Causal Discovery in Symmetric Dynamic Systems with Convergent Cross Mapping

TL;DR

This paper examines how symmetry in chaotic attractors affects causality detection using convergent cross mapping and introduces a k-means clustering method to improve accuracy in symmetric systems.

Contribution

It presents a novel k-means clustering approach to correctly identify causality in symmetric chaotic systems, addressing limitations of existing methods.

Findings

The method recovers the symmetry of chaotic attractors.

It accurately detects causality without external information.

It outperforms traditional convergent cross mapping in symmetric cases.

Abstract

This paper systematically discusses how the inherent properties of chaotic attractors influence the results of discovering causality from time series using convergent cross mapping, particularly how convergent cross mapping misleads bidirectional causality as unidirectional when the chaotic attractor exhibits symmetry. We propose a novel method based on the k-means clustering method to address the challenges when the chaotic attractor exhibits two-fold rotation symmetry. This method is demonstrated to recover the symmetry of the latent chaotic attractor and discover the correct causality between time series without introducing information from other variables. We validate the accuracy of this method using time series derived from low-dimension and high-dimensional chaotic symmetric attractors for which convergent cross mapping may conclude erroneous results.