Multivariate time-series analysis and diffusion maps
Lian W, Talmon R, Zaveri H, Carin L, Coifman R. Multivariate time-series analysis and diffusion maps. Signal Processing 2015, 116: 13-28. DOI: 10.1016/j.sigpro.2015.04.003.Peer-Reviewed Original ResearchStatistical manifoldMultivariate time series analysisNonlinear dimensionality reduction frameworkDiffusion mapsEfficient parameter estimationPairwise geodesic distancesTime-evolving distributionsFinancial data analysisBayesian generative modelKullback-Leibler divergenceNonstationary time seriesDimensionality reduction frameworkEfficient approximationParameter estimationLow-dimensional representationAffinity kernelsParametric distributionTime series analysisDimensionality reduction methodologyGeodesic distanceLocal statisticsReduction frameworkReduction methodologyManifoldDimensionality reductionManifold Learning for Latent Variable Inference in Dynamical Systems
Talmon R, Mallat S, Zaveri H, Coifman R. Manifold Learning for Latent Variable Inference in Dynamical Systems. IEEE Transactions On Signal Processing 2015, 63: 3843-3856. DOI: 10.1109/tsp.2015.2432731.Peer-Reviewed Original ResearchDynamical systemsLatent variable inferenceOutput signal measurementsNonlinear observerEigenvector problemLaplace operatorSignal geometryIntrinsic distanceSignal measurementsAccurate recoveryIntrinsic variablesLatent variablesObserverInferenceMeasurement deviceManifoldOperatorsVariablesGeometryIntracranial electroencephalography signalsKernelDynamicsPropertiesProblemSolution