Low-Rank Tensor Decomposition for Cross-Bispectral Analysis of EEG Data

Abstract

Cross-bispectral measures provide a rich description of interactions in EEG signals, but their third-order tensor structure poses substantial challenges for interpretation and dimensionality reduction. We introduce a low-rank tensor decomposition framework specifically designed for cross-bispectral EEG data. The model expresses the bispectrum as a product of a single spatial mixing matrix and a compact source-interaction tensor, yielding a structured and interpretable representation of the data. Unlike classical tensor decompositions such as Tucker and its special case PARAFAC, where either the core tensor is unconstrained or restricted to rank-one terms, our formulation incorporates a source-space interpretation directly through the tensor Qmnp, making the decomposition well suited for identifying dominant coupling components. After obtaining the low-rank representation, spatial demixing is performed using MOCA to derive clear and interpretable source maps. Through simulations, we show that the method consistently retrieves the dominant structure of the bispectrum across a wide range of conditions, including changes in SNR, dipole orientation, amplitude balance, and source complexity. Applied to resting-state EEG, the method produces anatomically plausible parietal generators associated with the strongest alpha-band bispectral interactions. Overall, the framework provides a principled and computationally efficient approach for reducing and interpreting cross-bispectral EEG data, offering source-level insights that are difficult to obtain using standard tensor factorization techniques.