Time topological analysis of EEG using signature theory
<|reference_start|>Time topological analysis of EEG using signature theory: Anomaly detection in multivariate signals is a task of paramount importance in many disciplines (epidemiology, finance, cognitive sciences and neurosciences, oncology, etc.). In this perspective, Topological Data Analysis (TDA) offers a battery of "shape" invariants that can be exploited for the implementation of an effective detection scheme. Our contribution consists of extending the constructions presented in \cite{chretienleveraging} on the construction of simplicial complexes from the Signatures of signals and their predictive capacities, rather than the use of a generic distance as in \cite{petri2014homological}. Signature theory is a new theme in Machine Learning arXiv:1603.03788 stemming from recent work on the notions of Rough Paths developed by Terry Lyons and his team \cite{lyons2002system} based on the formalism introduced by Chen \cite{chen1957integration}. We explore in particular the detection of changes in topology, based on tracking the evolution of homological persistence and the Betti numbers associated with the complex introduced in \cite{chretienleveraging}. We apply our tools for the analysis of brain signals such as EEG to detect precursor phenomena to epileptic seizures.<|reference_end|>
@article{chrétien2024time,
    title={Time topological analysis of EEG using signature theory},
    author={St'ephane Chr'etien, Ben Gao, Astrid Thebault-Guiochon and R'emi
  Vaucher},
    journal={arXiv preprint arXiv:2404.15328},
    year={2024},
    archivePrefix={arXiv},
    eprint={2404.15328},
    primaryClass={eess.SP cs.LG stat.ML}
}