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 homo-logy 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 persistent 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 Phy-sioNet database and we have found numerical evidences that the methodology is able to detect the transition between the pre-ictal and ictal states.

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

MERELLI, Emanuela;PIANGERELLI, MARCO;
2016

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 homo-logy 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 persistent 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 Phy-sioNet database and we have found numerical evidences that the methodology is able to detect the transition between the pre-ictal and ictal states.
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EAI Endorsed Transactions on Self-Adaptive Systems 16(7), e5.pdf

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Descrizione: Articolo selezionato da: "BICT'15 - Proceedings of the 9th EAI International Conference on Bio-inspired Information and Communications Technologies (formerly BIONETICS)" e pubblicato nella collana "EAI Endorsed Transactions on Self-Adaptive Systems" - sas 16(7):e5 - https://eudl.eu/doi/10.4108/eai.3-12-2015.2262525
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Utilizza questo identificativo per citare o creare un link a questo documento: http://hdl.handle.net/11581/398502
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