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

Area of Science:

• Neuroscience
• Biophysics
• Signal Processing

Background:

• Cross-bispectral analysis reveals higher-order neural interactions but yields high-dimensional tensors difficult to interpret at the source level.
• Standard dimensionality reduction methods often lack a physical link to neural generators.

Purpose of the Study:

• Introduce a novel low-rank tensor decomposition framework for electroencephalography (EEG) signal analysis.
• Develop a physically grounded method for interpreting cross-bispectral data and identifying neural generators.
• Enable direct source-space interpretation and spatial demixing of EEG signals.

Main Methods:

• Developed a low-rank tensor decomposition framework based on EEG signal generation physics.
• Represented the cross-spectrum using a single spatial mixing matrix and a compact source-interaction tensor.
• Utilized MOCA for spatial demixing to recover distinct source maps.

Main Results:

• Simulations demonstrated robust capture of dominant bispectral structure under various conditions (SNR, dipole orientation, etc.).
• The method successfully identified anatomically plausible parietal generators linked to alpha-band bispectral interactions in resting-state EEG.
• The framework enforces a compact, interpretable source-interaction structure, improving localization and reducing variability compared to standard methods.

Conclusions:

• The proposed low-rank decomposition provides a principled, efficient method for reducing and interpreting cross-bispectral EEG data.
• Bridging tensor decomposition with biophysical source models offers novel insights into neural coupling.
• This approach surpasses standard matrix or tensor techniques for analyzing complex neural interactions.