Spike spectra for recurrences
- In recurrence analysis, the tau-recurrence rate encodes the periods of the cycles of the underlying high-dimensional time series. It, thus, plays a similar role to the autocorrelation for scalar time-series in encoding temporal correlations. However, its Fourier decomposition does not have a clean interpretation. Thus, there is no satisfactory analogue to the power spectrum in recurrence analysis. We introduce a novel method to decompose the tau-recurrence rate using an over-complete basis of Dirac combs together with sparsity regularization. We show that this decomposition, the inter-spike spectrum, naturally provides an analogue to the power spectrum for recurrence analysis in the sense that it reveals the dominant periodicities of the underlying time series. We show that the inter-spike spectrum correctly identifies patterns and transitions in the underlying system in a wide variety of examples and is robust to measurement noise.
Author details: | Kai Hauke KrämerORCiDGND, Frank HellmannORCiD, Mehrnaz AnvariORCiD, Jürgen KurthsORCiDGND, Norbert MarwanORCiDGND |
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DOI: | https://doi.org/10.3390/e24111689 |
ISSN: | 1099-4300 |
Pubmed ID: | https://pubmed.ncbi.nlm.nih.gov/36421545 |
Title of parent work (English): | Entropy : an international and interdisciplinary journal of entropy and information studies |
Publisher: | MDPI |
Place of publishing: | Basel |
Publication type: | Article |
Language: | English |
Date of first publication: | 2022/11/18 |
Publication year: | 2022 |
Release date: | 2024/09/11 |
Tag: | bifurcations; decomposition; frequency analysis; recurrence analysis |
Volume: | 24 |
Issue: | 11 |
Article number: | 1689 |
Number of pages: | 18 |
Funding institution: | German Research Foundation (DFG); [MA4759/8]; [MA4759/9] |
Organizational units: | Mathematisch-Naturwissenschaftliche Fakultät / Institut für Physik und Astronomie |
Mathematisch-Naturwissenschaftliche Fakultät / Institut für Geowissenschaften | |
DDC classification: | 5 Naturwissenschaften und Mathematik / 53 Physik / 530 Physik |
Peer review: | Referiert |
Publishing method: | Open Access / Gold Open-Access |
DOAJ gelistet | |
License (German): | CC-BY - Namensnennung 4.0 International |