2023
Reduced-order modeling and analysis of dynamic cerebral autoregulation via diffusion maps
dos Santos K, Katsidoniotaki M, Miller E, Petersen N, Marshall R, Kougioumtzoglou I. Reduced-order modeling and analysis of dynamic cerebral autoregulation via diffusion maps. Physiological Measurement 2023, 44: 044001. PMID: 36963111, PMCID: PMC11271258, DOI: 10.1088/1361-6579/acc780.Peer-Reviewed Original ResearchConceptsDiffusion mapsState-space descriptionReduced-order modelingIntrinsic dynamicsTime derivativeLow-dimensional representationRandom walkMarkov matrixParsimonious modelingSignificant eigenvaluesEigenvalue ratioFurther dimension reductionEigenvalue analysisTransfer function analysisDimension reductionData-driven techniquesMain resultsDynamicsEigenvaluesFlow velocityModelingSuperior performanceMap techniqueGraphWalk
2009
Detecting intrinsic slow variables in stochastic dynamical systems by anisotropic diffusion maps
Singer A, Erban R, Kevrekidis IG, Coifman RR. Detecting intrinsic slow variables in stochastic dynamical systems by anisotropic diffusion maps. Proceedings Of The National Academy Of Sciences Of The United States Of America 2009, 106: 16090-16095. PMID: 19706457, PMCID: PMC2752552, DOI: 10.1073/pnas.0905547106.Peer-Reviewed Original ResearchConceptsStochastic dynamical systemsModel reduction approachHigh dimensional dynamic dataDynamical systemsNonlinear independent component analysisLocal principal component analysisSlow variablesMarkov matrixGood observablesDiffusion mapsNetwork simulationAnisotropic diffusionReduction approachData analysis techniqueAnalysis techniquesEigenvectorsDynamic dataObservablesIndependent component analysisComponent analysisSimulationsMatrix
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
2005
Geometric diffusions as a tool for harmonic analysis and structure definition of data: Multiscale methods
Coifman RR, Lafon S, Lee AB, Maggioni M, Nadler B, Warner F, Zucker SW. Geometric diffusions as a tool for harmonic analysis and structure definition of data: Multiscale methods. Proceedings Of The National Academy Of Sciences Of The United States Of America 2005, 102: 7432-7437. PMID: 15899969, PMCID: PMC1140426, DOI: 10.1073/pnas.0500896102.Peer-Reviewed Original ResearchMarkov matrixMacroscopic descriptionGeometric diffusionMultiscale methodDiffusion semigroupsScaling functionsMultiscale natureNewtonian paradigmHarmonic analysisN algorithmMultiscale analysisComplex structureHeterogeneous structureGeometric organizationSemigroupsData representationMatrixSystem leadCompanion articleDifferent scalesGeneralizationGraphDescriptionAlgorithmProblemGeometric diffusions as a tool for harmonic analysis and structure definition of data: Diffusion maps
Coifman RR, Lafon S, Lee AB, Maggioni M, Nadler B, Warner F, Zucker SW. Geometric diffusions as a tool for harmonic analysis and structure definition of data: Diffusion maps. Proceedings Of The National Academy Of Sciences Of The United States Of America 2005, 102: 7426-7431. PMID: 15899970, PMCID: PMC1140422, DOI: 10.1073/pnas.0500334102.Peer-Reviewed Original ResearchMarkov matrixMacroscopic descriptionGeometric diffusionMultiscale geometryDiffusion semigroupsNewtonian paradigmHarmonic analysisDiffusion mapsUnified viewNumerical analysisComplex structureLocal transitionsGeometric organizationEigenfunctionsSemigroupsMachine learningMatrixSystem leadGeneralizationDifferent scalesGraphDescriptionData analysisGeometryTransition
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