Supervised factor selection in tensor decomposition of EEG signal

Tensor decomposition methods are important tools for multidimensional data analysis, which have also proved useful for EEG signal processing. However, their direct application for tasks involving supervised training, such as EEG data classification in systems based on brain-computer interfaces, is limited by the inherently unsupervised nature of the optimization algorithms used for tensor factorization.

In this work, we propose a solution for a motor imagery classification task based on parallel factor analysis (PARAFAC) of EEG data. The individual factors obtained through PARAFAC decomposition are subjected to statistical analysis, enabling us to select signal components relevant to the classification problem. To choose the rank of the decomposition, we propose a special score function based on cosine similarity of all possible pairs of decompositions.

The proposed method was shown to significantly increase the classification accuracy in the case of the best-performing subjects, when provided with an EEG signal satisfying certain conditions, such as sufficient trial length. Besides, representation of the statistically significant components in the form of a heatmap, defined over the space-frequency plane, proved suitable for direct interpretation in the context of event-related synchronization/desynchronization of cortical activity.

The proposed approach, joining universal tensor decomposition methods with statistical evaluation of the obtained components, has the potential to yield high accuracy and explainability of the results while significantly reducing the input space dimensionality.