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
Fast and accurate Polar Fourier transform
Averbuch A, Coifman R, Donoho D, Elad M, Israeli M. Fast and accurate Polar Fourier transform. Applied And Computational Harmonic Analysis 2006, 21: 145-167. DOI: 10.1016/j.acha.2005.11.003.Peer-Reviewed Original ResearchPolar coordinatesFourier transformContinuous formulationApplied problemsCartesian gridTwo-dimensional signalsInitial gridSize n×nContinuum ideasInterpolation operationError analysisAlgorithm complexityFFT methodConversion processPolar Fourier transformInverse transformPolar systemsFFTGridCentral toolCoordinatesInterpolationTransformProblemN×nDiffusion 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
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 problemOn local orthonormal bases for classification and regression
Saito N, Coifman R. On local orthonormal bases for classification and regression. 2013 IEEE International Conference On Acoustics, Speech And Signal Processing 1995, 3: 1529-1532 vol.3. DOI: 10.1109/icassp.1995.479852.Peer-Reviewed Original ResearchOrthonormal basisRegression problemsLocal orthonormal basisRelative entropyRegression errorsStatistical methodsSynthetic examplesSignificant coordinatesBasis functionsLinear discriminant analysisRegression methodEnergy distributionRegression treesProblemClassification problemTime-frequency planeSignal classificationEntropyTraditional methodsCoordinatesDimensionalityTime-frequency energy distributionSmall number
1994
Selection of best bases for classification and regression
Coifman R, Saito N. Selection of best bases for classification and regression. 1994, 51. DOI: 10.1109/wits.1994.513882.Peer-Reviewed Original Research