedforeachbandhyperspectralimagedataasalevelexpressionoftheoverallimagingspectrometerdatatothethree-dimensionalcoordinatespace,thusconstitutingacompositesequencecomposedbyband,withmultiplelevelsofdatacube.ShowninFigure1.1,hyperspectralimagingspectrometertechnologycombinetraditionalremotesensingimagingtechnologyandnewspectroscopictechniques,differentsubstancescorrespondingtodifferentspectralcharacteristics.Becauseinacertainwavelengthrange(e.g.visible-nearinfrared,visible-shortwaveinfrared),spectraloverlapwithadjacentbands,whichisacontinuousspectrumimage,resultinginahighspectralcubeofeachimagepixelmaybeacontinuousextractionthespectralcurve,whichisthespectralfingerprinteffect.Imagingspectrometeraccordingtoanimageobtainedcanberecordedusingthefullspectraofthevariousobservedfeatureinformation,whichmakesuseofthehighspectraldatainversionfeatureofdetailaspossible,sothatqualitativeanalysisfromremotesensingtechnologytoquantitativeanalysisofchangesinthequantitativeremotesensingtechnologyandtheorytoestablishthetechnicalbasis.figure1.1HyperspectralimageschematicdiagramGaussiandiscriminantanalysis（Proposedmethod）Thefirstgenerativelearningalgorithmthatwe'lllookatisGaussiandiscriminantanalysis(GDA).Inthismodel,we'llassumethatp(x|y)isdistributedaccordingtoamultivariatenormaldistribution.Let’stalkbrieflyaboutthepropertiesofmultivariatenormaldistributionsbeforemovingontotheGDAmodelitself.Themultivariatenormaldistributioninn-dimensions,alsocalledthemultivariateGaussiandistribution,isparameterizedbyameanvectorμ∈RnandacovariancematrixΣ∈RN*N,whereΣ≥0issymmetricandpositivesemi-definite.AlsowrittenN(μ,Σ)itsdensityisgivenby:p(x;μ,Σ)=1(2π)𝑛2|Σ|12exp(−12(𝑥−μ)𝑇Σ−1(𝑥−μ))ForarandomvariableXdistributedN(μ,Σ)themeanisgivenbyμ:[]=∫p(x;μ,Σ)𝑥=μThecovarianceofavector-valuedrandomvariableZisdefinedas()=[(−[[])(−())𝑇]Thisgeneralizesthenotionofthevarianceofareal-valuedrandomvariable.Thecovariancecanalsobedefinedas()=[𝑇]−([])([])𝑇IfX∼N(μ,Σ)ThenCov(X)=ΣWhenwehaveaclassificationprobleminwhichtheinputfeaturesxarecontinuous-valuedrandomvariables,wecanthenusetheGaussianDiscriminantAnalysis(GDA)model,whichmodelsusingamultivariatenormaldistribution.Themodelis:y∼Bernoulli(φ)x|y=0∼N(μ0,Σ)x|y=1∼N(μ1,Σ)Writingoutthedistributions,thisis:Thelog-likelihoodofthedataisgivenbyBymaximi