Determining embedding dimension for phase-space reconstruction using a geometrical construction.

@article{Kennel1992DeterminingED,
  title={Determining embedding dimension for phase-space reconstruction using a geometrical construction.},
  author={Kennel and Brown and Abarbanel},
  journal={Physical review. A, Atomic, molecular, and optical physics},
  year={1992},
  volume={45 6},
  pages={
          3403-3411
        }
}
  • KennelBrownAbarbanel
  • Published 15 March 1992
  • Mathematics
  • Physical review. A, Atomic, molecular, and optical physics
We examine the issue of determining an acceptable minimum embedding dimension by looking at the behavior of near neighbors under changes in the embedding dimension from d\ensuremath{\rightarrow}d+1. When the number of nearest neighbors arising through projection is zero in dimension ${\mathit{d}}_{\mathit{E}}$, the attractor has been unfolded in this dimension. The precise determination of ${\mathit{d}}_{\mathit{E}}$ is clouded by ``noise,'' and we examine the manner in which noise changes the… 

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DETERMINATION OF EMBEDDING DIMENSION USING MULTIPLE TIME SERIES BASED ON SINGULAR VALUE DECOMOPOSITION

In this paper, singular value decomposition approach for computing the optimum embedding dimension is considered and the inefficiency of the method for some univariate time series is shown, and the idea of using interaction between multiple timeseries is presented.
...

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Physical and numerical experiments show that deterministic noise, or chaos, is ubiquitous. While a good understanding of the onset of chaos has been achieved, using as a mathematical tool the

Determining embedding dimension for phase-space reconstruction using a geometrical construction

  • Phys Rev A
  • 1992