Optimizing Spectral Graph Kernels for Time-Delay Embedding of Multichannel EEG Data

The task of determining the dynamic patterns of causal connectivity among brain regions from EEG data is challenging due to inherent noise in EEG signals, sparse connections. High volume and dimensionality of data add substantial computational demands. Koopman embedding kernels offer a promising approach for capturing the low-dimensional linear embeddings of complex nonlinear system dynamics. This study focuses on leveraging the Graph Kernel Koopman Embedding (GKKE) method to extract latent factors, a novel application within the realm of EEG analysis. Specifically, the research pioneers the adaptation of the GKKE algorithm to estimate the inherent connectivity substructures, that enable investigations of the neuro-markers of cognitive load states and disorders like seizures from EEG signals. The graph for each segment was constructed by computing the correlation coefficients among the channel pairs. The algorithmic workflow was applied to a labelled cognitive load dataset from an online repository. The features were extracted in terms of Koopman-spectral decomposed clusters of eigenfunctions of the gram matrices produced by two different graph kernels applied for approximation of the Koopman operator over each EEG-segment. These features, representing the latent metastable states, were fed into machine learning classifiers, including SVM and Random Forest, and Decision Tree classifiers. Weisfeiler-Lehman Kernel (WL)-Kernel yielded an average accuracy of around 84% for all the classifiers and outperformed the Random-walk kernel. The significance of this work lies in its pioneering use of graph Koopman spectral decomposition-based low-dimensional embedding of the metastable structures of connectivity to provide an algorithm that enables neuro-marker estimation. Specific contribution is the workflow that determines the optimal combination of the graph kernel and classifier ensemble. This equips deeper understanding of the connectivity dynamics of brain regions related to cognitive states offers a new avenue for prognosis and training protocols to improve cognitive states.