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 reductionManifold Learning for Latent Variable Inference in Dynamical Systems
Talmon R, Mallat S, Zaveri H, Coifman R. Manifold Learning for Latent Variable Inference in Dynamical Systems. IEEE Transactions On Signal Processing 2015, 63: 3843-3856. DOI: 10.1109/tsp.2015.2432731.Peer-Reviewed Original ResearchDynamical systemsLatent variable inferenceOutput signal measurementsNonlinear observerEigenvector problemLaplace operatorSignal geometryIntrinsic distanceSignal measurementsAccurate recoveryIntrinsic variablesLatent variablesObserverInferenceMeasurement deviceManifoldOperatorsVariablesGeometryIntracranial electroencephalography signalsKernelDynamicsPropertiesProblemSolution
2006
Diffusion wavelets
Coifman R, Maggioni M. Diffusion wavelets. Applied And Computational Harmonic Analysis 2006, 21: 53-94. DOI: 10.1016/j.acha.2006.04.004.Peer-Reviewed Original ResearchPseudo-differential operatorsFast multipole methodClass of operatorsNon-homogeneous mediaAssociated Green's functionSpectral theorySymmetric operatorsMultiresolution analysisText documentsDownsampling operatorNumerical rankCoarse grainingCalderón–ZygmundStable algorithmMultiscale computationsData cloudOrthonormal scaling functionsMultipole methodDirectory structureOperator TScaling functionsGreen's functionDiffusion waveletsManifoldMultiscale analysis
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