# Linear and nonlinear multidimensional functional connectivity methods reveal similar networks for semantic processing in EEG/MEG data

## TL;DR

This paper introduces a new nonlinear method for analyzing brain connectivity in EEG/MEG data and compares it to a linear approach, finding that linear methods may be sufficient for most practical purposes.

## Contribution

The paper introduces nTL-MDPC, a novel nonlinear functional connectivity method for EEG/MEG data, and compares it to linear approaches.

## Key findings

- Nonlinear TL-MDPC achieves up to 15% higher explained variance than linear TL-MDPC with sufficient trial numbers.
- Real EEG/MEG data showed only subtle increases in nonlinear connectivity strength with no significant differences between methods.
- Linear methods may be sufficient for practical brain connectivity analysis due to their lower computational demands.

## Abstract

Investigating task- and stimulus-dependent connectivity is key to understanding how the interactions between brain regions underpin complex cognitive processes. Yet, the connections identified depend on the assumptions of the connectivity method. To date, methods designed for time-resolved electroencephalography/magnetoencephalography (EEG/MEG) data typically reduce signals in regions to one time course per region. This may fail to identify critical relationships between activation patterns across regions. Time-Lagged Multidimensional Pattern Connectivity (TL-MDPC) is a promising new EEG/MEG functional connectivity method improving previous approaches by assessing multidimensional relationships between patterns of brain activity. However, TL-MDPC remains linear and may therefore miss nonlinear interactions among brain areas.

Thus, we introduce Nonlinear TL-MDPC (nTL-MDPC), a novel bivariate functional connectivity method for event-related EEG/MEG applications, and compare its performance to the original linear TL-MDPC. nTL-MDPC describes how well patterns in ROI
X
at a time point
tx
can predict patterns of ROI
Y
at a time point
ty
using artificial neural networks.

Applying this method and its linear counterpart to simulated data demonstrates that both can identify nonlinear dependencies, with nTL-MDPC achieving up to ~0.75 explained variance under optimal conditions (e.g., high SNR), compared to ~0.65 with TL-MDPC. However, with a sufficient number of trials- e.g., a trials-to-vertex ratio ≥10:1 - nTL-MDPC achieves up to 15% higher explained variance than the linear method. Nevertheless, application to a real EEG/MEG dataset demonstrated only subtle increases in nonlinear connectivity strength at longer time lags with no significant differences between the two approaches.

Overall, this suggests that linear multidimensional methods may be a reasonable practical choice to approximate brain connectivity, given the additional computational demands of nonlinear methods.