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Recurrence plot statistics and the effect of embedding
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UNSPECIFIED (2005) Recurrence plot statistics and the effect of embedding. PHYSICA D-NONLINEAR PHENOMENA, 200 (1-2). pp. 171-184. doi:10.1016/j.physd.2004.11.002 ISSN 0167-2789.
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Official URL: http://dx.doi.org/10.1016/j.physd.2004.11.002
Abstract
Recurrence plots provide a graphical representation of the recurrent patterns in a timeseries, the quantification of which is a relatively new field. Here we derive analytical expressions which relate the values of key statistics, notably determinism and entropy of line length distribution, to the correlation sum as a function of embedding dimension. These expressions are obtained by deriving the transformation which generates an embedded recurrence plot from an unembedded plot. A single unembedded recurrence plot thus provides the statistics of all possible embedded recurrence plots. If the correlation sum scales exponentially with embedding dimension, we show that these statistics are determined entirely by the exponent of the exponential. This explains the results of Iwanski and Bradley [J.S. Iwanski, E. Bradley, Recurrence plots of experimental data: to embed or not to embed? Chaos 8 (1998) 861-871] who found that certain recurrence plot statistics are apparently invariant to embedding dimension for certain low-dimensional systems. We also examine the relationship between the mutual information content of two timeseries and the common recurrent structure seen in their recurrence plots. This allows time-localized contributions to mutual information to be visualized. This technique is demonstrated using geomagnetic index data; we show that the AU and AL geomagnetic indices share half their information, and find the timescale on which mutual features appear. (C) 2004 Elsevier B.V. All rights reserved.
Item Type: | Journal Article | ||||
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Subjects: | Q Science > QA Mathematics Q Science > QC Physics |
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Journal or Publication Title: | PHYSICA D-NONLINEAR PHENOMENA | ||||
Publisher: | ELSEVIER SCIENCE BV | ||||
ISSN: | 0167-2789 | ||||
Official Date: | 1 January 2005 | ||||
Dates: |
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Volume: | 200 | ||||
Number: | 1-2 | ||||
Number of Pages: | 14 | ||||
Page Range: | pp. 171-184 | ||||
DOI: | 10.1016/j.physd.2004.11.002 | ||||
Publication Status: | Published |
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