2021
Doubly Stochastic Normalization of the Gaussian Kernel Is Robust to Heteroskedastic Noise.
Landa B, Coifman RR, Kluger Y. Doubly Stochastic Normalization of the Gaussian Kernel Is Robust to Heteroskedastic Noise. SIAM Journal On Mathematics Of Data Science 2021, 3: 388-413. PMID: 34124607, PMCID: PMC8194191, DOI: 10.1137/20m1342124.Peer-Reviewed Original ResearchStochastic normalizationHeteroskedastic noiseGaussian kernelHigh-dimensional settingsMatrix convergesAmbient dimensionDifferent noise variancesEuclidean spaceData pointsNoise varianceSymmetric normalizationCertain normalizationAffinity matrixClean counterpartsPairwise distancesKernelNoiseData analysis techniqueSingle-cell RNA-sequencing dataParticular directionSpaceWidespread approachConvergesMatrixHeteroskedasticity
2015
Hölder–Lipschitz Norms and Their Duals on Spaces with Semigroups, with Applications to Earth Mover’s Distance
Leeb W, Coifman R. Hölder–Lipschitz Norms and Their Duals on Spaces with Semigroups, with Applications to Earth Mover’s Distance. Journal Of Fourier Analysis And Applications 2015, 22: 910-953. DOI: 10.1007/s00041-015-9439-5.Peer-Reviewed Original Research
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
2007
Diffusion Maps and Geometric Harmonics for Automatic Target Recognition (ATR). Volume 2. Appendices
Zucker S, Coifman R. Diffusion Maps and Geometric Harmonics for Automatic Target Recognition (ATR). Volume 2. Appendices. 2007 DOI: 10.21236/ada476152.Peer-Reviewed Original ResearchAutomatic target recognitionIntegration of audioGeometric harmonicsLow-dimensional Euclidean spaceVideo streamsAudio streamAutomatic recognitionSimilarity measureDifferent sensorsTarget recognitionDiffusion mapsFirst versionProblem formulationEuclidean coordinatesMeasurement spaceSignal interpretationRecognitionWright-Patterson Air Force BaseAudioEuclidean spaceSoftwareStreamsAFRLDimensional Euclidean spaceSpace
1990
Multiresolution Analysis in Non-Homogeneous Media
Coifman R. Multiresolution Analysis in Non-Homogeneous Media. Inverse Problems And Theoretical Imaging 1990, 259-262. DOI: 10.1007/978-3-642-75988-8_25.Peer-Reviewed Original Research
1989
Multiresolution Analysis in Non-Homogeneous Media
Coifman R. Multiresolution Analysis in Non-Homogeneous Media. Inverse Problems And Theoretical Imaging 1989, 259-262. DOI: 10.1007/978-3-642-97177-8_25.Peer-Reviewed Original ResearchMultiresolution 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
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
1982
A theory of complex interpolation for families of Banach spaces
Coifman R, Cwikel M, Rochberg R, Sagher Y, Weiss G. A theory of complex interpolation for families of Banach spaces. Advances In Mathematics 1982, 43: 203-229. DOI: 10.1016/0001-8708(82)90034-2.Peer-Reviewed Original Research