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
Data Fusion and Multicue Data Matching by Diffusion Maps
Lafon S, Keller Y, Coifman RR. Data Fusion and Multicue Data Matching by Diffusion Maps. IEEE Transactions On Pattern Analysis And Machine Intelligence 2006, 28: 1784-1797. PMID: 17063683, DOI: 10.1109/tpami.2006.223.Peer-Reviewed Original ResearchConceptsData fusionData matchingImage sequence alignmentHigh-dimensional data analysisGraph alignmentFundamental taskMatching schemeExtension algorithmGeometric harmonicsDiffusion mapsTaskMatchingDiffusion frameworkSequence alignmentInvariant embeddingData analysisSchemeDifferent sourcesAlgorithmEmbeddingFusionLipreadingData assimilationFrameworkAlignmentGeometric harmonics: A novel tool for multiscale out-of-sample extension of empirical functions
Coifman R, Lafon S. Geometric harmonics: A novel tool for multiscale out-of-sample extension of empirical functions. Applied And Computational Harmonic Analysis 2006, 21: 31-52. DOI: 10.1016/j.acha.2005.07.005.Peer-Reviewed Original ResearchEntire space RnProlate spheroidal wave functionsLaplace-Beltrami operatorSpheroidal wave functionsFunction fSubmanifold of RnNyström methodSpace RnFourier modesSample extensionGeometric harmonicsEmpirical functionWave functionsSimple schemeExtension schemeLarge domainsSpecific familySchemeRnIntrinsic frequency spectrumExtensionFrequency spectrumSubmanifoldsEigenfunctionsSlepian