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

1992/03/01 by Matthew B. Kennel, Reggie Brown, Henry D. I. Abarbanel · 34 citations
Computer Science · Economics, Econometrics and Finance · Physics and Astronomy · #Chaos control and synchronization #Complex Systems and Time Series Analysis #Nonlinear Dynamics and Pattern Formation

paper · doi:10.1103/physreva.45.3403

openalex publication_date 1992/03/01 · openalex created_date 2016/06/24 · openalex updated_date 2026/07/30

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→d+1. When the number of nearest neighbors arising through projection is zero in dimension d_E, the attractor has been unfolded in this dimension. The precise determination of d_E is clouded by ``noise,'' and we examine the manner in which noise changes the determination of d_E. Our criterion also indicates the error one makes by choosing an embedding dimension smaller than d_E. This knowledge may be useful in the practical analysis of observed time series.

Citations

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