Optimal Estimation of Recurrence Structures from Time Series

TL;DR

This paper introduces a stochastic Markov model to optimally select distance thresholds in recurrence analysis of time series, validated on Lorenz systems and applied to neurophysiological data to classify states of consciousness.

Contribution

It provides an analytical criterion for optimal recurrence threshold selection, improving the detection of recurrent dynamics in complex systems.

Findings

Validated on Lorenz system and stochastic surrogates

Revealed novel dynamic features in neurophysiological data

Proposed recurrence domain count as a consciousness classifier

Abstract

Recurrent temporal dynamics is a phenomenon observed frequently in high-dimensional complex systems and its detection is a challenging task. Recurrence quantification analysis utilizing recurrence plots may extract such dynamics, however it still encounters an unsolved pertinent problem: the optimal selection of distance thresholds for estimating the recurrence structure of dynamical systems. The present work proposes a stochastic Markov model for the recurrent dynamics that allows to derive analytically a criterion for the optimal distance threshold. The goodness of fit is assessed by a utility function which assumes a local maximum for that threshold reflecting the optimal estimate of the system's recurrence structure. We validate our approach by means of the nonlinear Lorenz system and its linearized stochastic surrogates. The final application to neurophysiological time series obtained from anesthetized animals illustrates the method and reveals novel dynamic features of the underlying system. As a conclusion, we propose the number of optimal recurrence domains as a statistic for classifying an animals' state of consciousness.