Robust graph topology inference for multiple brain EEG networks

In EEG-based connectivity analysis, multiple graphs are typically available, as obtained from measurements taken under different conditions, such as frequency bands, trials, or patients' states. Identifying stable patterns of interaction among brain regions, such as functional communities, can provide valuable insight into brain organization and its changes across tasks or conditions. It is then of interest to find a method to properly combine these different graphs to obtain a clustering that is sufficiently stable and representative of brain functionalities. In this paper, we propose a method to obtain robust spectral clustering. The method relies on a statistical characterization of the multiple graphs and a small perturbation analysis of the eigen-decomposition of graphs affected by random perturbations to derive the optimal weighting that minimizes the variance of the eigenvalues. The proposed method is first tested on synthetic data, to assess its advantages with respect to conventional approaches under controllable conditions, and then it is applied to real EEG data in both healthy individuals performing motor imagery tasks and patients affected by Alzheimer's disease. The results show the ability of the method to reliably detect functional communities and quantify connectivity reorganization during cognitive tasks. Our results suggest that the proposed approach provides a valid new strategy to combine multiple graphs taking into account the statistical properties of each graph in the presence of uncertainties.