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