Topological signatures of periodic-like signals

Wojciech Reise; Bertrand Michel; Frédéric Chazal

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arXiv · 2306.13453

Topological signatures of periodic-like signals

Wojciech Reise·Bertrand Michel·Frédéric Chazal

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Abstract

We present a method to construct signatures of periodic-like data. Based on topological considerations, our construction encodes information about the order and values of local extrema. Its main strength is robustness to reparametrisation of the observed signal, so that it depends only on the form of the periodic function. The signature converges as the observation contains increasingly many periods. We show that it can be estimated from the observation of a single time series using bootstrap techniques.

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Wojciech Reise, Bertrand Michel, Frédéric Chazal. 2023-06-23. Topological signatures of periodic-like signals. https://arxiv.org/abs/2306.13453

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