Persistent homology of spike trains with the Curto-Itskov filtration: stability and applications
Louise Martineau, Christophe Pouzat, Ségolen Geffray · HAL (Le Centre pour la Communication Scientifique Directe) · 2026
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.