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 analysisSimulationsMatrix
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