Empirical intrinsic geometry for nonlinear modeling and time series filtering

Ronen Talmon, Ronald R. Coifman

Research output: Contribution to journalArticlepeer-review


In this paper, we present a method for time series analysis based on empirical intrinsic geometry (EIG). EIG enables one to reveal the low-dimensional parametric manifold as well as to infer the underlying dynamics of high-dimensional time series. By incorporating concepts of information geometry, this method extends existing geometric analysis tools to support stochastic settings and parametrizes the geometry of empirical distributions. However, the statistical models are not required as priors; hence, EIG may be applied to a wide range of real signals without existing definitive models. We show that the inferred model is noise-resilient and invariant under different observation and instrumental modalities. In addition, we show that it can be extended efficiently to newly acquired measurements in a sequential manner. These two advantages enable us to revisit the Bayesian approach and incorporate empirical dynamics and intrinsic geometry into a nonlinear filtering framework. We show applications to nonlinear and non-Gaussian tracking problems as well as to acoustic signal localization.

Original languageEnglish
Pages (from-to)12535-12540
Number of pages6
JournalProceedings of the National Academy of Sciences of the United States of America
Issue number31
StatePublished - 30 Jul 2013
Externally publishedYes


  • Anisotropic diffusion
  • Manifold learning
  • Signal processing

All Science Journal Classification (ASJC) codes

  • General


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