Séminaire Datashape
Using signature theory for the creation of simplicial complexes on time evolving signals
05
fév. 2025
Intervenant : Rémi Vaucher
Institution : Université Lyon 2 et Halias Technologies
Heure : 11h00 - 12h00
Lieu : 2L8

The theory of signatures, developed by K.T. Chen in the 1950s, studies the geometry of paths through iterations of the Stieltjes integral. This tool, originally rooted in pure differential geometry, was later introduced into probability theory and subsequently into machine learning by Terry Lyons.

Initially used in rough path theory, it gained some recognition for its application in extracting geometric features for machine learning, reaching outstanding results.

In this presentation, we will first examine the signature of a rough path and then explore how its remarkable properties can be leveraged to construct a simplicial complex that reflects explainability within a family of time series signals. Initially applied to univariate signals, we will see how this method can be extended to more complex data, such as multivariate signals with non-homogeneous dimensions.

 

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