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
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
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 dataAnalogyFieldPerspectives 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
2000
Challenges in Analysis
Coifman R. Challenges in Analysis. Modern Birkhäuser Classics 2000, 471-480. DOI: 10.1007/978-3-0346-0425-3_2.Peer-Reviewed Original Research
1985
Some new function spaces and their applications to Harmonic analysis
Coifman R, Meyer Y, Stein E. Some new function spaces and their applications to Harmonic analysis. Journal Of Functional Analysis 1985, 62: 304-335. DOI: 10.1016/0022-1236(85)90007-2.Peer-Reviewed Original ResearchTent spacesHarmonic analysisHardy spacesFamily of spacesNew function spaceLipschitz curvesFunction spacesAtomic decompositionCauchy integralCarleson inequalitySquare functionMaximal functionSpaceTheoryBasic techniquesInequalitySimplificationIntegralsCorollaryMultilinear analysisApplicationsFunctionExtensionUnification