BDAN-SPD

1 BDAN-SPD

BDAN-SPD is a cross-subject MI-BCI domain-adversarial decoder whose acronym “SPD” stands for spatiotemporal pattern differences (left-minus-right hemisphere EEG, not symmetric-positive-definite) — the model uses no Riemannian/SPD-manifold layers.

Ref: @weiBDANSPDBrainDecoding2024

Venue: IEEE Transactions on Industrial Informatics, DOI 10.1109/TII.2024.3450010.

Overview

• Problem: cross-subject MI-BCI fails under distribution shift and scarce calibration data; prior domain-adversarial methods only design discriminators, ignore MI prior knowledge, and let decision boundaries bias toward the source domain.
• Idea: (1) motor-lateralization prior — hemisphere (left-minus-right electrode) difference as SPD guidance; (2) CNN+transformer hybrid feature extractor for local and global temporal information; (3) EEGMix convex-combination augmentation of target calibration data; (4) a dynamic adversarial factor $\omega$ balancing marginal ($L_g$) and classwise conditional ($L_{cl}$) distribution alignment.
• Datasets (exactly three): BCI Competition IV Dataset 2a (9 subjects), BCI Competition IV Dataset 2b (9 subjects), and OpenBMI = Korea University Dataset (MI-KU or Lee2019 or OpenBMI) (54 subjects).
• Preprocessing: 2a/2b: 4–40 Hz band-pass, ~4 s segmentation after cue onset, bad trials removed; OpenBMI: 8–30 Hz band-pass, [0,4] s windows; Euclidean alignment (EA) with the subject’s mean covariance as reference ${\tilde{X}}_i={\bar{R}}^{-1/2}{X}_i$ applied before augmentation.
• Protocol: leave-one-subject-out (LOSO) cross-subject with labeled target calibration (not calibration-free), 9 or 54 tasks.

Architecture

Five modules: EEGMix augmentation → hemisphere-difference capture → hybrid feature extractor $G_f$ → dynamic domain discriminator $G_d$ → task classifier $G_y$.

1. EEGMix: within each class subset, each target trial is split into $N=3$ non-overlapping short series; same-order segments from two trials of the same class are mixed by convex combination

$$x_{\mathrm{new}}=\beta \frac{x_i-\mu (x_j)}{\sigma (x_j)}\sigma (X)+(1-\beta )\mu (X),\beta \sim \mathrm{Beta}(\alpha ,\alpha ),$$

using the subject’s global mean $\mu (X)$/std $\sigma (X)$ while preserving local short-time structure; segments are re-concatenated in temporal order. Augmentation volume equals calibration size: 288 / 400 / 100 augmented trials for 2a / 2b / OpenBMI.
2. Spatiotemporal pattern differences: CBAM-style channel attention on the 3-D trial ($X_i\in {\mathbb{R}}^{E\times 1\times T}$): $M_c(F)=\sigma (W_1(W_0(F_{avg}^c))+W_1(W_0(F_{max}^c)))$, refined data ${\tilde{X}}_i=M_c(F)\odot X_i$; electrodes split into left/right groups (midline included because foot imagery ERD is central), and the difference tensor is

$${\tilde{X}}_i^D={\tilde{X}}_i^{\mathrm{Left}}-{\tilde{X}}_i^{\mathrm{Right}}.$$

3. CNN for local features: temporal conv 20 kernels of size $1\times 25$ with ELU; spatial conv 40 kernels of size $E/2\times 1$; batch norm, dropout, average pooling.
4. Transformer for global features: CNN features reshaped to $F_c\in {\mathbb{R}}^{T\times K}$ (time points as tokens), scaled dot-product attention with 5 heads:

$$\mathrm{Attention}(Q,K,V)=\mathrm{Softmax}\left(\frac{Q{K}^{\top }}{\sqrt{d}}\right)V.$$

5. Dynamic domain adaptation: global discriminator $G_d$ on marginal loss $L_g$; $C$ classwise discriminators $G_{cd}$ on conditional loss $L_{cl}$ using classifier output probabilities as soft class assignments; A-distance estimates $d_{A,g}=2(1-2L_g)$, $d_{A,l}^c=2(1-2L_{cl}^c)$ give

$$\omega =\frac{d_{A,g}}{d_{A,g}+\frac{1}{C}{\sum }_c{d}_{A,l}^c},L=L_y-\lambda ((1-\omega )L_g+\omega L_{cl}),\lambda =0.05,$$

trained as a two-player game: ${\min }_{{\theta }_f,{\theta }_y}{\max }_{{\theta }_d}L$.

No SPD-manifold layer is used (no BiMap/ReEig/LogEig); “SPD” is the hemisphere-difference prior. EA alignment is Euclidean.

Model Parameters

• CNN: temporal 20 × (1×25) ELU → spatial 40 × (E/2×1) → BN → dropout → average pooling.
• Transformer: 5 heads, token dim = number of conv kernels $K$; layer depth/dimensions beyond this: not reported.
• Discriminators: one global + $C$ classwise subdomain discriminators.
• EEGMix: 3 slices; Beta mixing parameter value: not reported.
• Total trainable parameters: not reported.

Training Parameters

• Optimizer: Adam, ${\beta }_1=0.9$, ${\beta }_2=0.999$; learning rate 0.0005; batch size 64.
• Loss: cross-entropy for classifier and discriminators; adversarial weight $\lambda =0.05$; dynamic factor $\omega$ updated during training.
• Dropout rate, number of epochs, initialization, seeds: not reported.
• Augmentation: 288 (2a) / 400 (2b) / 100 (OpenBMI) EEGMix trials.

Results

Paper main results (LOSO with labeled target calibration; means ± SD over subjects):

Dataset	Accuracy	Kappa (paper text)	Kappa (audited table)
BCIC-IV-2a	77.49 ± 15.22	0.6905	0.6998
BCIC-IV-2b	85.19 ± 13.36	0.6919	0.6916
OpenBMI	79.37 ± 12.99	0.5874	0.5874

Per-subject 2a values quoted in the t-SNE discussion: S01 88.97, S03 92.67, S07 93.14, S08 88.93, S09 87.50; BCI-illiteracy subjects S02 57.24, S04 74.56, S05 55.80, S06 58.60.