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
2019
Two-sample statistics based on anisotropic kernels
Cheng X, Cloninger A, Coifman RR. Two-sample statistics based on anisotropic kernels. Information And Inference A Journal Of The IMA 2019, 9: 677-719. PMID: 32929389, PMCID: PMC7478116, DOI: 10.1093/imaiai/iaz018.Peer-Reviewed Original Research
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
2009
Detecting intrinsic slow variables in stochastic dynamical systems by anisotropic diffusion maps
Singer A, Erban R, Kevrekidis IG, Coifman RR. Detecting intrinsic slow variables in stochastic dynamical systems by anisotropic diffusion maps. Proceedings Of The National Academy Of Sciences Of The United States Of America 2009, 106: 16090-16095. PMID: 19706457, PMCID: PMC2752552, DOI: 10.1073/pnas.0905547106.Peer-Reviewed Original ResearchConceptsStochastic dynamical systemsModel reduction approachHigh dimensional dynamic dataDynamical systemsNonlinear independent component analysisLocal principal component analysisSlow variablesMarkov matrixGood observablesDiffusion mapsNetwork simulationAnisotropic diffusionReduction approachData analysis techniqueAnalysis techniquesEigenvectorsDynamic dataObservablesIndependent component analysisComponent analysisSimulationsMatrix
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
1991
Fast wavelet transforms and numerical algorithms I
Beylkin G, Coifman R, Rokhlin V. Fast wavelet transforms and numerical algorithms I. Communications On Pure And Applied Mathematics 1991, 44: 141-183. DOI: 10.1002/cpa.3160440202.Peer-Reviewed Original ResearchPseudo-differential operatorsClass of algorithmsLinear operatorsTheory of waveletsN matrixNumerical experimentsArbitrary vectorOrder ONumerical applicationsNarrow classAlgorithm IOperatorsDetailed analytical informationIntractable problemClassAlgorithmMatrixAnalytical informationVectorTheorySchemeO operationsProblemWavelets