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Learning Cortico-Muscular Dependence through Orthonormal Decomposition of Density Ratios
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Applies orthonormal density-ratio decomposition (FMCA) with a new matrix-trace cost (FMCA-T) to unlabeled EEG-EMG pairs to learn cortico-muscular dependence, yielding eigenfunctions that classify movements and subjects and localized channel/temporal dependence maps.
Problem
Modeling high-level, contextual and localized (channel- and time-level) cortico-muscular connectivity between EEG and EMG, which scalar dependence measures like coherence, KICA, HSIC and MINE fail to provide robustly.
Approach
Replaces the log-determinant cost of FMCA with a matrix trace cost (FMCA-T) that optimizes the sum of top eigenvalues of the density ratio, and adds a top-down channel/temporal localization scheme so eigenfunctions and density ratios can be attributed to EEG channels and time steps.
Key results
- FMCA-T reaches 0.994 inter-subject 3-class accuracy versus 0.907 for Vanilla and 0.904 for EEGNet, using eigenfunctions as features.
- In cross-subject 3-class classification FMCA-T achieves 0.540 accuracy, outperforming the best baseline (VicReg 0.449) by over 9 points.
- FMCA-T's density ratio is invariant to white, nonstationary and pink noise and random delays on SinWav, while MINE fails to converge.
Measured effects reported in the paper
| What was changed | Where | Measured | Effect |
|---|---|---|---|
| use EEG eigenfunctions learned with FMCA-T instead of CSP-RLDA features | EEG-EMG-Fusion inter-subject 3-class classification · EEG-EMG-Fusion inter-subject 3-class | accuracy: 0.985±0.019 -> 0.994±0.002 | Helped |
| use EEG eigenfunctions learned with FMCA-T instead of Deep4 features | EEG-EMG-Fusion inter-subject 11-class classification · EEG-EMG-Fusion inter-subject 11-class | accuracy: 0.274±0.001 -> 0.320±0.009 | Helped |
| use EEG eigenfunctions learned with FMCA-T instead of EEGNet | EEG-EMG-Fusion inter-subject subject classification · EEG-EMG-Fusion inter-subject subject classification | accuracy: 0.988±0.007 -> 0.998±0.004 | Helped |
| use EEG eigenfunctions learned with FMCA-T instead of VicReg features | EEG-EMG-Fusion cross-subject 3-class classification · EEG-EMG-Fusion cross-subject 3-class | accuracy: 0.449±0.016 -> 0.540±0.012 | Helped |
| use EEG eigenfunctions learned with FMCA-T instead of Deep4 features | EEG-EMG-Fusion cross-subject 11-class classification · EEG-EMG-Fusion cross-subject 11-class | accuracy: 0.140±0.000 -> 0.121±0.002 | Hurt |
| use matrix trace cost rather than log-determinant cost (ablation) | FMCA EEG eigenfunction classifier · EEG-EMG-Fusion inter-subject 3-class | accuracy: 0.985±0.003 -> 0.994±0.002 | Helped |
| use matrix trace cost rather than log-determinant cost (ablation) | FMCA EEG eigenfunction classifier · EEG-EMG-Fusion inter-subject 11-class | accuracy: 0.257±0.011 -> 0.320±0.009 | Helped |
| use matrix trace cost rather than log-determinant cost (ablation) | FMCA EEG eigenfunction classifier · EEG-EMG-Fusion inter-subject subject classification | accuracy: 0.989±0.007 -> 0.998±0.004 | Helped |
| use matrix trace cost rather than log-determinant cost (ablation) | FMCA EEG eigenfunction classifier · EEG-EMG-Fusion cross-subject 3-class | accuracy: 0.509±0.014 -> 0.540±0.012 | Helped |
| use matrix trace cost rather than log-determinant cost (ablation) | FMCA EEG eigenfunction classifier · EEG-EMG-Fusion cross-subject 11-class | accuracy: 0.115±0.003 -> 0.121±0.002 | Helped |
| replace the log-determinant objective with the matrix trace objective (ablation) | FMCA dependence estimation · EEG-EMG-Fusion training | training stability | Helped |
Surprising findings
- Cross-subject 11-class accuracy for FMCA-T (0.121) is close to chance (0.09) and below Deep4 (0.140), indicating limited generalization for fine-grained movements.
- MINE fails to converge and produce stable results on SinWav.
Limitations
- Cross-subject performance drops, likely due to the limited 25-participant dataset.
- Fine-grained 11-class cross-subject accuracy is near chance.
- Evaluation relies partly on simulated data and t-SNE visual inspection of clusters.
Experimental setup
Datasets: EEG-EMG-Fusion (public GigaDB dataset) SinWav (simulated) Simulated EEG-EMG dataset via EEGSourceSim
Benchmarks: EEG-EMG-Fusion inter-subject and cross-subject classification (3-class, 11-class, subject) SinWav robustness
Metrics: classification accuracy dependence measure stability
Baselines: KICA HSIC MINE CC MIR CMC EEGNet EEG-Conformer Deep4 CSP-RLDA Barlow Twins SimCLR
Builds on: Functional Maximal Correlation Algorithm (FMCA) MINE KICA HSIC
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