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

Matthew B. Kennel, Reggie Brown, and Henry D. I. Abarbanel
Phys. Rev. A 45, 3403 – Published 1 March 1992
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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 dd+1. When the number of nearest neighbors arising through projection is zero in dimension dE, the attractor has been unfolded in this dimension. The precise determination of dE is clouded by ‘‘noise,’’ and we examine the manner in which noise changes the determination of dE. Our criterion also indicates the error one makes by choosing an embedding dimension smaller than dE. This knowledge may be useful in the practical analysis of observed time series.

  • Received 24 April 1991

DOI:https://doi.org/10.1103/PhysRevA.45.3403

©1992 American Physical Society

Authors & Affiliations

Matthew B. Kennel

  • Institute for Nonlinear Science and Department of Physics, University of California, San Diego, La Jolla, California 92093-0402

Reggie Brown

  • Institute for Nonlinear Science, University of California, San Diego, La Jolla, California 92093-0402

Henry D. I. Abarbanel

  • Institute for Nonlinear Science, Department of Physics,
  • Marine Physical Laboratory, Scripps Institution of Oceanography, University of California, San Diego, Mail Code R-002, La Jolla, California 92093-0402

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Issue

Vol. 45, Iss. 6 — March 1992

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