Convergent cross sorting for estimating dynamic coupling

Leo Breston,Michael Tolston,Eric J Leonardis,Andrea A Chiba,Laleh K Quinn,Janet Wiles

doi:10.1038/s41598-021-98864-2

Abstract

Natural systems exhibit diverse behavior generated by complex interactions between their constituent parts. To characterize these interactions, we introduce Convergent Cross Sorting (CCS), a novel algorithm based on convergent cross mapping (CCM) for estimating dynamic coupling from time series data. CCS extends CCM by using the relative ranking of distances within state-space reconstructions to improve the prior methods’ performance at identifying the existence, relative strength, and directionality of coupling across a wide range of signal and noise characteristics. In particular, relative to CCM, CCS has a large performance advantage when analyzing very short time series data and data from continuous dynamical systems with synchronous behavior. This advantage allows CCS to better uncover the temporal and directional relationships within systems that undergo frequent and short-lived switches in dynamics, such as neural systems. In this paper, we validate CCS on simulated data and demonstrate its applicability to electrophysiological recordings from interacting brain regions.

Highlights

Natural systems exhibit diverse behavior generated by complex interactions between their constituent parts
Convergent Cross Mapping (CCM) is an approach, based on state space reconstruction (SSR), which is best suited for complex, nonlinear systems, such as those found in neuroscience, ecology, and the social s ciences[1,2,3,4,5,6,7,8,9]
To cover a wide range of potential signal properties, we considered three types of model systems: Van der Pol oscillators (VDP), Logistic Maps (LM) and Autoregressive Models (AR) (Fig. 1A, SI Simulated Data)

Summary

Introduction

Natural systems exhibit diverse behavior generated by complex interactions between their constituent parts. Convergent Cross Mapping (CCM) is an approach, based on state space reconstruction (SSR) ( referred to as phase space reconstruction), which is best suited for complex, nonlinear systems, such as those found in neuroscience, ecology, and the social s ciences[1,2,3,4,5,6,7,8,9] These systems’ myriad feedback loops and deterministic components cause the information about their variables to become inseparably m ixed[1]. Ye et al introduced lagged CCM estimates to improve performance on strongly coupled variables, while Ma et al introduced Cross Map Smoothness to reduce the required time series length[2,8] Though these approaches were successful, they only address individual failure modes. This approach affords multiple advantages including selectively sampling the most informative distances and normalizing for geometric transformations that distort absolute distance but preserve relative order

Methods

Results

Conclusion