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 discovering 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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18 June 2024
A correction has been published.
Notes
- 1.
for time dependent Signatures.
- 2.
The k-truncated version of the signature is \(S^{(1)}(X)\oplus S^{(2)}(X)\oplus \dots \oplus S^{(k)}(X)\).
- 3.
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Chrétien, S., Gao, B., Thébault Guiochon, A., Vaucher, R. (2024). Leveraging the Power of Signatures for the Construction of Topological Complexes for the Analysis of Multivariate Complex Dynamics. In: Cherifi, H., Rocha, L.M., Cherifi, C., Donduran, M. (eds) Complex Networks & Their Applications XII. COMPLEX NETWORKS 2023. Studies in Computational Intelligence, vol 1141. Springer, Cham. https://doi.org/10.1007/978-3-031-53468-3_24
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