Detection of linear dependencies in EEG oscillatory sources via PARALIND and block-term decomposition: A comparative study

Objectives: Narrowband oscillatory rhythms in electroencephalogram (EEG) signals are fundamental signatures of neural dynamics, crucial for brain-computer interfaces (BCIs) and monitoring neurological disorders. While traditionally detected and analyzed via Independent or Principal Component Analysis in the time-space domain, tensor decomposition in the time-space-frequency domain offers superior resolution. The CANDECOMP/PARAFAC (CP) model is widely used for this purpose due to its simplicity and interpretability. However, it often fails to resolve rhythms or requires excessive components when source collinearity exists (i.e., a situation where oscillatory rhythms share characteristics across temporal, spatial, or frequency modes), leading to instability and increased computational complexity. Approach: This study evaluates two alternative tensor decomposition models - Parallel Profiles with Linear Dependencies (PARALIND) and Block-Term Decomposition (BTD) - which explicitly accommodate linear dependencies among latent components. We compared these models against CP using simulated EEG data with known ground-truth structures and real-world recordings. Main results: PARALIND and BTD achieved interpretability comparable to CP while providing more stable factor estimates at moderate noise levels in simulated data, although both models struggled to identify the true latent structure under challenging conditions. Overall, when their modelling assumptions were satisfied, PARALIND and BTD successfully disentangled complex, overlapping neural sources that CP struggled to isolate. In real data, both models recovered a latent structure similar to that identified by CP, but with fewer loadings. Following the principle of parsimony, PARALIND and BTD may therefore be preferable in this setting. Significance: By overcoming the collinearity limitations inherent in CP decomposition, these findings establish a more reliable framework for neurophysiologically interpretable tensor decomposition of EEG signals. While clinical translation was not evaluated in this work, this methodological advance provides a foundation for future research aimed at enhancing BCI stability and investigating biomarkers of neurological conditions.