2015
Information 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
Diffusion Maps for Signal Processing: A Deeper Look at Manifold-Learning Techniques Based on Kernels and Graphs
Talmon R, Cohen I, Gannot S, Coifman R. Diffusion Maps for Signal Processing: A Deeper Look at Manifold-Learning Techniques Based on Kernels and Graphs. IEEE Signal Processing Magazine 2013, 30: 75-86. DOI: 10.1109/msp.2013.2250353.Peer-Reviewed Original ResearchParametric statistical inferenceDigital signal processing systemsMachine-learning approachesKernel-based methodsSignal processingManifold learning techniquesComputational capabilitiesSignal processing systemGraphical modelsStatistical inferenceMore computationSignal processing methodsBayesian networkDSP systemsEfficient algorithmProcessing systemComputational burdenLinear filterDiffusion mapsAlgorithmProcessing methodsTraditional methodsProcessingNetworkGraph
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
2007
Variable-free exploration of stochastic models: A gene regulatory network example
Erban R, Frewen TA, Wang X, Elston TC, Coifman R, Nadler B, Kevrekidis IG. Variable-free exploration of stochastic models: A gene regulatory network example. The Journal Of Chemical Physics 2007, 126: 155103. PMID: 17461667, DOI: 10.1063/1.2718529.Peer-Reviewed Original ResearchConceptsStochastic modelEquation-free approachLow-dimensional descriptionLong-time behaviorNetwork exampleAppropriate observablesStochastic simulationGood observablesGene regulatory networksObservablesComplex systemsDiffusion mapsSimulation dataPhysical variablesPrevious paperLong-term dynamicsAppropriate valuesDynamicsEigenvectorsLaplacianComputationRegulatory networksGraphModelRestriction procedures
2006
Diffusion wavelet packets
Bremer J, Coifman R, Maggioni M, Szlam A. Diffusion wavelet packets. Applied And Computational Harmonic Analysis 2006, 21: 95-112. DOI: 10.1016/j.acha.2006.04.005.Peer-Reviewed Original ResearchDiffusion waveletsWavelet packetEfficient algorithmImage denoisingSame algorithmMultiscale representationPacketsSignal processingWaveletsAlgorithmDenoisingGraphLower dimensionHigher dimensionsApplicationsTime-frequency basisComputationTaskCompressionAnisotropic settingProcessingRepresentationExampleOperatorsTool
2005
Geometric diffusions for the analysis of data from sensor networks
Coifman RR, Maggioni M, Zucker SW, Kevrekidis IG. Geometric diffusions for the analysis of data from sensor networks. Current Opinion In Neurobiology 2005, 15: 576-584. PMID: 16150587, DOI: 10.1016/j.conb.2005.08.012.Peer-Reviewed Original ResearchConceptsSensor networksGeometric diffusionMathematical developmentComplex data setsHarmonic analysisNeural information processingActivity datasetsCertain analogyComputer modelingData setsInformation processingManifoldNetworkModelingGraphData analysisAlgorithmNew toolDatasetAnalysis of dataAnalogyFieldComparison of Systems using Diffusion Maps
Vaidya U, Hagen G, Lafon S, Banaszuk A, Mezic I, Coifman R. Comparison of Systems using Diffusion Maps. 2005, 7931-7936. DOI: 10.1109/cdc.2005.1583444.Peer-Reviewed Original ResearchDiffusion mapsDynamical system modelWork of CoifmanSingular value decompositionPhase spaceLow-dimensional embeddingAcoustic oscillationsIntrinsic geometryQualitative behaviorDimensional embeddingCandidate modelsValue decompositionAssociated dynamicsData setsSystem modelComparison of systemsModel validationSpectral propertiesEfficient methodEigenvectorsCoifmanEt alGraphSimple metricLafon