2008
Diffusion Maps, Reduction Coordinates, and Low Dimensional Representation of Stochastic Systems
Coifman R, Kevrekidis I, Lafon S, Maggioni M, Nadler B. Diffusion Maps, Reduction Coordinates, and Low Dimensional Representation of Stochastic Systems. Multiscale Modeling And Simulation 2008, 7: 842-864. DOI: 10.1137/070696325.Peer-Reviewed Original ResearchStochastic systemsEffective free energy surfaceHigh-dimensional stochastic systemsLow-dimensional representationDimensional stochastic systemsRandom walk matrixHigh-dimensional systemsDiffusion maps spaceDimensional representationDiffusion mapsMean squared error criterionReduction coordinatesSquared error criterionComputational physicsDiffusion operatorDimensional systemsFinite differencesRestriction operatorOriginal spaceComputational experimentsFree energy surfaceError criterionEigenfunctionsSimulation runsDifferent simulation runs
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