Mutual information, strange attractors, and the optimal estimation of dimension
- 1 May 1992
- journal article
- research article
- Published by American Physical Society (APS) in Physical Review A
- Vol. 45 (10) , 7058-7064
- https://doi.org/10.1103/physreva.45.7058
Abstract
It has been shown that the appropriate setting of data windows is crucial to a successful estimation of a time-series correlation dimension using the Grassberger-Procaccia algorithm [Physica 9D, 189 (1983); Phys. Rev. Lett. 50, 346 (1983)], and it has been proposed that the first minimum of the corresponding mutual-information function may be an appropriate window value. We have tested this hypothesis against data generated by the Rössler equations, the Lorenz equations, and a three-dimensional irrational torus. We conclude that mutual information is not consistently successful in identifying the optimal window.Keywords
This publication has 15 references indexed in Scilit:
- Using higher-order correlations to define an embedding windowPhysica D: Nonlinear Phenomena, 1991
- The Claude Bernard Lecture, 1989 - Deterministic chaos: the science and the fictionProceedings of the Royal Society of London. Series A. Mathematical and Physical Sciences, 1990
- Intrinsic limits on dimension calculationsPhysics Letters A, 1988
- Singular-value decomposition and the Grassberger-Procaccia algorithmPhysical Review A, 1988
- Do climatic attractors exist?Nature, 1986
- Spurious dimension from correlation algorithms applied to limited time-series dataPhysical Review A, 1986
- Resonances of chaotic dynamical systemsPhysical Review Letters, 1986
- Using Mutual Information to Estimate Metric EntropyPublished by Springer Nature ,1986
- Characterization of Strange AttractorsPhysical Review Letters, 1983
- On the dimension of the compact invariant sets of certain non-linear mapsPublished by Springer Nature ,1981