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Quantitative Assessment of the Log-Log-Step Method for Pattern Detection in Noise-Prone Environments


Gomez, F; Stoop, R (2011). Quantitative Assessment of the Log-Log-Step Method for Pattern Detection in Noise-Prone Environments. PLoS ONE, 6(12):e28107.

Abstract

Staircase-like structures in the log-log correlation plot of a time series indicate patterns against a noisy background, even under condition of strong jitter. We analyze the method for different jitter-noise-combinations, using quantitative criteria to measure the achievement by the method. A phase diagram shows the remarkable potential of this method even under very unfavorable conditions of noise and jitter. Moreover, we provide a novel and compact analytical derivation of the upper and lower bounds on the number of steps observable in the ideal noiseless case, as a function of pattern length and embedding dimension. The quantitative measure developed combined with the ideal bounds can serve as guiding lines for determining potential periodicity in noisy data.

Abstract

Staircase-like structures in the log-log correlation plot of a time series indicate patterns against a noisy background, even under condition of strong jitter. We analyze the method for different jitter-noise-combinations, using quantitative criteria to measure the achievement by the method. A phase diagram shows the remarkable potential of this method even under very unfavorable conditions of noise and jitter. Moreover, we provide a novel and compact analytical derivation of the upper and lower bounds on the number of steps observable in the ideal noiseless case, as a function of pattern length and embedding dimension. The quantitative measure developed combined with the ideal bounds can serve as guiding lines for determining potential periodicity in noisy data.

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Additional indexing

Item Type:Journal Article, refereed, original work
Communities & Collections:07 Faculty of Science > Institute of Neuroinformatics
Dewey Decimal Classification:570 Life sciences; biology
Language:English
Date:2011
Deposited On:03 Sep 2014 13:05
Last Modified:05 Aug 2017 01:24
Publisher:Public Library of Science (PLoS)
Series Name:PloS One
Number of Pages:1
ISSN:1932-6203
Free access at:PubMed ID. An embargo period may apply.
Publisher DOI:https://doi.org/10.1371/journal.pone.0028107
PubMed ID:22174769

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Licence: Creative Commons: Attribution 4.0 International (CC BY 4.0)