Leveraging the Power of Signatures for the Construction of Topological Complexes for the Analysis of Multivariate Complex Dynamics - Equipe de Recherche en Ingénierie des Connaissances Access content directly
Conference Papers Year : 2024

Leveraging the Power of Signatures for the Construction of Topological Complexes for the Analysis of Multivariate Complex Dynamics

Abstract

Topological Data Analysis is a field of great interest in many applications such as finance or neuroscience. The goal of the present paper is to propose a novel approach to building simplicial complexes that capture the multiway ordered interactions in the components of high-dimensional time series using the theory of Signatures. Signatures represent one of the most powerful transforms for extracting group-wise structural features and we put them to work in the task of discover- ing statistically meaningful simplices from a complex that we estimate sequentially. Numerical experiments on an fMRI dataset illustrates the efficiency and relevance of our approach.
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hal-04590221 , version 1 (30-05-2024)

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Stéphane Chrétien, Ben Gao, Astrid Thébault Guiochon, Rémi Vaucher. Leveraging the Power of Signatures for the Construction of Topological Complexes for the Analysis of Multivariate Complex Dynamics. The Twelfth International Conference on Complex Networks and their Applications, Nov 2023, Menton Riviera, France. pp.283-294, ⟨10.1007/978-3-031-53468-3_24⟩. ⟨hal-04590221⟩
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