Detecting synchronization clusters in multivariate time series via coarse-graining of Markov chains

TL;DR

This paper introduces a novel synchronization cluster detection method based on Markov chain coarse-graining, improving accuracy over previous eigenvector-based techniques, and demonstrates robustness with small sample sizes.

Contribution

The paper develops a new clustering approach using Markov process coarse-graining, addressing limitations of eigenvector methods in synchronization analysis.

Findings

The new method outperforms previous eigenvector-based approaches.

It effectively detects clusters in simulated coupled Lorenz oscillators.

The approach remains robust with small sample sizes.

Abstract

Synchronization cluster analysis is an approach to the detection of underlying structures in data sets of multivariate time series, starting from a matrix R of bivariate synchronization indices. A previous method utilized the eigenvectors of R for cluster identification, analogous to several recent attempts at group identification using eigenvectors of the correlation matrix. All of these approaches assumed a one-to-one correspondence of dominant eigenvectors and clusters, which has however been shown to be wrong in important cases. We clarify the usefulness of eigenvalue decomposition for synchronization cluster analysis by translating the problem into the language of stochastic processes, and derive an enhanced clustering method harnessing recent insights from the coarse-graining of finite-state Markov processes. We illustrate the operation of our method using a simulated system of coupled Lorenz oscillators, and we demonstrate its superior performance over the previous approach. Finally we investigate the question of robustness of the algorithm against small sample size, which is important with regard to field applications.