Determination of the number of components in the PARAFAC model with a nonnegative tensor structure: a simulated EEG data study

Abstract

Parallel factor analysis (PARAFAC) is a powerful tool for detecting latent components in human electroencephalogram (EEG) in the time-space-frequency domain. As an essential parameter, the number of latent components should be set in advance. However, any component number selection method already proposed in the literature became a rule of thumb. Existing studies have demonstrated the methods’ performance on artificial data with a simplified structure, often not mimicking a real data character. On the other hand, the ground-truth latent structure is not always known for real-world data. With the objective to provide a comprehensive overview of component number selection methods and discuss their applicability to EEG, our study focuses on nontrivial and nonnegative simulated data structures resembling real EEG properties as closely as possible. This is achieved through an accurate head model and well-controlled cortical activation sources. By considering different noise levels and disruptions from the optimal structure, the performance of the twelve component number selection methods is closely inspected. Moreover, we validate a new approach for component number selection, which we recently proposed and applied to EEG tasks. We found that methods based on the eigenvalue analysis, variance explained, or presence of redundant components are inappropriate for component number selection in EEG tensor decomposition. On the other hand, three existing methods and the newly proposed approach produced promising results on nontrivial simulated EEG data. Nevertheless, component number selection for PARAFAC analysis of EEG is a complex yet unresolved problem, and new approaches are needed.