Teaching ordinal patterns to a computer. Efficient encoding algorithms based on the Lehmer code
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Autor:innen
Autor:in (Körperschaft)
Publikationsdatum
2019
Typ der Arbeit
Studiengang
Sammlung
Typ
01A - Beitrag in wissenschaftlicher Zeitschrift
Herausgeber:innen
Herausgeber:in (Körperschaft)
Betreuer:in
Übergeordnetes Werk
Entropy
Themenheft
DOI der Originalpublikation
Link
Reihe / Serie
Reihennummer
Jahrgang / Band
21
Ausgabe / Nummer
10
Seiten / Dauer
1023
Patentnummer
Verlag / Herausgebende Institution
MDPI
Verlagsort / Veranstaltungsort
Auflage
Version
Programmiersprache
Abtretungsempfänger:in
Praxispartner:in/Auftraggeber:in
Zusammenfassung
Ordinal patterns are the common basis of various techniques used in the study of dynamical systems and nonlinear time series analysis. The present article focusses on the computational problem of turning time series into sequences of ordinal patterns. In a first step, a numerical encoding scheme for ordinal patterns is proposed. Utilising the classical Lehmer code, it enumerates ordinal patterns by consecutive non-negative integers, starting from zero. This compact representation considerably simplifies working with ordinal patterns in the digital domain. Subsequently, three algorithms for the efficient extraction of ordinal patterns from time series are discussed, including previously published approaches that can be adapted to the Lehmer code. The respective strengths and weaknesses of those algorithms are discussed, and further substantiated by benchmark results. One of the algorithms stands out in terms of scalability: its run-time increases linearly with both the pattern order and the sequence length, while its memory footprint is practically negligible. These properties enable the study of high-dimensional pattern spaces at low computational cost. In summary, the tools described herein may improve the efficiency of virtually any ordinal pattern-based analysis method, among them quantitative measures like permutation entropy and symbolic transfer entropy, but also techniques like forbidden pattern identification. Moreover, the concepts presented may allow for putting ideas into practice that up to now had been hindered by computational burden. To enable smooth evaluation, a function library written in the C programming language, as well as language bindings and native implementations for various numerical computation environments are provided in the supplements.
Schlagwörter
Lehmer code, Ordinal patterns, Symbolic dynamics, Permutation entropy, Symbolic transfer entropy
Fachgebiet (DDC)
600 - Technik, Medizin, angewandte Wissenschaften
Veranstaltung
Startdatum der Ausstellung
Enddatum der Ausstellung
Startdatum der Konferenz
Enddatum der Konferenz
Datum der letzten Prüfung
ISBN
ISSN
1099-4300
Sprache
Englisch
Während FHNW Zugehörigkeit erstellt
Ja
Zukunftsfelder FHNW
Publikationsstatus
Veröffentlicht
Begutachtung
Peer-Review der ganzen Publikation
Open Access-Status
Gold
Lizenz
Zitation
BERGER, Sebastian, Andrii KRAVTSIV, Gerhard SCHNEIDER und Denis JORDAN, 2019. Teaching ordinal patterns to a computer. Efficient encoding algorithms based on the Lehmer code. Entropy. 2019. Bd. 21, Nr. 10, S. 1023. DOI 10.3390/e21101023. Verfügbar unter: https://doi.org/10.26041/fhnw-9523