Intrinsic modeling of stochastic dynamical systems using empirical geometry
Talmon R, Coifman R. Intrinsic modeling of stochastic dynamical systems using empirical geometry. Applied And Computational Harmonic Analysis 2015, 39: 138-160. DOI: 10.1016/j.acha.2014.08.006.Peer-Reviewed Original ResearchLow-dimensional manifoldDynamical systemsEmpirical geometryReal-world dynamical systemsStochastic dynamical systemsNon-Gaussian tracking problemsNonlinear filtering applicationsNonlinear differential equationsIntrinsic Riemannian metricMarkov chain schemeEmpirical probability densityLocal tangent spaceIntrinsic modelDifferential equationsIntrinsic modelingKnowledge of modelsTangent spaceProbability densityMathematical calibrationTracking problemInverse problemRiemannian metricLaplace operatorRandom measurementsSmall perturbationsManifold 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