Maître de Conférences

Département de Physique
Ecole Normale Supérieure de Lyon
France
Information Theory for Signal Analysis (ITSA)

This toolbox illustrates the use of auto-mutual information (mutual information between subsets of the same signal) and entropy rate as powerful tools to assess refined dependencies of any order in signal temporal dynamics.
It shows how two-point auto-mutual information and entropy rate unveil information conveyed by higher order statistic and thus capture details of temporal dynamics that are overlooked by the (two-point) correlation function. Notably, it presents how Auto Mutual Information (and entropy rate) permits to discriminate between several different non Gaussian processes, having exactly the same marginal distribution and covariance function.
Further, this toolbox proposes a generalization to multi-point auto-correlation that is able to assess higher order statistics and unveils the global dependence structure.
This methodology has been developed at ENS de Lyon during the PhD of Carlos Granero Belinchon under the supervision of Stéphane G. Roux and Nicolas B. Garnier, and has been described and used in the following articles : This Matlab toolbox uses the fonction knnsearch which requires the "statistics" toolbox to be installed within Matlab. This toolbox is not suitable for analyzing large dataset but it's provided as a proof of concept.

Content.

The toolbox contains the following scripts : the following functions : and a directory data with some processes.