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Volumn 70, Issue 25, 1993, Pages 3872-3875

Plateau onset for correlation dimension: When does it occur?

Author keywords

[No Author keywords available]

Indexed keywords

EID: 0000822478 PISSN: 00319007 EISSN: None Source Type: Journal
DOI: 10.1103/PhysRevLett.70.3872 Document Type: Article

Times cited : (171)

References (31)

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8
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- To get a rough idea of how widespread the misconception about the relevance of embedding to dimension estimation is, we conducted a literature search using the Science Citation Index for the years from 1987 to 1992 by looking for papers citing both Ref. [1] and Ref. [3]. We found 183 such papers. We then randomly selected a sample of 22 of these papers for closer examination. The following is what we found. Among the 22 papers there are 15 of them that calculate correlation dimension from time series. Five of these 15 papers make explicit connections between 2D + 1 and dimension estimation. The rest of these papers ignore this issue entirely. Based on this information we estimate that, during the period from 1987 to 1992, there are at least 42 papers (probably many more) where the authors implicitly or explicitly assumed that a one-to-one embedding is needed for dimension calculation. In addition, among the papers we researched for this work, only [8] and [9] imply that m >= D2 is sufficient for estimating D2, although no justification is given.

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