Reliable detection of directional couplings using cross-vector measures.

Area of Science:

• Dynamical Systems and Complexity Science
• Time Series Analysis
• Neuroscience and Biomedical Engineering

Background:

• Understanding directional couplings is vital for analyzing complex dynamical systems.
• Existing state-space methods, including prior cross-distance vector measures, have limitations in robustness and applicability.
• New approaches are needed to improve the detection of causal relationships in time series data.

Purpose of the Study:

• To develop and evaluate novel cross-vector measures for detecting directional couplings in time series.
• To compare the performance of these new measures against established state-space-based methods.
• To assess the utility of the proposed measures in real-world applications, specifically in analyzing electroencephalographic (EEG) data.

Main Methods:

• Development of two new cross-vector measures utilizing ranks and time series estimates.
• Analysis of deterministic and stochastic dynamics to compare novel measures with existing state-space approaches.
• Application of rank-based cross-vector measures combined with surrogate data analysis on EEG recordings from epilepsy patients.

Main Results:

• The novel cross-vector measures, particularly the rank-based variant, demonstrate superior performance in identifying coupling direction across various dynamics.
• The rank-based cross-vector measure exhibits enhanced robustness to noise and reduced sensitivity to linear cross-correlation compared to established methods.
• Improved discrimination between seizure onset and non-onset brain regions in EEG data was achieved using the cross-rank vector measure, which also showed robustness to non-stationarity.

Conclusions:

• The developed cross-vector approach, especially the rank-based variant, offers a powerful and robust tool for directional coupling detection.
• This method enhances the analysis of complex time series, outperforming existing techniques in noise and non-stationarity resilience.
• The findings support the application of the cross-vector approach in both fundamental research on dynamical systems and clinical diagnostics, such as in epilepsy monitoring.