DETERMINING EMBEDDING DIMENSION FOR PHASE-SPACE RECONSTRUCTION USING A GEOMETRICAL CONSTRUCTION
DETERMINING EMBEDDING DIMENSION FOR PHASE-SPACE RECONSTRUCTION USING A GEOMETRICAL CONSTRUCTION
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DOI：
10.1103/physreva.45.3403
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发表时间：
1992-03-15
影响因子：
2.9
通讯作者：
ABARBANEL, HDI
中科院分区：
文献类型：
--
作者：
KENNEL, MB;BROWN, R;ABARBANEL, HDI
我们研究的问题，确定一个可接受的最小嵌入维数的行为下的嵌入维数从d -> d + 1的变化看近邻。当通过投影产生的最近邻的数量在维度d（E）中为零时，吸引子在该维度中已经展开。d（E）的精确测定被“噪声”所干扰，我们研究噪声改变d（E）测定的方式。我们的准则还指出了通过选择小于d（E）的嵌入维数所产生的误差。这一知识可能是有用的，在实际分析观察到的时间序列。
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 --> 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.