Key points are not available for this paper at this time.
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+1. When the number of nearest neighbors arising through projection is zero in dimension d₄, the attractor has been unfolded in this dimension. The precise determination of d₄ is clouded by ``noise, '' and we examine the manner in which noise changes the determination of d₄. Our criterion also indicates the error one makes by choosing an embedding dimension smaller than d₄. This knowledge may be useful in the practical analysis of observed time series.
Kennel et al. (Sun,) studied this question.