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
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
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 dataAnalogyFieldComparison 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
2001
Low bit-rate efficient compression for seismic data
Averbuch A, Meyer R, Stromberg J, Coifman R, Vassiliou A. Low bit-rate efficient compression for seismic data. IEEE Transactions On Image Processing 2001, 10: 1801-1814. PMID: 18255520, DOI: 10.1109/83.974565.Peer-Reviewed Original ResearchCompression algorithmHigh compression ratioData compressionCompression ratioData setsSeismic data setsNew compression algorithmModerate compression ratiosHuffman coding schemeHigher-dimensional transformsSeismic data compressionFast processing speedLocal cosine transformMultimedia applicationsData operationsEfficient compressionCompression schemeDifferent data setsCompression artifactsCompression techniquesImage processingCosine transformCoding schemeCompression resultsData dynamic range