2024
Estimating Position-Dependent and Anisotropic Diffusivity Tensors from Molecular Dynamics Trajectories: Existing Methods and Future Outlook
Domingues T, Coifman R, Haji-Akbari A. Estimating Position-Dependent and Anisotropic Diffusivity Tensors from Molecular Dynamics Trajectories: Existing Methods and Future Outlook. Journal Of Chemical Theory And Computation 2024, 20: 4427-4455. PMID: 38815171, DOI: 10.1021/acs.jctc.4c00148.Peer-Reviewed Original ResearchKernel-based methodsMolecular dynamicsMolecular dynamics trajectoriesAnisotropic diffusion tensorPhysicochemical properties of materialsClosed-form analytical solutionMD trajectoriesMobility statisticsComputational chemistryHeuristic extensionMD simulationsProperties of materialsAlgorithmDynamics trajectoriesDiffusion tensorEstimated diffusivityVariable spaceMaterial propertiesDiscretization techniqueNatural extensionPosition-dependentFokker-Planck equationSpatial binsAnalytical solutionTracer particles
2018
Parsimonious representation of nonlinear dynamical systems through manifold learning: A chemotaxis case study
Dsilva C, Talmon R, Coifman R, Kevrekidis I. Parsimonious representation of nonlinear dynamical systems through manifold learning: A chemotaxis case study. Applied And Computational Harmonic Analysis 2018, 44: 759-773. DOI: 10.1016/j.acha.2015.06.008.Peer-Reviewed Original ResearchNonlinear dynamical systemsDiffusion mapsLocal linear regressionNonlinear manifold learning algorithmDynamical systemsDynamical behaviorStochastic modelIntrinsic geometryEmbedding coordinatesSystem dimensionalitySynthetic data setsEigendirectionsComplex data setsParsimonious representationData setsSuch algorithmsManifold learning algorithmReal dataTrue dimensionalityManifold learningLearning algorithmAlgorithmCoordinatesDimensionalityManifold
2014
Quantitative Arbor Analytics: Unsupervised Harmonic Co-Clustering of Populations of Brain Cell Arbors Based on L-Measure
Lu Y, Carin L, Coifman R, Shain W, Roysam B. Quantitative Arbor Analytics: Unsupervised Harmonic Co-Clustering of Populations of Brain Cell Arbors Based on L-Measure. Neuroinformatics 2014, 13: 47-63. PMID: 25086878, DOI: 10.1007/s12021-014-9237-2.Peer-Reviewed Original ResearchConceptsCo-clustering methodAnalytics systemSynthetic datasetsThree-dimensional visualizationAnalysis ToolkitHeterogeneous ensembleDistance measureAlgorithmMultivariate data pointsData smoothingData pointsWavelet basisData matrixHarmonic analysis theoryL-measureNeuroMorpho databaseDatasetAnalysis theoryToolkitVisualizationEnsembleRobustnessDatabaseSuperiorityMethod
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
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 techniqueImagesMetricsDimensionalitySchemeFrameworkInformationSensingDataDiffusion Maps - a Probabilistic Interpretation for Spectral Embedding and Clustering Algorithms
Nadler B, Lafon S, Coifman R, Kevrekidis I. Diffusion Maps - a Probabilistic Interpretation for Spectral Embedding and Clustering Algorithms. Lecture Notes In Computational Science And Engineering 2008, 58: 238-260. DOI: 10.1007/978-3-540-73750-6_10.Peer-Reviewed Original ResearchSpectral clusteringGraph LaplacianRandom walkSpectral embeddingMean exit timeNormalized graph LaplacianComplex high dimensional datasetsHigh-dimensional datasetsNon-linear dimensionality reductionMultiscale methodEmbedding algorithmClustering algorithmAdjacency matrixDimensional datasetsExit timeProbabilistic interpretationRelaxation timeDimensionality reductionMultiscale dataDiffusion mapsNecessary conditionEuclidean distanceProbabilistic analysisCharacteristic relaxation timeAlgorithmA Framework for Discrete Integral Transformations IThe Pseudopolar Fourier Transform
Averbuch A, Coifman R, Donoho D, Israeli M, Shkolnisky Y. A Framework for Discrete Integral Transformations IThe Pseudopolar Fourier Transform. SIAM Journal On Scientific Computing 2008, 30: 764-784. DOI: 10.1137/060650283.Peer-Reviewed Original ResearchSame complexity orderDirect inversion algorithmFrequency gridGram operatorOne-dimensional operationsDiscrete gridDiscrete caseFrequency domain structureComplexity orderContinuous functionsIterative algorithmExact analogueFast algorithmPolar coordinatesInversion algorithmPseudopolar gridApproximate interpolationAnalogous toolsContinuum phenomenaRadial densityPseudopolar Fourier transformDifferent raysAlgorithmGridDiscrete Fourier transform
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 assimilationFrameworkAlignmentDiffusion 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 dataAnalogyField
2001
Multi-Layered Image Representation
Meyer F, Averbuch A, Coifman R. Multi-Layered Image Representation. Computational Imaging And Vision 2001, 19: 281-304. DOI: 10.1007/978-94-015-9715-9_10.Peer-Reviewed Original ResearchImage representationMulti-layer approachVideo codingImage compressionLossy wayImage understandingDifferent bitratesDifferent transformsMulti-layered representationRepresentation techniquesTexture layerMain contributionSparse representationDecomposition algorithmBasis functionsAlgorithmNew paradigmPrevious compressionImagesRepresentationBeautiful applicationsBitrateMeaningful way
1998
Adapted waveform analysis in sound processing
Coifman R. Adapted waveform analysis in sound processing. The Journal Of The Acoustical Society Of America 1998, 103: 2821-2822. DOI: 10.1121/1.421920.Peer-Reviewed Original ResearchFast numerical analysisLibrary of waveformsComputational algorithmFourier methodMore complex signalsTime/frequency analysisNumerical analysisAcoustic designTime localizationAutomatic speech segmentationWavelet packetCharacteristic durationComplex signalsFast searchWaveform analysisSimple signalsProcessing toolkitTraditional spectrogramsWaveformsLocal structureSpeech segmentationFrequency analysisSuperpositionAlgorithmCosineFast wavelet packet image compression
Meyer F, Averbuch A, Stromberg J, Coifman R. Fast wavelet packet image compression. Proceedings DCC '98 Data Compression Conference (Cat No98TB100225) 1998, 563. DOI: 10.1109/dcc.1998.672305.Peer-Reviewed Original Research
1997
Brushlets: A Tool for Directional Image Analysis and Image Compression
Meyer F, Coifman R. Brushlets: A Tool for Directional Image Analysis and Image Compression. Applied And Computational Harmonic Analysis 1997, 4: 147-187. DOI: 10.1006/acha.1997.0208.Peer-Reviewed Original ResearchMotion compensation of wavelet coefficients for very low bit rate video coding
Meyer F, Averbuch A, Coifman R. Motion compensation of wavelet coefficients for very low bit rate video coding. 1997, 3: 638-641 vol.3. DOI: 10.1109/icip.1997.632202.Peer-Reviewed Original Research
1995
Local discriminant bases and their applications
Saito N, Coifman R. Local discriminant bases and their applications. Journal Of Mathematical Imaging And Vision 1995, 5: 337-358. DOI: 10.1007/bf01250288.Peer-Reviewed Original ResearchOrthonormal basisStatistical methodsClassification problemSignificant coordinatesBasis functionsSignal classification problemsTrigonometric basisLocal trigonometric basesLinear discriminant analysisInput signalDirect applicationRegression treesProblemBest basis algorithmAlgorithmTime-frequency planeSignal componentsFurther applicationCoordinatesDimensionalityImage classification problemsApplicationsSmall numberTexture classification problemWavelet packets as a tool for sound processing
Coifman R. Wavelet packets as a tool for sound processing. The Journal Of The Acoustical Society Of America 1995, 97: 3287-3287. DOI: 10.1121/1.411553.Peer-Reviewed Original ResearchFeature Extraction by Best-Basis and Wavelet Methods.
Wickerhauser M, Weiss G, Coifman R. Feature Extraction by Best-Basis and Wavelet Methods. 1995 DOI: 10.21236/ada299572.Peer-Reviewed Original ResearchImage compression algorithmCompression algorithmMedical imagesCompress imagesFeature extractionAnalysis libraryCommercial software packagesWavelet technologyIdentification systemDriver simulationSoftware packageNew algorithmNew waveletWavelet packetAlgorithmSoftwareImage analysis softwareWaveletsAnalysis softwareImagesWavelet methodPacketsTechnical reportTechnologyCommercial products
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
1989
Multiresolution 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