Estimating Good Discrete Partitions from Observed Data: Symbolic False Nearest Neighbors

Matthew B. Kennel and Michael Buhl
Phys. Rev. Lett. 91, 084102 – Published 21 August 2003
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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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  • Received 1 October 2002

DOI:https://doi.org/10.1103/PhysRevLett.91.084102

©2003 American Physical Society

Authors & Affiliations

Matthew B. Kennel* and Michael Buhl

  • Institute For Nonlinear Science, University of California, San Diego, La Jolla, California 92093-0402, USA

  • *Electronic address: mkennel@ucsd.edu
  • Electronic address: mbuhl@ucsd.edu

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Issue

Vol. 91, Iss. 8 — 22 August 2003

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