date: 2022-11-18T15:11:47Z
pdf:unmappedUnicodeCharsPerPage: 12
pdf:PDFVersion: 1.7
pdf:docinfo:title: Spike Spectra for Recurrences
xmp:CreatorTool: LaTeX with hyperref
Keywords: decomposition; frequency analysis; recurrence analysis; bifurcations
access_permission:modify_annotations: true
access_permission:can_print_degraded: true
subject: In recurrence analysis, the -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 -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.
dc:creator: K. Hauke Kraemer, Frank Hellmann, Mehrnaz Anvari, Jürgen Kurths and Norbert Marwan
dcterms:created: 2022-11-18T15:03:03Z
Last-Modified: 2022-11-18T15:11:47Z
dcterms:modified: 2022-11-18T15:11:47Z
dc:format: application/pdf; version=1.7
title: Spike Spectra for Recurrences
Last-Save-Date: 2022-11-18T15:11:47Z
pdf:docinfo:creator_tool: LaTeX with hyperref
access_permission:fill_in_form: true
pdf:docinfo:keywords: decomposition; frequency analysis; recurrence analysis; bifurcations
pdf:docinfo:modified: 2022-11-18T15:11:47Z
meta:save-date: 2022-11-18T15:11:47Z
pdf:encrypted: false
dc:title: Spike Spectra for Recurrences
modified: 2022-11-18T15:11:47Z
cp:subject: In recurrence analysis, the -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 -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.
pdf:docinfo:subject: In recurrence analysis, the -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 -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.
Content-Type: application/pdf
pdf:docinfo:creator: K. Hauke Kraemer, Frank Hellmann, Mehrnaz Anvari, Jürgen Kurths and Norbert Marwan
X-Parsed-By: org.apache.tika.parser.DefaultParser
creator: K. Hauke Kraemer, Frank Hellmann, Mehrnaz Anvari, Jürgen Kurths and Norbert Marwan
meta:author: K. Hauke Kraemer, Frank Hellmann, Mehrnaz Anvari, Jürgen Kurths and Norbert Marwan
dc:subject: decomposition; frequency analysis; recurrence analysis; bifurcations
meta:creation-date: 2022-11-18T15:03:03Z
created: 2022-11-18T15:03:03Z
access_permission:extract_for_accessibility: true
access_permission:assemble_document: true
xmpTPg:NPages: 18
Creation-Date: 2022-11-18T15:03:03Z
pdf:charsPerPage: 3586
access_permission:extract_content: true
access_permission:can_print: true
meta:keyword: decomposition; frequency analysis; recurrence analysis; bifurcations
Author: K. Hauke Kraemer, Frank Hellmann, Mehrnaz Anvari, Jürgen Kurths and Norbert Marwan
producer: pdfTeX-1.40.21
access_permission:can_modify: true
pdf:docinfo:producer: pdfTeX-1.40.21
pdf:docinfo:created: 2022-11-18T15:03:03Z