Time topological analysis of EEG using signature theory

TL;DR

This paper introduces a novel topological data analysis method using signal signatures to detect changes in EEG signals, particularly for identifying precursors to epileptic seizures, advancing the application of TDA in neuroscience.

Contribution

It extends existing topological methods by utilizing signal signatures for simplicial complex construction, improving anomaly detection in multivariate signals like EEG.

Findings

Effective detection of seizure precursors in EEG signals.

Enhanced topological analysis using signature-based simplicial complexes.

Potential for early intervention in neurological disorders.

Abstract

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.