2007
Diffusion Maps and Geometric Harmonics for Automatic Target Recognition (ATR). Volume 2. Appendices
Zucker S, Coifman R. Diffusion Maps and Geometric Harmonics for Automatic Target Recognition (ATR). Volume 2. Appendices. 2007 DOI: 10.21236/ada476152.Peer-Reviewed Original ResearchAutomatic target recognitionIntegration of audioGeometric harmonicsLow-dimensional Euclidean spaceVideo streamsAudio streamAutomatic recognitionSimilarity measureDifferent sensorsTarget recognitionDiffusion mapsFirst versionProblem formulationEuclidean coordinatesMeasurement spaceSignal interpretationRecognitionWright-Patterson Air Force BaseAudioEuclidean spaceSoftwareStreamsAFRLDimensional Euclidean spaceSpace
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