Permutation Entropy and Its Main Biomedical and Econophysics Applications: A Review

被引:485
作者
Zanin, Massimiliano [1 ,2 ,3 ,7 ]
Zunino, Luciano [4 ,5 ]
Rosso, Osvaldo A. [6 ,8 ]
Papo, David [1 ]
机构
[1] Univ Politecn Madrid, Ctr Biomed Technol, Madrid 28223, Spain
[2] Univ Nova Lisboa, Dept Engn Electrotecn, Fac Ciencias & Tecnol, P-2829516 Caparica, Portugal
[3] Innaxis Fdn, Madrid 28006, Spain
[4] CONICET La Plata CIC, Ctr Invest Opt, RA-1897 Gonnet, Argentina
[5] UNLP, Fac Ingn, Dept Ciencias Basicas, RA-1900 La Plata, Argentina
[6] Univ Fed Alagoas, LaCCAN CPMAT Inst Comp, BR-57072970 Maceio, Alagoas, Brazil
[7] Res Inst Jos Ortega & Gasset 20, Madrid 28006, Spain
[8] Univ Buenos Aires, Lab Sistemas Complejos, Fac Ingn, Ciudad Autonoma Buenos, Argentina
关键词
permutation entropy; forbidden patterns; Shannon entropy; econophysics; EEG; epilepsy; COUPLED SEMICONDUCTOR-LASERS; FRACTIONAL BROWNIAN-MOTION; ANESTHETIC DEPTH INDEXES; SURFACE-EMITTING LASERS; TIME-DELAY SIGNATURE; STATISTICAL COMPLEXITY; ORDER PATTERNS; CAUSALITY PLANE; DYNAMICS; CHAOS;
D O I
10.3390/e14081553
中图分类号
O4 [物理学];
学科分类号
0702 ;
摘要
Entropy is a powerful tool for the analysis of time series, as it allows describing the probability distributions of the possible state of a system, and therefore the information encoded in it. Nevertheless, important information may be codified also in the temporal dynamics, an aspect which is not usually taken into account. The idea of calculating entropy based on permutation patterns (that is, permutations defined by the order relations among values of a time series) has received a lot of attention in the last years, especially for the understanding of complex and chaotic systems. Permutation entropy directly accounts for the temporal information contained in the time series; furthermore, it has the quality of simplicity, robustness and very low computational cost. To celebrate the tenth anniversary of the original work, here we analyze the theoretical foundations of the permutation entropy, as well as the main recent applications to the analysis of economical markets and to the understanding of biomedical systems.
引用
收藏
页码:1553 / 1577
页数:25
相关论文
共 110 条
[1]   Combinatorial detection of determinism in noisy time series [J].
Amigo, J. M. ;
Zambrano, S. ;
Sanjuan, M. A. F. .
EPL, 2008, 83 (06)
[2]   True and false forbidden patterns in deterministic and random dynamics [J].
Amigo, J. M. ;
Zambrano, S. ;
Sanjuan, M. A. F. .
EPL, 2007, 79 (05)
[3]   Order patterns and chaos [J].
Amigo, JM ;
Kocarev, L ;
Szczepanski, J .
PHYSICS LETTERS A, 2006, 355 (01) :27-31
[4]  
Amigo JM, 2010, SPRINGER SER SYNERG, P1, DOI 10.1007/978-3-642-04084-9
[5]   The permutation entropy rate equals the metric entropy rate for ergodic information sources and ergodic dynamical systems [J].
Amigó, JM ;
Kennel, MB ;
Kocarev, L .
PHYSICA D-NONLINEAR PHENOMENA, 2005, 210 (1-2) :77-95
[6]   Direction of coupling from phases of interacting oscillators: A permutation information approach [J].
Bahraminasab, A. ;
Ghasemi, F. ;
Stefanovska, A. ;
McClintock, P. V. E. ;
Kantz, H. .
PHYSICAL REVIEW LETTERS, 2008, 100 (08)
[7]   Ordinal time series analysis [J].
Bandt, C .
ECOLOGICAL MODELLING, 2005, 182 (3-4) :229-238
[8]   Permutation entropy: A natural complexity measure for time series [J].
Bandt, C ;
Pompe, B .
PHYSICAL REVIEW LETTERS, 2002, 88 (17) :4
[9]   Order patterns in time series [J].
Bandt, Christoph ;
Shiha, Faten .
JOURNAL OF TIME SERIES ANALYSIS, 2007, 28 (05) :646-665
[10]  
Beggs JM, 2003, J NEUROSCI, V23, P11167