Teaching ordinal patterns to a computer. Efficient encoding algorithms based on the Lehmer code
Loading...
Author (Corporation)
Publication date
2019
Typ of student thesis
Course of study
Collections
Type
01A - Journal article
Editors
Editor (Corporation)
Supervisor
Parent work
Entropy
Special issue
DOI of the original publication
Link
Series
Series number
Volume
21
Issue / Number
10
Pages / Duration
1023
Patent number
Publisher / Publishing institution
MDPI
Place of publication / Event location
Edition
Version
Programming language
Assignee
Practice partner / Client
Abstract
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.
Keywords
Lehmer code, Ordinal patterns, Symbolic dynamics, Permutation entropy, Symbolic transfer entropy
Subject (DDC)
Event
Exhibition start date
Exhibition end date
Conference start date
Conference end date
Date of the last check
ISBN
ISSN
1099-4300
Language
English
Created during FHNW affiliation
Yes
Strategic action fields FHNW
Publication status
Published
Review
Peer review of the complete publication
Open access category
Gold
License
Citation
Berger, S., Kravtsiv, A., Schneider, G., & Jordan, D. (2019). Teaching ordinal patterns to a computer. Efficient encoding algorithms based on the Lehmer code. Entropy, 21(10), 1023. https://doi.org/10.3390/e21101023