2015
Multivariate time-series analysis and diffusion maps
Lian W, Talmon R, Zaveri H, Carin L, Coifman R. Multivariate time-series analysis and diffusion maps. Signal Processing 2015, 116: 13-28. DOI: 10.1016/j.sigpro.2015.04.003.Peer-Reviewed Original ResearchStatistical manifoldMultivariate time series analysisNonlinear dimensionality reduction frameworkDiffusion mapsEfficient parameter estimationPairwise geodesic distancesTime-evolving distributionsFinancial data analysisBayesian generative modelKullback-Leibler divergenceNonstationary time seriesDimensionality reduction frameworkEfficient approximationParameter estimationLow-dimensional representationAffinity kernelsParametric distributionTime series analysisDimensionality reduction methodologyGeodesic distanceLocal statisticsReduction frameworkReduction methodologyManifoldDimensionality reduction
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