2024/04/06 by Stéphane Chrétien, Chrétien, Stéphane, Ben Gao +4
Computer Science · Engineering · #Artificial Immune Systems Applications #FOS: Computer and information sciences #FOS: Electrical engineering #Machine Learning (cs.LG) #Machine Learning (stat.ML) #Signal Processing (eess.SP) #Topological and Geometric Data Analysis #electronic engineering #information engineering
paper · pdf · doi:10.48550/arxiv.2404.15328
openalex publication_date 2024/04/06 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
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 \citechretienleveraging 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 \citepetri2014homological. 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 \citelyons2002system based on the formalism introduced by Chen \citechen1957integration. 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 \citechretienleveraging. We apply our tools for the analysis of brain signals such as EEG to detect precursor phenomena to epileptic seizures.