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28 March 2024
 
  » arxiv » nlin.CD/0304054

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Estimating good discrete partitions from observed data: symbolic false nearest neighbors
Matthew B. Kennel ; Michael Buhl ;
Date 27 Apr 2003
Subject Chaotic Dynamics | nlin.CD
AffiliationInstitute For Nonlinear Science, University of California, San Diego
AbstractA symbolic analysis of observed time series data requires making a discrete partition of a continuous state space containing observations of the dynamics. A particular kind of partition, called ``generating’’, preserves all dynamical information of a deterministic map in the symbolic representation, but such partitions are not obvious beyond one dimension, and existing methods to find them require significant knowledge of the dynamical evolution operator or the spectrum of unstable periodic orbits. We introduce a statistic and algorithm to refine empirical partitions for symbolic state reconstruction. This method optimizes an essential property of a generating partition: avoiding topological degeneracies. It requires only the observed time series and is sensible even in the presence of noise when no truly generating partition is possible. Because of its resemblance to a geometrical statistic frequently used for reconstructing valid time-delay embeddings, we call the algorithm ``symbolic false nearest neighbors’’.
Source arXiv, nlin.CD/0304054
Other source [GID 336401] pmid14525241
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