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Kennel MB, Buhl M. Estimating good discrete partitions from observed data: symbolic false nearest neighbors. Phys Rev Lett. 2003;91(8):084102doi: 10.1103/PhysRevLett.91.084102.
Kennel, M. B., & Buhl, M. (2003). Estimating good discrete partitions from observed data: symbolic false nearest neighbors. Physical review letters, 91(8), 084102. https://doi.org/10.1103/PhysRevLett.91.084102
Kennel, Matthew B, and Buhl, Michael. "Estimating good discrete partitions from observed data: symbolic false nearest neighbors." Physical review letters vol. 91,8 (2003): 084102. doi: https://doi.org/10.1103/PhysRevLett.91.084102
Kennel MB, Buhl M. Estimating good discrete partitions from observed data: symbolic false nearest neighbors. Phys Rev Lett. 2003 Aug 22;91(8):084102. doi: 10.1103/PhysRevLett.91.084102. Epub 2003 Aug 21. PMID: 14525241.
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Phys Rev Lett. 2003 Aug 22;91(8):084102. doi: 10.1103/PhysRevLett.91.084102. Epub 2003 Aug 21.

Estimating good discrete partitions from observed data: symbolic false nearest neighbors.

Physical review letters

Matthew B Kennel, Michael Buhl

Affiliations

  1. Institute For Nonlinear Science, University of California-San Diego, La Jolla, CA 92093-0402, USA. [email protected]

PMID: 14525241 DOI: 10.1103/PhysRevLett.91.084102

Abstract

A symbolic analysis of observed time series requires a discrete partition of a continuous state space containing the dynamics. A particular kind of partition, called "generating," preserves all deterministic dynamical information in the symbolic representation, but such partitions are not obvious beyond one dimension. Existing methods to find them require significant knowledge of the dynamical evolution operator. 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, by minimizing the number of "symbolic false nearest neighbors." It requires only the observed time series and is sensible even in the presence of noise when no truly generating partition is possible.

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