1 SPD-DANN

SPD-DANN is a single-source unsupervised domain-adversarial network that extracts manifold-valued EEG features and aligns their marginal and class-conditional distributions with Log-Euclidean losses.

Ref: @SPDDANNSPDManifold

Code not available.

Overview

SPD-DANN uses labeled trials from one source subject and unlabeled data from one target subject. It combines a gradient-reversal domain discriminator with explicit alignment of SPD feature means and pseudo-labeled class prototypes.

Datasets:

BCI Competition IV Dataset 2a: 9 subjects, 22 EEG + 3 EOG channels, 250 Hz, four classes, two sessions, 72 trials/class/session.
BCI Competition IV Dataset 2b: 9 subjects, 3 EEG + 3 EOG channels, 250 Hz, binary MI, five sessions; the first 120 trials of each session selected.
BCI Competition III Dataset IIIa: 3 subjects, 60 channels, 250 Hz, four classes; 40 trials per experiment, imagery 3-7 s.
BCI Competition III Dataset IVa: 5 subjects, 118 channels, 1,000 Hz, binary right-hand vs right-foot MI, 280 trials per subject, imbalanced classes.

Preprocessing: downsample all datasets to 128 Hz; remove irrelevant channels (incl. EOG); band-pass 8-32 Hz; retain 3 s after cue onset for 2a, 4 s for 2b and IIIa, and the first 3 s for IVa.

Protocol: every ordered source-target subject pair is evaluated for cross-subject transfer. For 2a, target session 1 is available for unsupervised adaptation/training and session 2 for testing; for 2b, target sessions 1-3 for adaptation/training and 4-5 for testing; IIIa and IVa are randomly divided into training and test sets “in proportion” (proportion not reported). No target labels are used for training, although confident target pseudo-labels are used by the prototype loss.

Architecture

The feature extractor is

EEG → convolution → batch normalization → split into n temporal/feature parts → covariance → trace normalization → manifold attention → ReEig.

For each part $f_{i}$ , the covariance $X_{i}^{'}$ is transformed into

X_{i} = \frac{X _{i}^{'}}{trace ( X _{i}^{'} )} + ϵ I, ϵ = 1 0^{- 5} .

The manifold attention module uses three BiMap transformations to construct SPD queries, keys, and values. Attention-weighted values are aggregated with a Log-Euclidean mean; ReEig then rectifies the resulting SPD representation.

Two heads receive this feature:

Class head: LogEig → Euclidean layers → source-class prediction.
Domain head: gradient reversal → LogEig → a deeper Euclidean network → source/target prediction.

The class loss and binary domain loss are

L_{C} = - \frac{1}{N _{s}} i = 1 \sum N_{s} y_{i} lo g \overset{y}{^}_{i}, L_{D} = - \frac{1}{N} i = 1 \sum N [d_{i} lo g \hat{d}_{i} + (1 - d_{i}) lo g (1 - \hat{d}_{i})] .

SPD Domain Feature Alignment

For source features ${S_{i}}$ and target features ${T_{i}}$ , compute Log-Euclidean means

\overset{ˉ}{S} = exp (\frac{1}{n} i \sum lo g S_{i}), \overset{ˉ}{T} = exp (\frac{1}{n} i \sum lo g T_{i}),

and the alignment loss

L_{M} = lo g \overset{ˉ}{S} - lo g \overset{ˉ}{T}_{F} .

SPD Class Prototype Pair Loss

Source prototype for class $i$ :

F_{S}^{i} = exp (\frac{1}{n _{i}} j \sum lo g S_{ij}) .

Target pseudo-label confidence is measured by entropy $H (p) = - \sum_{i = 1}^{m} p_{i} lo g p_{i}$ ; only the 50% of target samples with lowest entropy are retained. With Log-Euclidean distance $d_{lem}$ , the margin loss is

L_{P} = i = 1 \sum m j \neq = i \sum max (d_{lem} (F_{S}^{i}, F_{T}^{i}) - d_{lem} (F_{T}^{i}, F_{T}^{j}) + ω, 0) + max (d_{lem} (F_{S}^{i}, F_{T}^{i}) - d_{lem} (F_{T}^{i}, F_{S}^{j}) + ω, 0),

with $ω = 0.1$ .

The full objective is

min L_{C} - λ_{D} L_{D} + L_{M} + λ_{P} L_{P},

where $λ_{D}$ follows the dynamic DANN schedule and $L_{M}$ is added with unit weight.

Model Parameters

Covariance regularizer: $ϵ = 1 0^{- 5}$ .
Covariance scale normalization: divide by trace.
Target pseudo-label retention: 50% lowest-entropy predictions.
Prototype margin: $ω = 0.1$ .
Prototype-loss weight at the reported optimum: $λ_{P} = 0.1$ (sensitivity tested in {0, 0.01, 0.02, 0.05, 0.1, 0.15, 0.2}).
Number of convolution filters, temporal parts, BiMap output dimensions, ReEig threshold, and classifier/discriminator layer widths: not reported.

Training Parameters

Framework: PyTorch.
Optimizer: Riemannian Adam.
Learning rate: $1 0^{- 2}$ .
Weight decay: $1 0^{- 3}$ .
Batch size: 32.
Classification loss: source cross-entropy; domain loss: binary cross-entropy optimized adversarially through gradient reversal.
$λ_{D}$ : dynamically updated according to the cited DANN strategy.
Epochs, early stopping, LR schedule, random-seed count, and hardware: not reported.

Results

Cross-subject accuracy (%). BCIC-IV-2a:

Method	A1	A2	A3	A4	A5	A6	A7	A8	A9	Avg
DALN	40.4	25.0	40.1	39.4	28.9	36.5	38.4	35.4	32.6	35.2
DANN	39.5	24.6	37.2	38.5	26.9	35.0	36.7	32.2	30.4	33.4
MCD	43.4	30.7	43.4	41.9	32.9	38.6	39.8	38.1	36.2	38.3
JDD	43.0	26.8	45.1	43.0	29.0	36.9	40.7	39.0	39.5	38.1
SPD-DANN	49.7	38.5	50.5	44.5	41.5	45.4	43.5	46.5	44.2	44.9

SPD-DANN exceeds MCD by 6.6 pp and DANN by 11.5 pp.

BCIC-IV-2b:

Method	B1	B2	B3	B4	B5	B6	B7	B8	B9	Avg
DALN	69.9	50.9	67.8	61.9	66.9	69.8	68.3	66.9	65.8	65.3
DDAN	71.8	59.0	66.3	65.2	66.2	71.9	69.0	66.3	70.5	67.4
DANN	64.6	60.7	58.3	60.9	63.3	64.8	69.9	59.5	64.2	62.9
JDD	70.7	50.8	61.9	64.7	69.4	71.0	70.7	66.6	66.8	65.8
SPD-DANN	78.5	77.0	75.4	76.2	74.6	77.6	77.5	73.9	77.7	76.5

BCIC-III IIIa:

Method	K3b	K6b	L1b	Avg
DALN	33.6	37.5	37.8	36.3
MCD	38.2	40.6	39.8	39.5
JDD	38.8	40.3	39.2	39.4
SPD-DANN	41.6	55.9	50.7	49.4

BCIC-III IVa:

Method	aa	al	av	aw	ay	Avg
DDAN	66.7	67.5	63.6	65.5	61.6	65.0
JDD	67.9	67.2	65.2	67.2	66.2	66.7
SPD-DANN	72.1	76.7	69.9	81.3	73.9	74.7

Ablation on 2a: without both losses 39.8; $L_{M}$ only 41.7; $L_{P}$ only 42.4; full 44.9. Removing $L_{P}$ reduces accuracy by 3.2 points; removing $L_{M}$ by 2.5 points.

Notes

The random train/test proportion for IIIa and IVa is not specified.

Lucas Heck's Notes

Explorer

SPD-DANN