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
2006
Diffusion 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 simulations