Low-rank tensor decomposition for cross-bispectral analysis of EEG data

Cross-bispectral analysis identifies higher-order neural interactions, but the resulting high-dimensional tensors are difficult to interpret at the source level. Standard dimensionality reduction often lacks a physical link to the underlying neural generators.

We introduce a low-rank tensor decomposition framework explicitly grounded in the physics of EEG signal generation. The method represents the cross-bispectrum using a single spatial mixing matrix and a compact source-interaction tensor, yielding a structured and physically interpretable model. This formulation enables a direct source-space interpretation and supports subsequent spatial demixing using MOCA to recover distinct source maps.

Through extensive simulations, we show that the method robustly captures the dominant bispectral structure across a range of conditions, including varying signal-to-noise ratio, dipole orientation, amplitude balance, and source complexity. Applied to resting-state EEG, the approach identifies anatomically plausible parietal generators associated with prominent alpha-band bispectral interactions.

In contrast to standard tensor decompositions such as Tucker and PARAFAC, which rely on unconstrained cores or rank-one assumptions, the proposed framework enforces a compact and interpretable source-interaction structure. This structure significantly improves interpretability and spatial localization while suppressing spurious high-dimensional variability.

The proposed low-rank decomposition offers a principled and computationally efficient approach for reducing and interpreting cross-bispectral EEG data. By bridging tensor decomposition with biophysical source models, it enables insights into complex neural coupling that are inaccessible with standard matrix or tensor techniques.