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Determining embedding dimension for phase-space reconstruction using a geometrical construction
Abstract
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 determination of ${\mathit{d}}_{\mathit{E}}$. Our criterion also indicates the error one makes by choosing an embedding dimension smaller than ${\mathit{d}}_{\mathit{E}}$. This knowledge may be useful in the practical analysis of observed time series.
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Cited by
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Metadata
- Authors
- Kennel, M. B., Brown, R., & Abarbanel, H. D. I.
- Venue
- Physical Review A
- Publisher
- American Physical Society (APS)
- Published
- 1992-03-01
- Volume
- 45
- Issue
- 6
- Pages
- 3403-3411
- ISSN
- 0556-2791 (ISSN-L)
- 1050-2947
- 1094-1622
- OpenAlex
- W2031365860
- Cited by
- 3,776
- References
- 0
- FWCI
- 12.40
- Type
- journal article
- Language
- en
- Open access
- closed
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- Kennel, M. B., Brown, R., & Abarbanel, H. D. I. (1992). Determining embedding dimension for phase-space reconstruction using a geometrical construction. Physical Review A. https://doi.org/10.1103/physreva.45.3403
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