Estimating dynamical dimensions from noisy observations

Jack Murdoch Moore; Michael Small

doi:10.1016/j.ins.2018.06.011

Estimating dynamical dimensions from noisy observations

Jack Murdoch Moore, Michael Small

School of Physics, Mathematics and Computing

Research output: Contribution to journal › Article › peer-review

2 Citations (Scopus)

26 Downloads (Pure)

Abstract

Knowledge of the dynamical dimension mitigates the “curse of dimensionality” by permitting analysis in dimension lower than that of the original state vectors. The description length quantifies complexity and so allows us to use Occam's razor to estimate the dynamical dimension underlying noisily observed data. Applying our method, based on the description length, to a coarsely sampled scalar time series requires the choice of only one parameter; an embedding dimension. For the three systems considered in this study observed amid observational noise, a single choice of embedding dimension does provide reasonable estimates of the dynamical dimension. The spatial distribution of local estimates of dynamical dimension aids visualisation and provides extra insight into the geometric structure of many systems.

Original language	English
Pages (from-to)	55-75
Number of pages	21
Journal	Information Sciences
Volume	462
DOIs	https://doi.org/10.1016/j.ins.2018.06.011
Publication status	Published - 1 Sep 2018

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10.1016/j.ins.2018.06.011

Moore & Small, 2018 Estimating dynamical dimensions from noisy observationsAccepted author manuscript, 2.42 MBLicence: CC BY-NC-ND

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AB - Knowledge of the dynamical dimension mitigates the “curse of dimensionality” by permitting analysis in dimension lower than that of the original state vectors. The description length quantifies complexity and so allows us to use Occam's razor to estimate the dynamical dimension underlying noisily observed data. Applying our method, based on the description length, to a coarsely sampled scalar time series requires the choice of only one parameter; an embedding dimension. For the three systems considered in this study observed amid observational noise, a single choice of embedding dimension does provide reasonable estimates of the dynamical dimension. The spatial distribution of local estimates of dynamical dimension aids visualisation and provides extra insight into the geometric structure of many systems.

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Estimating dynamical dimensions from noisy observations

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