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
2005
Partial least squares, Beer's law and the net analyte signal: statistical modeling and analysis
Nadler B, Coifman R. Partial least squares, Beer's law and the net analyte signal: statistical modeling and analysis. Journal Of Chemometrics 2005, 19: 45-54. DOI: 10.1002/cem.906.Peer-Reviewed Original ResearchRegression vectorFinite training setNet analyte signal vectorInput-output samplesJoint probability distributionPartial least squaresCommon regression algorithmsNoise-free caseNoise-free samplesRandom variablesRandom realizationsLinear multivariate modelProbability distributionAsymptotic optimalityInfinite numberK iterationLinear mixture modelMean squared errorSpecific probabilistic modelMixture modelSignal vectorUnstructured noiseLeast squaresPLS algorithmProbabilistic model