sas 16(7): e5

Research Article

A topological approach for multivariate time series characterization: the epileptic brain

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  • @ARTICLE{10.4108/eai.3-12-2015.2262525,
        author={Emanuela Merelli and Marco Piangerelli and Matteo Rucco and Daniele Toller},
        title={A topological approach for multivariate time series characterization: the epileptic brain},
        journal={EAI Endorsed Transactions on Self-Adaptive Systems},
        volume={2},
        number={7},
        publisher={ACM},
        journal_a={SAS},
        year={2016},
        month={5},
        keywords={topological data analysis, multivariate time series, complex systems, epilepsy, entropy, signal analysis},
        doi={10.4108/eai.3-12-2015.2262525}
    }
    
  • Emanuela Merelli
    Marco Piangerelli
    Matteo Rucco
    Daniele Toller
    Year: 2016
    A topological approach for multivariate time series characterization: the epileptic brain
    SAS
    EAI
    DOI: 10.4108/eai.3-12-2015.2262525
Emanuela Merelli1, Marco Piangerelli1,*, Matteo Rucco1, Daniele Toller1
  • 1: School of Science and Technology, Computer Science Division, University of Camerino
*Contact email: marco.piangerelli@unicam.it

Abstract

In this paper we propose a methodology based on Topogical Data Analysis (TDA) for capturing when a complex system, represented by a multivariate time series, changes its internal organization. The modification of the inner organization among the entities belonging to a complex system can induce a phase transition of the entire system. In order to identify these reorganizations, we designed a new methodology that is based on the representation of time series by simplicial complexes. The topologization of multivariate time series successfully pinpoints out when a complex system evolves. Simplicial complexes are characterized by persistent homology techniques, such as the clique weight rank persistent homology and the topological invariants are used for computing a new entropy measure, the so-called weighted per- sistent entropy. With respect to the global invariants, e.g. the Betti numbers, the entropy takes into account also the topological noise and then it captures when a phase transition happens in a system. In order to verify the reliability of the methodology, we have analyzed the EEG signals of PhysioNet database and we have found numerical evidences that the methodology is able to detect the transition between the pre-ictal and ictal states.