The permutation entropy rate equals the metric entropy rate for ergodic information sources and ergodic dynamical systems

作者: José M. Amigó , Matthew B. Kennel , Ljupco Kocarev

DOI: 10.1016/J.PHYSD.2005.07.006

关键词: Quantum relative entropyMathematicsEntropy power inequalityMin entropyEntropy rateDiscrete mathematicsJoint quantum entropyMaximum entropy probability distributionDifferential entropyRényi entropyStatistical and Nonlinear PhysicsCondensed matter physics

摘要: … entropy quantifies the diversity of values. We show that the metric and permutation entropy … We demonstrate numerical results on time series from the logistic map x n + 1 = A x n ( 1 − x …

参考文章(16)
I. Kontoyiannis, P.H. Algoet, Yu.M. Suhov, A.J. Wyner, Nonparametric entropy estimation for stationary processes and random fields, with applications to English text IEEE Transactions on Information Theory. ,vol. 44, pp. 1319- 1327 ,(1998) , 10.1109/18.669425
A. Lempel, J. Ziv, On the Complexity of Finite Sequences IEEE Transactions on Information Theory. ,vol. 22, pp. 75- 81 ,(1976) , 10.1109/TIT.1976.1055501
Michael Buhl, Matthew B. Kennel, Statistically relaxing to generating partitions for observed time-series data. Physical Review E. ,vol. 71, pp. 046213- 046213 ,(2005) , 10.1103/PHYSREVE.71.046213
Thomas M. Cover, Joy A. Thomas, Elements of information theory ,(1991)
Matthew B. Kennel, Jonathon Shlens, Henry D. I. Abarbanel, E. J. Chichilnisky, Estimating Entropy Rates with Bayesian Confidence Intervals Neural Computation. ,vol. 17, pp. 1531- 1576 ,(2005) , 10.1162/0899766053723050
S. P. Strong, Roland Koberle, Rob R. de Ruyter van Steveninck, William Bialek, Entropy and Information in Neural Spike Trains Physical Review Letters. ,vol. 80, pp. 197- 200 ,(1998) , 10.1103/PHYSREVLETT.80.197
José M. Amigó, Janusz Szczepański, Elek Wajnryb, Maria V. Sanchez-Vives, Estimating the Entropy Rate of Spike Trains via Lempel-Ziv Complexity Neural Computation. ,vol. 16, pp. 717- 736 ,(2004) , 10.1162/089976604322860677
J. Ziv, A. Lempel, Compression of individual sequences via variable-rate coding IEEE Transactions on Information Theory. ,vol. 24, pp. 530- 536 ,(1978) , 10.1109/TIT.1978.1055934