2015
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 reduction
2013
Empirical intrinsic geometry for nonlinear modeling and time series filtering
Talmon R, Coifman RR. Empirical intrinsic geometry for nonlinear modeling and time series filtering. Proceedings Of The National Academy Of Sciences Of The United States Of America 2013, 110: 12535-12540. PMID: 23847205, PMCID: PMC3732962, DOI: 10.1073/pnas.1307298110.Peer-Reviewed Original ResearchIntrinsic geometryNon-Gaussian tracking problemsHigh-dimensional time seriesNonlinear filtering frameworkTime series filteringInformation geometryStochastic settingParametric manifoldTracking problemStatistical modelBayesian approachNonlinear modelingEmpirical distributionFiltering frameworkEmpirical dynamicsInstrumental modalitiesInferred modelGeometryTime seriesTime series analysisDifferent observationsReal signalsSeries analysisDynamicsAnalysis tools