Towards adaptive synchronization measurement of large-scale non-stationary non-linear data

• We designed an approach to measure the synchronization strength of non-stationary nonlinear data against phase differences.
• We demonstrated that the synchronization analysis was an effective indicator of an epileptic focus location.
• We developed a parallelized approach with general-purpose computing on the graphics processing unit (GPGPU), and it largely improved the scalability of data processing.

Synchronization measurement of non-stationary nonlinear data is an ongoing problem in the study of complex systems, e.g., neuroscience. Existing methods are largely based on Fourier transform and wavelet transform, and there is a lack of methods capable of (1) measuring the synchronization strength of multivariate data by adapting to non-stationary, non-linear dynamics, and (2) meeting the needs of sophisticated scientific or engineering applications. This study proposes an approach that measures the synchronization strength of bivariate non-stationary nonlinear data against phase differences. The approach (briefed as AD-PDSA) relies on adaptive algorithms for data decomposition. A parallelized approach was also developed with general-purpose computing on the graphics processing unit (GPGPU), which largely improved the scalability of data processing, namely, GAD-PDSA. We developed a model on the basis of GAD-PDSA to verify its effectiveness in analyzing multi-channel, event-related potential (ERP) recordings against Daubechies (DB) wavelet with reference to the Morlet wavelet transform (MWT). GAD-PDSA was applied to an EEG dataset obtained from epilepsy patients, and the synchronization analysis manifested an effective indicator of epileptic focus localization.