Optimizing Spectral Graph Kernels for Time-Delay Embedding of Multichannel EEG Data
Bibliographic record
Abstract
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.
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How this classification was reachedexpand
Full frame machine prediction
Teacher imitationNot calibrated prevalence, not ground truth. Human validation pending. The Gemma side is a direct model label for every work in the frame, read from the title-only record. The Codex side is a classifier learned from the 10,348 direct Codex labels and calibrated to design-weighted sample rates; fields without enough sample support carry no Codex call. Candidate is the union of the two sides; consensus is their intersection. These outputs are machine_predicted_unvalidated and are not human labels.
Distilled classifier scores by category (both heads)
| Category | Codex | Gemma |
|---|---|---|
| Metaresearch | 0.001 | 0.006 |
| Meta-epidemiology (narrow) | 0.001 | 0.000 |
| Meta-epidemiology (broad) | 0.001 | 0.001 |
| Bibliometrics | 0.001 | 0.001 |
| Science and technology studies | 0.000 | 0.001 |
| Scholarly communication | 0.001 | 0.002 |
| Open science | 0.001 | 0.001 |
| Research integrity | 0.001 | 0.001 |
| Insufficient payload (model declined to judge) | 0.001 | 0.001 |
Machine scores (provisional)
The two teacher heads of the student model, read on this work. A score orders the frame for review; it never asserts a category, and the validation status ships verbatim with every row.
Baseline scores from an immature model (maturity gate not passed, 7 training rounds). Scores rank; they never assert a category.
score_only:v0-immature-baseline · verbatim from the scoring run: score_only means the number may rank works, and no category label ships from itClassification
machine, unvalidatedMachine predicted; a candidate call from one source (direct Gemma or distilled Codex), not a consensus.
How this classification was reached, model by model and score by score, is at the end of the page under "How this classification was reached".