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KDHNet: A Knowledge-Driven Hybrid Network for Limited-Calibration SSVEP Decoding

Zhentao He, Ziwei Wang, Dongrui Wu

arXiv:2610.33058v1cs.CVcs.AI

TL;DR

Limited-calibration SSVEP decoding must reconcile the low-data reliability of analytical filters with the representational flexibility of deep models. KDHNet combines a fixed analytical spatial-filtering prior with a learnable Transformer decoder and evaluates it across intra- and inter-subject settings. It achieves the strongest or near-strongest reported performance across these settings, with gains generally larger when calibration is scarce.

  • Problem

    Analytical spatial filters have limited representation capacity, while deep decoders can be unstable with few subject-specific trials; existing hybrids also leave Transformer-based sequence modeling uncoupled from task-discriminative spatial priors.

    Source: §I · p. 2

  • Method

    KDHNet combines a closed-form TD-RCA spatial-filtering front-end with an SSVEPformer decoder and uses target-guided LST to adapt source data for inter-subject training.

    Source: §I · p. 2

  • Results

    KDHNet achieved the highest mean accuracy and ITR in 14 of 15 intra-subject window settings and all ten calibration-ratio settings, and ranked best on two inter-subject datasets and second on the third.

    Source: §VIII · p. 11

  • Takeaways & Limitations

    The results support combining a fixed analytical prior with trainable neural modules for limited-calibration SSVEP decoding.

    Source: §VII · p. 11, §VIII · p. 11

    The filter-bank sub-band boundaries are hand-crafted rather than learned, and LST requires a source domain large enough to estimate reliable class-wise transformations.

    Source: §VII · p. 11

Abstract

from arXiv · show

Steady-state visual evoked potential (SSVEP)-based brain-computer interfaces (BCIs) achieve high information transfer rates but often require sufficient subject-specific calibration data for reliable decoding. Analytical spatial filters are effective with limited data, but their linear formulations constrain representation capacity. Deep models learn more flexible representations but are prone to overfitting when calibration data are scarce. We propose KDHNet, which combines knowledge-driven analytical processing with data-driven representation learning. After filter-bank preprocessing, cascaded task-discriminant component analysis (TDCA) and task-related component analysis (TRCA) extract discriminative and trial-reproducible components. Learnable sub-band weighting then fuses spectral information, and an SSVEPformer decoder learns temporal and spectral representations for classification. For inter-subject decoding, a target-guided least-squares transformation aligns source trials using one labeled target trial per class. Extensive experiments were performed on three public datasets, covering intra- and inter-subject protocols, five analysis windows, and multiple calibration ratios. In intra-subject evaluation, KDHNet achieved the highest mean accuracy and information transfer rate in 14 of 15 window settings and all ten calibration-ratio settings. In inter-subject evaluation, KDHNet obtained the best or second-best performance, and the gains were generally larger with less calibration data. Ablation studies indicated that the estimated TDCA projection performed better when fixed than when optimized from analytical or random initialization. Combining fixed knowledge priors with trainable neural modules is effective for low-calibration SSVEP decoding. This framework supports more practical, robust, and plug-and-play BCIs. Code is available at https://github.com/2665023991/KDHNet.

I. INTRODUCTION

KDHNet combines analytical spatial filtering with Transformer-based representation learning and uses one decoder for limited-calibration intra- and inter-subject SSVEP decoding. The paper evaluates this approach across public benchmarks and identifies gaps in existing decoders that motivate the design.

I. INTRODUCTION

  • Analytical decoders remain reliable with few calibration trials but have limited capacity for complex discriminative patterns, while deep models can become unstable with sparse subject-specific data.The paper frames these as complementary constraints of knowledge-driven and data-driven approaches.Source: §I · p. 1
  • Existing hybrids generally use CNN backbones or shallow prediction-level fusion, leaving task-discriminative spatial priors uncoupled from Transformer sequence modeling.Source: §I · p. 2
  • KDHNet couples a closed-form TD-RCA spatial-filtering front-end with a Transformer decoder to combine analytical priors and deep sequence modeling.The front-end enhances task-discriminative and reproducible components, while the decoder models temporal-spectral dependencies.Source: §I · p. 2
  • The same framework serves intra- and inter-subject decoding: it trains on limited target trials for the former and incorporates target-guided aligned source trials for the latter.Source: §I · p. 2
  • KDHNet outperformed representative baselines in 14 of 15 intra-subject window settings, all ten calibration-ratio settings, and two of three inter-subject benchmarks, with largest gains under scarcest calibration.The evaluation used three public benchmarks and covered intra- and inter-subject scenarios.Source: §I · p. 2

II. METHOD

KDHNet uses a shared decoder for intra- and inter-subject limited-calibration SSVEP decoding, with scenario-specific training-set construction. Its pipeline combines filter-bank preprocessing, a TD-RCA front-end, learnable sub-band weighting, and an SSVEPformer decoder.

A. Problem Formulation

  • Intra-subject training uses limited trials from the same subject; inter-subject evaluation uses LOSO, with one target subject, source subjects, and a small target calibration set.Source: A. Problem Formulation · p. 2
  • The same decoder trains directly on intra-subject calibration trials, while inter-subject training aligns source data to the target with LST and combines them with target calibration data.Source: A. Problem Formulation · p. 2

B. Overview of KDHNet

  • After scenario-specific training data are constructed, trials pass through filter-bank preprocessing, the TD-RCA knowledge front-end, learnable sub-band weighting, and the SSVEPformer decoder.The overview distinguishes frozen, closed-form TDCA projections from analytically initialized TRCA filters and sub-band weights that are trained with the decoder.Source: B. Overview of KDHNet · p. 3, Figure 1 · p. 3

C. Filter-Bank Preprocessing

Filter-bank preprocessing separates EEG trials into frequency bands to retain complementary harmonic information and suppress broadband noise. The TD-RCA front-end then extracts class-discriminative and reproducible task-related features.

C. Filter-Bank Preprocessing

  • Each EEG trial is split into sub-band signals because SSVEP responses concentrate around the stimulation frequency and its harmonics.The preprocessing is intended to capture complementary harmonic information and suppress broadband noise before feature extraction.Source: C. Filter-Bank Preprocessing · p. 3

D. TD-RCA Knowledge Front-End

  • The TD-RCA front-end cascades TDCA class-discriminative projections with TRCA filtering to enhance reproducibility of task-related components.Batch normalization and PReLU process the TDCA output before TRCA.Source: D. TD-RCA Knowledge Front-End · p. 3

1) TDCA stage:

  • TDCA computes a projection from between-class and within-class scatter, then transforms training trials into projected features followed by batch normalization and PReLU.Dropout is applied to the transformed feature before the trainable TRCA layer during end-to-end training.Source: 1) TDCA stage · pp. 3–4

2) TRCA stage:

The TRCA stage estimates spatial filters and computes class-wise responses. Learnable sub-band weighting fuses the resulting features while preserving complementary spectral information.

2) TRCA stage:

E. Sub-Band Weighting

  • Learnable coefficients weight each sub-band feature, with coefficients initialized using fixed constants.The resulting representation preserves complementary spectral information while adapting the bands’ relative contributions.Source: E. Sub-Band Weighting · p. 4

F. SSVEPformer Decoder

SSVEPformer classifies the fused TD-RCA features by learning temporal and spectral representations. For inter-subject decoding, class-specific LST aligns source trials before they are combined with target calibration trials for training.

F. SSVEPformer Decoder

  • The SSVEPformer decoder maps fused TD-RCA features to posterior probabilities over stimulus classes.It learns temporal and spectral representations and can be replaced by a compatible neural network with an adapted input layer.Source: F. SSVEPformer Decoder · p. 4

G. Target-Guided LST Alignment

  • For each source subject and class, a class-specific LST matrix is estimated using source and target calibration templates.The closed-form solution uses the Moore-Penrose pseudoinverse.Source: G. Target-Guided LST Alignment · p. 4
  • LST aligns each source trial by class, after which aligned source trials are concatenated with target calibration trials for training.This step reduces inter-subject distribution mismatch while retaining information from limited target calibration data.Source: G. Target-Guided LST Alignment · p. 4

H. Training Objective

Training uses cross-entropy, with TDCA projections fixed while TRCA filters and sub-band weights are updated alongside the decoder. Experiments use three public datasets and evaluate limited-calibration intra- and inter-subject protocols.

H. Training Objective

  • KDHNet is trained with cross-entropy using one-hot class labels and corresponding predicted probabilities.Source: H. Training Objective · p. 5
  • TDCA projections are estimated once in closed form and kept fixed, while TRCA filters, sub-band weights, and the decoder are updated during end-to-end training.Source: H. Training Objective · p. 5

A. Datasets

  • The evaluation uses Dataset I with 10 subjects and 12 targets, Dataset II with 35 subjects and 40 targets, and Dataset III with 70 subjects and 40 targets.The datasets contain 15, 6, and 4 trials per class, respectively; the latter two use nine posterior channels.Source: A. Datasets · p. 5

B. Preprocessing and Experimental Protocol

  • Experiments use a fixed 1.0 s window for split-ratio tests and 0.4–1.2 s windows for time-window tests, with intra-subject splits and leave-one-subject-out inter-subject evaluation.For inter-subject evaluation, one target calibration trial per class estimates class-wise LST matrices; remaining target trials are used for testing.Source: B. Preprocessing and Experimental… · p. 5

C. Compared Approaches

The comparisons cover representative template-based and deep-learning decoders under shared filter-bank input. Comparing KDHNet with SSVEPformer isolates the contribution of the TD-RCA front-end because both use the same decoder architecture.

C. Compared Approaches

  • All approaches received the same filter-bank input with three sub-bands, and template-based methods used specified weights to combine sub-band scores.Source: C. Compared Approaches · p. 6
  • The comparison includes FBCCA, TRCA, TDCA, EEGNet, CCNN, FBtCNN, SSVEPNet, and SSVEPformer.The methods span template-based spatial or correlation approaches and neural decoders.Source: C. Compared Approaches · p. 6
  • KDHNet and SSVEPformer share an architecture, so their comparison reflects the contribution of KDHNet’s TD-RCA front-end.Source: C. Compared Approaches · p. 6

D. Implementation Details

KDHNet and its baselines were trained under specified optimization settings, and performance was assessed using accuracy and ITR with subject-wise paired significance tests.

D. Implementation Details

  • KDHNet was trained for 100 epochs with batch size 30, SGD at 10^-3, momentum 0.9, weight decay 10^-4, and cosine-annealing decay.Each baseline used its recommended training configuration; SSVEPformer used KDHNet's optimizer, learning rate, and epoch count.Source: D. Implementation Details · p. 6

E. Evaluation Metrics and Statistical Analysis

  • Accuracy was the proportion of correct test trials, while ITR was measured in bits/min using stimulus-class count, accuracy, and decision duration.Decision duration equaled the decoding window length.Source: E. Evaluation Metrics and Statistical… · p. 6
  • Subject-wise accuracies were compared with paired, two-sided Wilcoxon signed-rank tests, with Holm-Bonferroni adjustment over eight baselines per dataset and protocol.With 10 pairs on Dataset I, the corrected minimum p-value was 1.56 × 10^-2, so even an all-subject win receives only one asterisk.Source: E. Evaluation Metrics and Statistical… · p. 6

IV. RESULTS

Across intra-subject settings, KDHNet led in nearly all window and calibration-ratio comparisons; it ranked first or second across all three inter-subject datasets. Its per-subject gains varied by dataset and baseline accuracy.

A. Intra-Subject Limited-Calibration Results; B. Effect of Training Ratio

  • KDHNet achieved the highest mean accuracy and ITR in 14 of 15 window-dataset settings and all ten calibration-ratio settings.Fig. 2 summarizes accuracy and ITR across windows; Fig. 3 shows them across training ratios.Source: A. Intra-Subject Limited-Calibration… · p. 6, Figure 2 · p. 7, B. Effect of Training Ratio · p. 7
  • KDHNet had the highest mean accuracy and ITR across all ten ratio–dataset settings; versus the strongest template-based baseline, its margins at the smallest training ratio were 1.86%, 2.14%, and 4.03% on Datasets I–III.At the largest training ratio, those margins decreased to 0.69%, 0.60%, and 2.74% on Datasets I, II, and III, respectively.Source: B. Effect of Training Ratio · p. 7

C. Per-Subject Improvement

  • At the 1.0 s setting, KDHNet outperformed the strongest template-based baseline for 7 of 10, 20 of 35, and 50 of 70 subjects on Datasets I, II, and III, respectively.On Datasets I and II, gains were concentrated in the lowest baseline-accuracy quartile; on Dataset III, gains were more evenly distributed.Source: C. Per-Subject Improvement · p. 7, Figure 4 · p. 8

D. Inter-Subject Results

  • On Dataset II, KDHNet exceeded SSVEPformer by 3.28% and TRCA by 17.00% in inter-subject accuracy.The reported template-based results on this 40-class dataset were lower than CCNN's 61.83% and SSVEPformer's 71.16%.Source: D. Inter-Subject Results · p. 7
  • With one target trial per class, KDHNet achieved the highest accuracy and ITR on Datasets I and II; on Dataset III, TRCA led with 46.29% accuracy versus KDHNet’s 43.31%.The 2.98% difference was not statistically significant; KDHNet had the best or second-best performance on all three datasets.Source: D. Inter-Subject Results · pp. 7–8

E. Statistical Significance

KDHNet was significantly better than deep baselines in nearly all tested comparisons, while its template-based comparisons were often significant or statistically comparable. Ablations favor a frozen TDCA stage and show front-end gains across decoder architectures.

E. Statistical Significance

  • KDHNet significantly outperformed deep baselines in 29 of 30 comparisons and was significantly better than or statistically comparable to template-based algorithms in all settings.It significantly exceeded FBCCA in five of six settings and TDCA in three of six; against TRCA, significance occurred in two settings.Source: E. Statistical Significance · p. 8, Table V · p. 9

A. Component-Wise Ablation

  • The default configuration achieved the highest three-dataset mean accuracy (86.02%) and ITR (219.35 bits/min), with TDCA analytical-frozen and TRCA and sub-band weighting analytical-trainable.Training TDCA from its analytical solution reduced mean accuracy to 41.96%, while random initialization reached 66.31%; the default was also more accurate than disabling TDCA (85.81%).Source: A. Component-Wise Ablation · p. 9, Table VI · p. 10
  • Freezing TDCA changed mean accuracy by only 0.21% relative to disabling it, while reducing subject-wise accuracy standard deviations on Datasets I and II versus random-trainable TDCA.The standard deviations were 7.92% and 13.10% with frozen TDCA, compared with 22.16% and 25.16% for random-trainable TDCA.Source: A. Component-Wise Ablation · p. 9

B. Replacing the Deep Decoder

  • The TD-RCA front-end significantly improved all four deep decoders on all three datasets, with gains ranging from 11.97% to 40.41%.With the front-end, SSVEPformer had the highest accuracy on all three datasets, and the front-end improved every evaluated decoder.Source: B. Replacing the Deep Decoder · p. 10, Figure 5 · p. 10

VI. INTERPRETABILITY ANALYSIS

KDHNet’s analytical front-end yields class-separable features, while its TDCA filter performs better when kept fixed than when trained end-to-end. Across the reported evaluations, KDHNet leads most intra-subject settings, with an inter-subject exception on Dataset III.

A. Spatial-Filter Structure

  • The fixed analytical TDCA filter retained a focal medial occipito-parietal pattern, while end-to-end-trained filters became diffuse and inconsistent across subjects.On Dataset II, mean accuracy was 91.83% with the closed-form filter, 37.03% after training from that solution, and 75.86% after training from random initialization.Source: A. Spatial-Filter Structure · p. 10, Figure 6 · p. 11

B. Feature Separability

  • Across Dataset I subjects, five-nearest-neighbor accuracy rose from 53.5% on raw signals to 91.6% on analytical front-end features, without decoder training.The features formed compact class-consistent clusters compared with the overlapping raw-signal trials.Source: B. Feature Separability · p. 11, Figure 7 · p. 11

VII. DISCUSSION

  • At the smallest training ratio, KDHNet’s margin over the strongest template-based baseline was 1.86%, 2.14%, and 4.03% on Datasets I, II, and III; inter-subject Dataset III was an exception.There, TRCA exceeded KDHNet by 2.98%, a difference that was not significant; the authors relate this to usable templates from one calibration trial per class and heterogeneous, low-SNR BETA recordings.Source: §VII · p. 11
  • The analytical front-end is best viewed as a structural prior: training TDCA removes its focal pattern and substantially reduces accuracy, while analytical stages alone yield largely class-separable features.Removing TDCA had little effect on accuracy, according to the ablation and interpretability analyses.Source: §VII · p. 11
  • KDHNet uses a hand-crafted filter-bank partition: it learns sub-band weights, but not the sub-band boundaries.The authors identify jointly optimized passbands as a direction for future work.Source: §VII · p. 11

VIII. CONCLUSION

  • KDHNet achieved the highest mean accuracy and ITR in 14 of 15 intra-subject window settings and all ten calibration-ratio settings, and ranked best on Datasets I and II and second-best on Dataset III inter-subject.The inter-subject comparison used one calibration trial per class and LST alignment.Source: §VIII · p. 11
  • The conclusion reports that TDCA was effective only with its analytical solution fixed, whereas TRCA and sub-band weighting were robust to initialization choice.Replacing SSVEPformer with EEGNet, CCNN, or FBtCNN improved each evaluated decoder on all three datasets.Source: §VIII · p. 11

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