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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 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 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 lyons2002system based on the formalism introduced by Chen 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 chretienleveraging. We apply our tools for the analysis of brain signals such as EEG to detect precursor phenomena to epileptic seizures.
Chrétien et al. (Sat,) studied this question.