Pré-Publication, Document De Travail Année : 2026

Persistent homology of spike trains with the Curto-Itskov filtration: stability and applications

Résumé

In this paper, we define a filtration for spike train data based on the frequencies of cofiring neurons. This filtration, called the Curto-Itskov filtration, allows to define the persistence diagram of a spike train. We then introduce a distance on the space of spike trains and prove the stability of persistence diagrams, with respect to this distance. Finally, we illustrate the behavior of the Curto-Itskov filtration with simulations, and apply it on a real dataset with a clustering goal.

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hal-05519731 , version 1 (19-02-2026)

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  • HAL Id : hal-05519731 , version 1

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Louise Martineau, Christophe Pouzat, Ségolen Geffray. Persistent homology of spike trains with the Curto-Itskov filtration: stability and applications. 2026. ⟨hal-05519731⟩
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