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 - 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
Coifman R, Lafon S. Diffusion maps. Applied And Computational Harmonic Analysis 2006, 21: 5-30. DOI: 10.1016/j.acha.2006.04.006.Peer-Reviewed Original ResearchMarkov matrixSpectral graph theoryDiffusion mapsGraph theoryMultiscale geometryGeometric descriptionGeometric counterpartMarkov processComplex geometric structuresData parametrizationGeometric structureEfficient representationDiffusion processDimensionality reductionSpectral propertiesData setsEigenfunctionsMachine learningMatrixParametrizationCoordinatesGeometryTheoryVariety of contextsFramework