2008
Diffusion Maps - a Probabilistic Interpretation for Spectral Embedding and Clustering Algorithms
Nadler B, Lafon S, Coifman R, Kevrekidis I. Diffusion Maps - a Probabilistic Interpretation for Spectral Embedding and Clustering Algorithms. Lecture Notes In Computational Science And Engineering 2008, 58: 238-260. DOI: 10.1007/978-3-540-73750-6_10.Peer-Reviewed Original ResearchSpectral clusteringGraph LaplacianRandom walkSpectral embeddingMean exit timeNormalized graph LaplacianComplex high dimensional datasetsHigh-dimensional datasetsNon-linear dimensionality reductionMultiscale methodEmbedding algorithmClustering algorithmAdjacency matrixDimensional datasetsExit timeProbabilistic interpretationRelaxation timeDimensionality reductionMultiscale dataDiffusion mapsNecessary conditionEuclidean distanceProbabilistic analysisCharacteristic relaxation timeAlgorithm
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