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DigitalSignalProcessingwithKernelMethods Digital Signal Processing with Kernel Methods JoséLuisRojo-Álvarez DepartmentofSignalTheoryandCommunications UniversityReyJuanCarlos Fuenlabrada(Madrid) and CenterforComputationalSimulation UniversidadPolitécnicadeMadrid,Spain ManelMartínez-Ramón DepartmentofElectricalandComputerEngineering TheUniversityofNewMexico Albuquerque,NewMexico USA JordiMuñoz-Marí DepartmentofElectronicsEngineering UniversitatdeValència Paterna(València),Spain GustauCamps-Valls DepartmentofElectronicsEngineering UniversitatdeValència Paterna(València),Spain Thiseditionfirstpublished ©JohnWiley&SonsLtd Allrightsreserved.Nopartofthispublicationmaybereproduced,storedinaretrievalsystem,or transmitted,inanyformorbyanymeans,electronic,mechanical,photocopying,recordingorotherwise, exceptaspermittedbylaw.Adviceonhowtoobtainpermissiontoreusematerialfromthistitleisavailable athttp://www.wiley.com/go/permissions. TherightofJoséLuisRojo-Álvarez,ManelMartínez-Ramón,JordiMuñoz-Marí,GustauCamps-Vallstobe identifiedastheauthorsoftheeditorialmaterialinthisworkhasbeenassertedinaccordancewithlaw. RegisteredOffices JohnWiley&Sons,Inc.,RiverStreet,Hoboken,NJ,USA JohnWiley&SonsLtd,TheAtrium,SouthernGate,Chichester,WestSussex,POSQ,UK EditorialOffice TheAtrium,SouthernGate,Chichester,WestSussex,POSQ,UK Fordetailsofourglobaleditorialoffices,customerservices,andmoreinformationaboutWileyproducts visitusatwww.wiley.com. Wileyalsopublishesitsbooksinavarietyofelectronicformatsandbyprint-on-demand.Somecontentthat appearsinstandardprintversionsofthisbookmaynotbeavailableinotherformats. LimitofLiability/DisclaimerofWarranty MATLABⓇandSimulinkisatrademarkofTheMathWorks,Inc.andisusedwithpermission.The MathWorksdoesnotwarranttheaccuracyofthetextorexercisesinthisbook.Thiswork’suseordiscussion ofMATLABⓇsoftwareorrelatedproductsdoesnotconstituteendorsementorsponsorshipbyThe MathWorksofaparticularpedagogicalapproachorparticularuseoftheMATLABⓇsoftware. Whilethepublisherandauthorshaveusedtheirbesteffortsinpreparingthiswork,theymakeno representationsorwarrantieswithrespecttotheaccuracyorcompletenessofthecontentsofthisworkand specificallydisclaimallwarranties,includingwithoutlimitationanyimpliedwarrantiesofmerchantability orfitnessforaparticularpurpose.Nowarrantymaybecreatedorextendedbysalesrepresentatives,written salesmaterialsorpromotionalstatementsforthiswork.Thefactthatanorganization,website,orproductis referredtointhisworkasacitationand/orpotentialsourceoffurtherinformationdoesnotmeanthatthe publisherandauthorsendorsetheinformationorservicestheorganization,website,orproductmay provideorrecommendationsitmaymake.Thisworkissoldwiththeunderstandingthatthepublisherisnot engagedinrenderingprofessionalservices.Theadviceandstrategiescontainedhereinmaynotbesuitable foryoursituation.Youshouldconsultwithaspecialistwhereappropriate.Further,readersshouldbeaware thatwebsiteslistedinthisworkmayhavechangedordisappearedbetweenwhenthisworkwaswrittenand whenitisread.Neitherthepublishernorauthorsshallbeliableforanylossofprofitoranyother commercialdamages,includingbutnotlimitedtospecial,incidental,consequential,orotherdamages. LibraryofCongressCataloging-in-Publicationdata Names:Rojo-Álvarez,JoséLuis,–author.|Martínez-Ramón,Manel,–author.| Muñoz-Marí,Jordi,author.|Camps-Valls,Gustau,–author. Title:Digitalsignalprocessingwithkernelmethods/byDr.JoséLuisRojo-Álvarez, Dr.ManelMartínez-Ramón,Dr.JordiMuñoz-Marí,Dr.GustauCamps-Valls. Description:Firstedition.|Hoboken,NJ:JohnWiley&Sons,.|Includesbibliographical referencesandindex.| Identifiers:LCCN(print)|LCCN(ebook)|ISBN(pdf)| ISBN(epub)|ISBN(cloth) Subjects:LCSH:Signalprocessing–Digitaltechniques. Classification:LCCTK.(ebook)|LCCTK..R(print)|DDC./–dc LCrecordavailableathttps://lccn.loc.gov/ CoverdesignbyWiley Coverimage:©AF-studio/Gettyimages Setin/ptWarnockbySPiGlobal,Pondicherry,India           v Contents AbouttheAuthors xiii Preface xvii Acknowledgements xxi ListofAbbreviations xxiii PartI FundamentalsandBasicElements  1 FromSignalProcessingtoMachineLearning  . ANewScienceisBorn:SignalProcessing  .. SignalProcessingBeforeBeingCoined  .. :BirthoftheInformationAge  .. s:AudioEngineeringCatalyzesSignalProcessing  . FromAnalogtoDigitalSignalProcessing  .. s:DigitalSignalProcessingBegins  .. s:DigitalSignalProcessingBecomesPopular  .. s:SiliconMeetsDigitalSignalProcessing  . DigitalSignalProcessingMeetsMachineLearning  .. s:NewApplicationAreas  .. s:NeuralNetworks,FuzzyLogic,andGeneticOptimization  . RecentMachineLearninginDigitalSignalProcessing  .. TraditionalSignalAssumptionsAreNoLongerValid  .. EncodingPriorKnowledge  .. LearningandKnowledgefromData  .. FromMachineLearningtoDigitalSignalProcessing  .. FromDigitalSignalProcessingtoMachineLearning  2 IntroductiontoDigitalSignalProcessing  . OutlineoftheSignalProcessingField  .. FundamentalsonSignalsandSystems  .. DigitalFiltering  .. SpectralAnalysis  .. Deconvolution  .. Interpolation  vi Contents .. SystemIdentification  .. BlindSourceSeparation  . FromTime–FrequencytoCompressedSensing  .. Time–FrequencyDistributions  .. WaveletTransforms  .. Sparsity,CompressedSensing,andDictionaryLearning  . MultidimensionalSignalsandSystems  .. MultidimensionalSignals  .. MultidimensionalSystems  . SpectralAnalysisonManifolds  .. TheoreticalFundamentals  .. LaplacianMatrices  . TutorialsandApplicationExamples  .. RealandComplexSignalProcessingandRepresentations  .. Convolution,FourierTransform,andSpectrum  .. Continuous-TimeSignalsandSystems  .. FilteringCardiacSignals  .. NonparametricSpectrumEstimation  .. ParametricSpectrumEstimation  .. SourceSeparation  .. Time–FrequencyRepresentationsandWavelets  .. ExamplesforSpectralAnalysisonManifolds  . QuestionsandProblems  3 SignalProcessingModels  . Introduction  . VectorSpaces,Basis,andSignalModels  .. BasicOperationsforVectors  .. VectorSpaces  .. HilbertSpaces  .. SignalModels  .. ComplexSignalModels  .. StandardNoiseModelsinDSP  .. TheRoleoftheCostFunction  .. TheRoleoftheRegularizer  . DigitalSignalProcessingModels  .. SinusoidalSignalModels  .. SystemIdentificationSignalModels  .. SincInterpolationModels  .. SparseDeconvolution  .. ArrayProcessing  . TutorialsandApplicationExamples  .. ExamplesofNoiseModels  .. AutoregressiveExogenousSystemIdentificationModels  .. NonlinearSystemIdentificationUsingVolterraModels  .. SinusoidalSignalModels  Contents vii .. Sinc-basedInterpolation  .. SparseDeconvolution  .. ArrayProcessing  . QuestionsandProblems  .A MATLABsimpleInterpToolboxStructure  4 KernelFunctionsandReproducingKernelHilbertSpaces  . Introduction  . KernelFunctionsandMappings  .. MeasuringSimilaritywithKernels  .. Positive-DefiniteKernels  .. ReproducingKernelinHilbertSpaceandReproducingProperty  .. Mercer’sTheorem  . KernelProperties  .. Tikhonov’sRegularization  .. RepresenterTheoremandRegularizationProperties  .. BasicOperationswithKernels  . ConstructingKernelFunctions  .. StandardKernels  .. PropertiesofKernels  .. EngineeringSignalProcessingKernels  . ComplexReproducingKernelinHilbertSpaces  . SupportVectorMachineElementsforRegressionandEstimation  .. SupportVectorRegressionSignalModelandCostFunction  .. MinimizingFunctional  . TutorialsandApplicationExamples  .. KernelCalculationsandKernelMatrices  .. BasicOperationswithKernels  .. ConstructingKernels  .. ComplexKernels  .. ApplicationExampleforSupportVectorRegressionElements  . ConcludingRemarks  . QuestionsandProblems  PartII FunctionApproximationandAdaptiveFiltering  5 ASupportVectorMachineSignalEstimationFramework  . Introduction  . AFrameworkforSupportVectorMachineSignalEstimation  . PrimalSignalModelsforSupportVectorMachineSignalProcessing  .. NonparametricSpectrumandSystemIdentification  .. OrthogonalFrequencyDivisionMultiplexingDigitalCommunications  .. ConvolutionalSignalModels  .. ArrayProcessing  . TutorialsandApplicationExamples  viii Contents .. NonparametricSpectralAnalysiswithPrimalSignalModels  .. SystemIdentificationwithPrimalSignalModelγ-filter  .. ParametricSpectralDensityEstimationwithPrimalSignalModels  .. TemporalReferenceArrayProcessingwithPrimalSignalModels  .. SincInterpolationwithPrimalSignalModels  .. OrthogonalFrequencyDivisionMultiplexingwithPrimalSignalModels  . QuestionsandProblems  6 ReproducingKernelHilbertSpaceModelsforSignalProcessing  . Introduction  . ReproducingKernelHilbertSpaceSignalModels  .. KernelAutoregressiveExogenousIdentification  .. KernelFiniteImpulseResponseandtheγ-filter  .. KernelArrayProcessingwithSpatialReference  .. KernelSemiparametricRegression  . TutorialsandApplicationExamples  .. NonlinearSystemIdentificationwithSupportVector Machine–AutoregressiveandMovingAverage  .. NonlinearSystemIdentificationwiththeγ-filter  .. ElectricNetworkModelingwithSemiparametricRegression  .. PromotionalData  .. SpatialandTemporalAntennaArrayKernelProcessing  . QuestionsandProblems  7 DualSignalModelsforSignalProcessing  . Introduction  . DualSignalModelElements  . DualSignalModelInstantiations  .. DualSignalModelforNonuniformSignalInterpolation  .. DualSignalModelforSparseSignalDeconvolution  .. SpectrallyAdaptedMercerKernels  . TutorialsandApplicationExamples  .. NonuniformInterpolationwiththeDualSignalModel  .. SparseDeconvolutionwiththeDualSignalModel  .. DopplerUltrasoundProcessingforFaultDetection  .. SpectrallyAdaptedMercerKernels  .. InterpolationofHeartRateVariabilitySignals  .. DenoisinginCardiacMotion-ModeDopplerUltrasoundImages  .. IndoorLocationfromMobileDevicesMeasurements  .. ElectroanatomicalMapsinCardiacNavigationSystems  . QuestionsandProblems  8 AdvancesinKernelRegressionandFunctionApproximation  . Introduction  . Kernel-BasedRegressionMethods  .. AdvancesinSupportVectorRegression  .. Multi-outputSupportVectorRegression  Contents ix .. KernelRidgeRegression  .. KernelSignal-to-NoiseRegression  .. Semi-supervisedSupportVectorRegression  .. ModelSelectioninKernelRegressionMethods  . BayesianNonparametricKernelRegressionModels  .. GaussianProcessRegression  .. RelevanceVectorMachines  . TutorialsandApplicationExamples  .. ComparingSupportVectorRegression,RelevanceVectorMachines,and GaussianProcessRegression  .. Profile-DependentSupportVectorRegression  .. Multi-outputSupportVectorRegression  .. KernelSignal-to-NoiseRatioRegression  .. Semi-supervisedSupportVectorRegression  .. BayesianNonparametricModel  .. GaussianProcessRegression  .. RelevanceVectorMachines  . ConcludingRemarks  . QuestionsandProblems  9 AdaptiveKernelLearningforSignalProcessing  . Introduction  . LinearAdaptiveFiltering  .. LeastMeanSquaresAlgorithm  .. RecursiveLeast-SquaresAlgorithm  . KernelAdaptiveFiltering  . KernelLeastMeanSquares  .. DerivationofKernelLeastMeanSquares  .. ImplementationChallengesandDualFormulation  .. ExampleonPredictionoftheMackey–GlassTimeSeries  .. PracticalKernelLeastMeanSquaresAlgorithms  . KernelRecursiveLeastSquares  .. KernelRidgeRegression  .. DerivationofKernelRecursiveLeastSquares  .. PredictionoftheMackey–GlassTimeSerieswithKernelRecursiveLeast Squares  .. BeyondtheStationaryModel  .. ExampleonNonlinearChannelIdentificationandReconvergence  . ExplicitRecursivityforAdaptiveKernelModels  .. RecursivityinHilbertSpaces  .. RecursiveFiltersinReproducingKernelHilbertSpaces  . OnlineSparsificationwithKernels  .. SparsitybyConstruction  .. SparsitybyPruning  . ProbabilisticApproachestoKernelAdaptiveFiltering  .. GaussianProcessesandKernelRidgeRegression  .. OnlineRecursiveSolutionforGaussianProcessesRegression  x Contents .. KernelRecursiveLeastSquaresTracker  .. ProbabilisticKernelLeastMeanSquares  . FurtherReading  .. SelectionofKernelParameters  .. Multi-KernelAdaptiveFiltering  .. RecursiveFilteringinKernelHilbertSpaces  . TutorialsandApplicationExamples  .. KernelAdaptiveFilteringToolbox  .. PredictionofaRespiratoryMotionTimeSeries  .. OnlineRegressionontheKINKDataset  .. TheMackey–GlassTimeSeries  .. ExplicitRecursivityonReproducingKernelinHilbertSpace andElectroencephalogramPrediction  .. AdaptiveAntennaArrayProcessing  . QuestionsandProblems  PartIII Classification,Detection,andFeatureExtraction  10 SupportVectorMachineandKernelClassificationAlgorithms  . Introduction  . SupportVectorMachineandKernelClassifiers  .. SupportVectorMachines  .. MulticlassandMultilabelSupportVectorMachines  .. Least-SquaresSupportVectorMachine  .. KernelFisher’sDiscriminantAnalysis  . AdvancesinKernel-BasedClassification  .. LargeMarginFiltering  .. Semi-supervisedLearning  .. MultipleKernelLearning  .. Structured-OutputLearning  .. ActiveLearning  . Large-ScaleSupportVectorMachines  .. Large-ScaleSupportVectorMachineImplementations  .. RandomFourierFeatures  .. ParallelSupportVectorMachine  .. Outlook  . TutorialsandApplicationExamples  .. ExamplesofSupportVectorMachineClassification  .. ExampleofLeast-SquaresSupportVectorMachine  .. Kernel-FilteringSupportVectorMachineforBrain–ComputerInterface SignalClassification  .. ExampleofLaplacianSupportVectorMachine  .. ExampleofGraph-BasedLabelPropagation  .. ExamplesofMultipleKernelLearning  . ConcludingRemarks  . QuestionsandProblems 

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A realistic and comprehensive review of joint approaches to machine learning and signal processing algorithms, with application to communications, multimedia, and biomedical engineering systems Digital Signal Processing with Kernel Methods reviews the milestones in the mixing of classical digital si
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