2017
Reconstruction of normal forms by learning informed observation geometries from data
Yair O, Talmon R, Coifman RR, Kevrekidis IG. Reconstruction of normal forms by learning informed observation geometries from data. Proceedings Of The National Academy Of Sciences Of The United States Of America 2017, 114: e7865-e7874. PMID: 28831006, PMCID: PMC5617245, DOI: 10.1073/pnas.1620045114.Peer-Reviewed Original ResearchNormal formNonlinear differential equationsDynamical systems theoryAppropriate normal formFundamental physical quantitiesDifferential equationsDynamical regimesState variablesPhysical quantitiesPhysical lawsSystems theoryGeometry learningEmpirical observationsObservation geometryHeart of scienceDynamicsPrior knowledgeEquationsRealizationLawParametersGeometryTheoryExplicit referenceForm
2015
Manifold Learning for Latent Variable Inference in Dynamical Systems
Talmon R, Mallat S, Zaveri H, Coifman R. Manifold Learning for Latent Variable Inference in Dynamical Systems. IEEE Transactions On Signal Processing 2015, 63: 3843-3856. DOI: 10.1109/tsp.2015.2432731.Peer-Reviewed Original ResearchDynamical systemsLatent variable inferenceOutput signal measurementsNonlinear observerEigenvector problemLaplace operatorSignal geometryIntrinsic distanceSignal measurementsAccurate recoveryIntrinsic variablesLatent variablesObserverInferenceMeasurement deviceManifoldOperatorsVariablesGeometryIntracranial electroencephalography signalsKernelDynamicsPropertiesProblemSolutionInformation Integration, Organization, and Numerical Harmonic Analysis
Coifman R, Talmon R, Gavish M, Haddad A. Information Integration, Organization, and Numerical Harmonic Analysis. 2015, 254-271. DOI: 10.1002/9781118853887.ch10.Peer-Reviewed Original ResearchPartial differential equationsHarmonic analysisLocal linear modelsLocal similarity modelNumerical harmonic analysisDifferential equationsMathematical frameworkNewtonian calculusGlobal solutionClassical toolsFunctional regressionLinear modelData matrixUnrelated approachesMathematicsSignal processingNumericsEquationsMachine learningGraphGlobal configurationCalculusData analysisGeometryModel
2014
Diffusion maps for changing data
Coifman R, Hirn M. Diffusion maps for changing data. Applied And Computational Harmonic Analysis 2014, 36: 79-107. DOI: 10.1016/j.acha.2013.03.001.Peer-Reviewed Original ResearchParameter spaceDiffusion mapsHigh-dimensional dataLow-dimensional spaceApproximation theoremGraph LaplacianIntrinsic geometryDimensional spaceSet of parametersNonlinear mappingDimensional dataGlobal behaviorEmbedding changesSpaceTypes of dataTheoremPowerful toolLaplacianGraphGeometryTermsEmbeddingDistanceParameters
2013
Empirical intrinsic geometry for nonlinear modeling and time series filtering
Talmon R, Coifman RR. Empirical intrinsic geometry for nonlinear modeling and time series filtering. Proceedings Of The National Academy Of Sciences Of The United States Of America 2013, 110: 12535-12540. PMID: 23847205, PMCID: PMC3732962, DOI: 10.1073/pnas.1307298110.Peer-Reviewed Original ResearchIntrinsic geometryNon-Gaussian tracking problemsHigh-dimensional time seriesNonlinear filtering frameworkTime series filteringInformation geometryStochastic settingParametric manifoldTracking problemStatistical modelBayesian approachNonlinear modelingEmpirical distributionFiltering frameworkEmpirical dynamicsInstrumental modalitiesInferred modelGeometryTime seriesTime series analysisDifferent observationsReal signalsSeries analysisDynamicsAnalysis toolsNonlinear Modeling and Processing Using Empirical Intrinsic Geometry with Application to Biomedical Imaging
Talmon R, Shkolnisky Y, Coifman R. Nonlinear Modeling and Processing Using Empirical Intrinsic Geometry with Application to Biomedical Imaging. Lecture Notes In Computer Science 2013, 8085: 441-448. DOI: 10.1007/978-3-642-40020-9_48.Peer-Reviewed Original ResearchNonlinear filtering problemInformation geometryFiltering problemDifferential geometryNonlinear filteringIntrinsic modelingIntrinsic geometryBayesian frameworkStatistical modelRandom observationsNonlinear modelingInstrumental modalitiesInferred modelGeometryNoise resilientReal signalsInvariantsModelingPhoton counterModelBiomedical imagingFilteringApplicationsProblem
2012
Harmonic Analysis of Databases and Matrices
Coifman R, Gavish M. Harmonic Analysis of Databases and Matrices. Applied And Numerical Harmonic Analysis 2012, 297-310. DOI: 10.1007/978-0-8176-8376-4_15.Peer-Reviewed Original Research
2011
Harmonic Analysis of Digital Data Bases
Coifman R, Gavish M. Harmonic Analysis of Digital Data Bases. Applied And Numerical Harmonic Analysis 2011, 161-197. DOI: 10.1007/978-0-8176-8095-4_9.Peer-Reviewed Original ResearchSpace of matricesData matrixData pointsEntropy conditionTensor productLaplacian eigenvectorsPotential operatorsDistribution geometryIterative procedureHarmonic analysisGraph oneAffinity graphLocal geometryEfficient reconstructionEigenvectorsGeometryData analysis methodsOperatorsGraphHaar-like basesMatrixAnalysis methodPartition treeExpansion coefficientVertices
2010
Diffusion Geometry Based Nonlinear Methods for Hyperspectral Change Detection
Coifman R, Coppi A, Hirn M, Warner F. Diffusion Geometry Based Nonlinear Methods for Hyperspectral Change Detection. 2010 DOI: 10.21236/ada524546.Peer-Reviewed Original ResearchSignal processing algorithmsChange detectionNonlinear signal processing algorithmsHyperspectral Change DetectionGroups of featuresProcessing algorithmsSpatio-spectral featuresProcessing toolboxSegmentation methodologyFeature spaceInvariant featuresSpectral signaturesHyperspectral imagesAnomaly assessmentTarget detectionDifferent conditionsDiffusion geometryTerms of similarityNonlinear methodsSceneGeometry
2006
Diffusion maps
Coifman R, Lafon S. Diffusion maps. Applied And Computational Harmonic Analysis 2006, 21: 5-30. DOI: 10.1016/j.acha.2006.04.006.Peer-Reviewed Original ResearchMarkov matrixSpectral graph theoryDiffusion mapsGraph theoryMultiscale geometryGeometric descriptionGeometric counterpartMarkov processComplex geometric structuresData parametrizationGeometric structureEfficient representationDiffusion processDimensionality reductionSpectral propertiesData setsEigenfunctionsMachine learningMatrixParametrizationCoordinatesGeometryTheoryVariety of contextsFramework
2005
Perspectives and Challenges to Harmonic Analysis and Geometry in High Dimensions: Geometric Diffusions as a Tool for Harmonic Analysis and Structure Definition of Data
Coifman R. Perspectives and Challenges to Harmonic Analysis and Geometry in High Dimensions: Geometric Diffusions as a Tool for Harmonic Analysis and Structure Definition of Data. Mathematical Physics Studies 2005, 27: 27-35. DOI: 10.1007/3-540-30434-7_3.Peer-Reviewed Original Research
1989
Multiresolution analysis in non-homogeneous media
Coifman R. Multiresolution analysis in non-homogeneous media. 1989, 107. DOI: 10.1109/mdsp.1989.97059.Peer-Reviewed Original ResearchPartial differential operatorsNon-homogeneous mediaDifferential operatorsVariable coefficientsMultiresolution analysisNumerical algorithmInvariant settingImage processing contextNonhomogeneous mediaEdge detection problemDetection problemVariable geometryProcessing contextTime-frequency analysisOperatorsWavelet analysisGeometryFrequency analysisAlgorithmSpaceSummary formProblemWavelets