2018
Parsimonious representation of nonlinear dynamical systems through manifold learning: A chemotaxis case study
Dsilva C, Talmon R, Coifman R, Kevrekidis I. Parsimonious representation of nonlinear dynamical systems through manifold learning: A chemotaxis case study. Applied And Computational Harmonic Analysis 2018, 44: 759-773. DOI: 10.1016/j.acha.2015.06.008.Peer-Reviewed Original ResearchNonlinear dynamical systemsDiffusion mapsLocal linear regressionNonlinear manifold learning algorithmDynamical systemsDynamical behaviorStochastic modelIntrinsic geometryEmbedding coordinatesSystem dimensionalitySynthetic data setsEigendirectionsComplex data setsParsimonious representationData setsSuch algorithmsManifold learning algorithmReal dataTrue dimensionalityManifold learningLearning algorithmAlgorithmCoordinatesDimensionalityManifold
2005
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 dataAnalogyField