Geometric diffusions for the analysis of data from sensor networks
Coifman RR, Maggioni M, Zucker SW, Kevrekidis IG. Geometric diffusions for the analysis of data from sensor networks. Current Opinion In Neurobiology 2005, 15: 576-584. PMID: 16150587, DOI: 10.1016/j.conb.2005.08.012.Peer-Reviewed Original ResearchConceptsSensor networksGeometric diffusionMathematical developmentComplex data setsHarmonic analysisNeural information processingActivity datasetsCertain analogyComputer modelingData setsInformation processingManifoldNetworkModelingGraphData analysisAlgorithmNew toolDatasetAnalysis of dataAnalogyFieldGeometric 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 analysisGeometryTransitionPerspectives and Challenges to Harmonic Analysis and Geometry in High Dimensions: Geometric Diffusions as a Tool for Harmonic Analysis and Structure Definition of Data
Coifman R. Perspectives and Challenges to Harmonic Analysis and Geometry in High Dimensions: Geometric Diffusions as a Tool for Harmonic Analysis and Structure Definition of Data. Mathematical Physics Studies 2005, 27: 27-35. DOI: 10.1007/3-540-30434-7_3.Peer-Reviewed Original Research
This site is protected by hCaptcha and its Privacy Policy and Terms of Service apply