2013
Multiscale data sampling and function extension
Bermanis A, Averbuch A, Coifman R. Multiscale data sampling and function extension. Applied And Computational Harmonic Analysis 2013, 34: 15-29. DOI: 10.1016/j.acha.2012.03.002.Peer-Reviewed Original ResearchSequence of approximationsGaussian kernel matrixData pointsAdaptive gridSpecial decompositionMultiscale schemeKernel matrixMultiscale decompositionGaussian kernelInterpolation methodMutual distanceData samplingFine hierarchyExtension methodEmpirical functionHierarchical procedureFunction extensionApproximationExtensionDecompositionPointKernelSchemeSubsamplingGrid
2009
Audio-Visual Group Recognition Using Diffusion Maps
Keller Y, Coifman R, Lafon S, Zucker S. Audio-Visual Group Recognition Using Diffusion Maps. IEEE Transactions On Signal Processing 2009, 58: 403-413. DOI: 10.1109/tsp.2009.2030861.Peer-Reviewed Original ResearchDifferent sensorsVisual speech recognitionDiffusion coordinatesMultisensory dataData fusionSpeech recognitionMultisensor acquisitionsEmbedding schemePrior approachesData sourcesPerformance improvementDiffusion mapsPhysical systemsNovel approachInput channelsDifferent sampling densitiesCommon approachDiffusion frameworkFundamental issuesPrevious workGroup recognitionRecognitionSchemeSampling densitySensors
2008
Compressive Mahalanobis Classifiers
Barbano P, Coifman R. Compressive Mahalanobis Classifiers. 2008, 345-349. DOI: 10.1109/mlsp.2008.4685504.Peer-Reviewed Original ResearchPre-processing schemeData acquisition levelClassification algorithmsCompressed SensingDetection/estimationHyperspectral imagesMahalanobis classifierMain ideaNew frameworkSalient informationAlgorithmGlobal metricsAcquisition levelClassifierNew techniqueImagesMetricsDimensionalitySchemeFrameworkInformationSensingData
2006
Data Fusion and Multicue Data Matching by Diffusion Maps
Lafon S, Keller Y, Coifman RR. Data Fusion and Multicue Data Matching by Diffusion Maps. IEEE Transactions On Pattern Analysis And Machine Intelligence 2006, 28: 1784-1797. PMID: 17063683, DOI: 10.1109/tpami.2006.223.Peer-Reviewed Original ResearchConceptsData fusionData matchingImage sequence alignmentHigh-dimensional data analysisGraph alignmentFundamental taskMatching schemeExtension algorithmGeometric harmonicsDiffusion mapsTaskMatchingDiffusion frameworkSequence alignmentInvariant embeddingData analysisSchemeDifferent sourcesAlgorithmEmbeddingFusionLipreadingData assimilationFrameworkAlignmentGeometric harmonics: A novel tool for multiscale out-of-sample extension of empirical functions
Coifman R, Lafon S. Geometric harmonics: A novel tool for multiscale out-of-sample extension of empirical functions. Applied And Computational Harmonic Analysis 2006, 21: 31-52. DOI: 10.1016/j.acha.2005.07.005.Peer-Reviewed Original ResearchEntire space RnProlate spheroidal wave functionsLaplace-Beltrami operatorSpheroidal wave functionsFunction fSubmanifold of RnNyström methodSpace RnFourier modesSample extensionGeometric harmonicsEmpirical functionWave functionsSimple schemeExtension schemeLarge domainsSpecific familySchemeRnIntrinsic frequency spectrumExtensionFrequency spectrumSubmanifoldsEigenfunctionsSlepian
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