Reliable Estimation of Minimum Embedding Dimension Through Statistical Analysis of Nearest Neighbors

David Chelidze

doi:10.1115/1.4036814

Abstract

False nearest neighbors (FNN) is one of the essential methods used in estimating the minimally sufficient embedding dimension in delay-coordinate embedding of deterministic time series. Its use for stochastic and noisy deterministic time series is problematic and erroneously indicates a finite embedding dimension. Various modifications to the original method have been proposed to mitigate this problem, but those are still not reliable for noisy time series. Here, nearest-neighbor statistics are studied for uncorrelated random time series and contrasted with the corresponding deterministic and stochastic statistics. New composite FNN metrics are constructed and their performance is evaluated for deterministic, correlates stochastic, and white random time series. In addition, noise-contaminated deterministic data analysis shows that these composite FNN metrics are robust to noise. All FNN results are also contrasted with surrogate data analysis to show their robustness. The new metrics clearly identify random time series as not having a finite embedding dimension and provide information about the deterministic part of correlated stochastic processes. These metrics can also be used to differentiate between chaotic and random time series.

Highlights

The estimation of optimal delay time can be approached from a purely geometrical perspective [5] or by considering linear/nonlinearcorrelations in the time series [6, 7]
Noise-contaminated deterministic data analysis shows that these composite false nearest neighbors (FNN) metrics are robust to noise
The FNN will separate if the data is embedded into a (d + 1)-dimensional space, while the true nearest neighbor (NN) will remain close.If one is able to detect all the FNN, the minimally sufficient embedding dimension can be identified as the least dimension needed to achieve zero fraction of the FNN

Summary

David Chelidze

Follow this and additional works at: https://digitalcommons.uri.edu/mcise_facpubs. The University of Rhode Island Faculty have made this article openly available. Please let us know how Open Access to this research benefits you. Reliable Estimation of Minimum Embedding Dimension Through Statistical Analysis of Nearest Neighbors. David Chelidze Professor, Member of ASME Nonlinear Dynamics Laboratory Department of Mechanical, Industrial and Systems Engineering University of Rhode Island, Kingston, RI 02881, USA

Lorenz Duffing Normal Uniform

Findings

Lorenz Duffing