2023
Robust Estimation of Position-Dependent Anisotropic Diffusivity Tensors from Molecular Dynamics Trajectories
Domingues T, Coifman R, Haji-Akbari A. Robust Estimation of Position-Dependent Anisotropic Diffusivity Tensors from Molecular Dynamics Trajectories. The Journal Of Physical Chemistry B 2023, 127: 8644-8659. PMID: 37757480, DOI: 10.1021/acs.jpcb.3c03581.Peer-Reviewed Original ResearchMechanical observablesDiffusivity tensorEfficient correction schemeAnisotropic diffusivity tensorStochastic counterpartSame qualitative featuresStochastic trajectoriesVan Hove correlation functionRobust estimationCovariance estimatorMolecular simulation communityCorrelation functionsDiffusivity profilesRotational symmetryLennard-Jones fluidEstimatorQualitative featuresDiffusion mapsSpatial profileObservablesTensorCorrection schemeTransport propertiesProperty functionsPrevious paper
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
2015
Multivariate time-series analysis and diffusion maps
Lian W, Talmon R, Zaveri H, Carin L, Coifman R. Multivariate time-series analysis and diffusion maps. Signal Processing 2015, 116: 13-28. DOI: 10.1016/j.sigpro.2015.04.003.Peer-Reviewed Original ResearchStatistical manifoldMultivariate time series analysisNonlinear dimensionality reduction frameworkDiffusion mapsEfficient parameter estimationPairwise geodesic distancesTime-evolving distributionsFinancial data analysisBayesian generative modelKullback-Leibler divergenceNonstationary time seriesDimensionality reduction frameworkEfficient approximationParameter estimationLow-dimensional representationAffinity kernelsParametric distributionTime series analysisDimensionality reduction methodologyGeodesic distanceLocal statisticsReduction frameworkReduction methodologyManifoldDimensionality reduction
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
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
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 analysisSimulationsMatrixAudio-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
Diffusion 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 timeAlgorithmDiffusion Maps, Reduction Coordinates, and Low Dimensional Representation of Stochastic Systems
Coifman R, Kevrekidis I, Lafon S, Maggioni M, Nadler B. Diffusion Maps, Reduction Coordinates, and Low Dimensional Representation of Stochastic Systems. Multiscale Modeling And Simulation 2008, 7: 842-864. DOI: 10.1137/070696325.Peer-Reviewed Original ResearchStochastic systemsEffective free energy surfaceHigh-dimensional stochastic systemsLow-dimensional representationDimensional stochastic systemsRandom walk matrixHigh-dimensional systemsDiffusion maps spaceDimensional representationDiffusion mapsMean squared error criterionReduction coordinatesSquared error criterionComputational physicsDiffusion operatorDimensional systemsFinite differencesRestriction operatorOriginal spaceComputational experimentsFree energy surfaceError criterionEigenfunctionsSimulation runsDifferent simulation runs
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 spaceSpaceVariable-free exploration of stochastic models: A gene regulatory network example
Erban R, Frewen TA, Wang X, Elston TC, Coifman R, Nadler B, Kevrekidis IG. Variable-free exploration of stochastic models: A gene regulatory network example. The Journal Of Chemical Physics 2007, 126: 155103. PMID: 17461667, DOI: 10.1063/1.2718529.Peer-Reviewed Original ResearchConceptsStochastic modelEquation-free approachLow-dimensional descriptionLong-time behaviorNetwork exampleAppropriate observablesStochastic simulationGood observablesGene regulatory networksObservablesComplex systemsDiffusion mapsSimulation dataPhysical variablesPrevious paperLong-term dynamicsAppropriate valuesDynamicsEigenvectorsLaplacianComputationRegulatory networksGraphModelRestriction proceduresValidation of low-dimensional models using Diffusion maps and Harmonic Averaging
Hagen G, Smith T, Banasuk A, Coifman R, Mezić I. Validation of low-dimensional models using Diffusion maps and Harmonic Averaging. 2007, 5353-5357. DOI: 10.1109/cdc.2007.4434821.Peer-Reviewed Original Research
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 maps, spectral clustering and reaction coordinates of dynamical systems
Nadler B, Lafon S, Coifman R, Kevrekidis I. Diffusion maps, spectral clustering and reaction coordinates of dynamical systems. Applied And Computational Harmonic Analysis 2006, 21: 113-127. DOI: 10.1016/j.acha.2005.07.004.Peer-Reviewed Original ResearchFokker-Planck operatorDynamical systemsDifferential operatorsHigh-dimensional stochastic systemsRandom walkProbability distributionDimensional stochastic systemsStochastic differential equationsCorresponding differential operatorComplex dynamical systemsTime evolutionLong-time asymptoticsLow-dimensional Euclidean spaceGeneral probability distributionNormalized graph LaplacianLaplace-Beltrami operatorDimensional Euclidean spaceDiffusion mapsLong-time evolutionSpectral clusteringStochastic systemsDifferential equationsHigh-dimensional dataSlow variablesLarge-scale simulationsDiffusion 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
2005
Comparison of Systems using Diffusion Maps
Vaidya U, Hagen G, Lafon S, Banaszuk A, Mezic I, Coifman R. Comparison of Systems using Diffusion Maps. 2005, 7931-7936. DOI: 10.1109/cdc.2005.1583444.Peer-Reviewed Original ResearchDiffusion mapsDynamical system modelWork of CoifmanSingular value decompositionPhase spaceLow-dimensional embeddingAcoustic oscillationsIntrinsic geometryQualitative behaviorDimensional embeddingCandidate modelsValue decompositionAssociated dynamicsData setsSystem modelComparison of systemsModel validationSpectral propertiesEfficient methodEigenvectorsCoifmanEt alGraphSimple metricLafon