2.1 Dataset

This study leverages two public EEG-MI datasets with distinct cohorts and acquisition setups. We analyze only EEG signals (ignoring auxiliary modalities), convert all recordings to a common montage, and harmonize sampling and preprocessing across datasets.

• Healthy dataset [2]. EEG Motor Movement/Imagery: 109 volunteers, 64-channel 10–10 montage, original sampling 160 Hz (EDF+). Each subject performed multiple MI runs comprising left/right hand, both fists, and feet tasks (executed and imagined). We used only MI runs (baselines discarded).
• Orthopedic-impairment dataset [1]. Multimodal MI in patients with orthopedic impairment: 7 participants, EEG montage with 18 channels, original sampling 500 Hz, MI trials recorded in multiple sessions. We use only the EEG stream for analysis.

Subject selection and class definition: To achieve parity in participant counts, we selected 7 subjects from the healthy dataset to match the impaired cohort; where age/sex metadata were available, we preferentially chose healthy subjects to approximate the clinical cohort’s demographics. We define a binary label for healthy (0) vs. orthopedic impairment (1). All per-window labels inherit the subject’s group label (task identity is used only as an auxiliary input where stated elsewhere).

Common montage: According to the channel-description files, both datasets share an identical subset of 11 electrodes: C3, Cz, C4, FC3, FCz, FC4, CP3, CPz, CP4, F3, F4. All subsequent analyses are confined to this montage; no interpolation or channel dropping is required.

Signal harmonization: All recordings are re-referenced as in their source datasets, notch-filtered, and band-pass filtered from 8–50 Hz using a zero-phase, fourth-order Butterworth design (filtfilt). Signals are then resampled to f_s = 125 Hz with zero-phase FIR decimation so that each 1 s epoch contains exactly 125 samples. To ensure consistency across datasets, only channels in the common montage are retained before resampling.

Segmentation and event handling: Following filtering, continuous recordings are segmented into non-overlapping 1 s windows (125 samples). For the healthy dataset we exclude baseline (eyes-open/closed) runs and retain only MI runs; for the impaired dataset we retain all MI trials. Trial/event markers are used solely to isolate MI segments; we do not stratify by MI task for the main binary classification unless otherwise stated.

Quality control and exclusion: We remove windows with missing event annotations and windows with non-physiological amplitudes (V after re-referencing). Remaining windows are z-scored per recording (mean and standard deviation computed from training data only to avoid leakage).

Balancing windows across groups: After selecting subjects, residual imbalances in the number of MI windows across groups and subjects are addressed in two steps: (i) per-subject stratified undersampling to equalize window counts across subjects within each group; and (ii) if a residual class imbalance remains, we apply inverse-frequency weights in the classification loss,

where N is the total number of training windows and N_c is the number from class c. In practice, after step (i) the classes are near-balanced and weights remain close to 1; we do not use extreme weights (the earlier placeholder is removed as a typographical artifact).

The final analysis set contains an equal number of participants per group (7 healthy, 7 impaired), a standardized 11-channel montage, and uniformly preprocessed EEG at 125 Hz segmented into 1 s windows. Dataset-specific acquisition details and accession information are given in [1,2]; our evaluation protocol (stratified 80/20 split and metrics) is described later.

Covariates sensitivity: EEG differs between individuals for reasons that are not related to the disease status, including age- and sex-related effects on rhythm power, peak frequencies, and long-range dependence. The two public datasets used here were curated independently and provide incomplete demographic metadata; consequently, a formal covariate-controlled analysis (e.g., regression or matched subsampling) cannot be reported without introducing unverifiable assumptions or discarding large portions of data.

Several design choices in the present study reduce—but do not eliminate—covariate influence: (i) a fixed stratified 80/20 split (subject proportions preserved) maintains class balance but does not enforce subject exclusivity; (ii) per-recording z-scoring removes absolute amplitude differences that can correlate with age/sex; (iii) a fixed 11-channel common montage avoids spatial-coverage disparities; and (iv) participant counts are balanced across cohorts. These steps improve comparability at the signal and sampling levels, yet unmeasured covariates (age, sex, medication, sleep, cap fit) may still contribute residual variance. Reported group differences should therefore be interpreted as condition-linked patterns within the recorded cohorts, not as causal effects independent of demographics. A covariate-adjusted evaluation requires complete metadata and is outside the scope of the current re-analysis of public datasets.

2.2 Preprocessing and enhancements

2.3 Feature extraction

All features are computed per 1 s window and per channel on z-scored data (mean and standard deviation estimated on the training split only to avoid leakage). Unless stated otherwise, logarithms are natural and constants are fixed across all experiments.

Short-Time Fourier Transform (STFT) band power: Each 1 s window has N = 125 samples at f_s = 125 Hz. We compute the magnitude STFT with a Hann window of length N_w = 64 samples and 75% overlap (hop h = 16), yielding frames per window. The DFT size is (zero-padding as needed). Let X(k,m) be the STFT at bin k and frame m, with bin frequency . Define band index sets

Log-power per band uses a stabilizer :

Hurst exponent (, rescaled range): For scales (50% overlap), we compute the classical rescaled-range statistic. Given a demeaned segment , form the cumulative deviate series (); the range is and the standard deviation . The segment statistic is . Averaging over the segments for each s, we fit

via OLS; the shortest scale is omitted when fewer than two cycles of the dominant rhythm fall within s.

Detrended Fluctuation Analysis (DFA): For each 1 s window, build the integrated profile , partition into non-overlapping segments of length , fit and subtract a least-squares linear trend Y_s(k) within each segment, then compute

The DFA exponent is the slope of vs. (OLS on valid scales).

KolmEn (permutation/ordinal entropy; KS proxy): We estimate complexity via permutation (ordinal) entropy as a finite-sample proxy for the KS entropy rate. Using embedding dimension m = 3 and delay , let be the ordinal patterns and the empirical frequency of pattern within the 1 s window. The KolmEn feature is

computed without normalization.

Correlation dimension (CD): With time-delay embedding and Theiler window to exclude temporal neighbours, we compute the Grassberger–Procaccia correlation sum

where are embedded vectors. Radii r are log-spaced over , with and set to the 5th and 95th percentiles of pairwise distances. The CD is the slope of vs. over the largest contiguous scaling region selected by maximal R² (plateau of local slopes).

Largest Lyapunov exponent (LLE): Using Rosenstein’s method with the same embedding and Theiler window W, for each state choose its nearest neighbor with . Track separations and average the log-divergence

The LLE is the slope of over a short linear regime ; we use , samples at  Hz, chosen to maximize linear fit R² while avoiding saturation.

Feature vector: Per channel, we concatenate

(8 scalars). Stacking across the 11-channel montage yields features per 1 s window. All logs use the natural base; features are computed on the z-scored signals using training-set statistics.

2.4 Feature–selection rationale

We retain six descriptors because they (i) capture complementary neurophysiological phenomena across spectral, statistical, and nonlinear dynamics and (ii) are fast enough for real-time use on 1 s windows ( ms per channel in our setup). Long-range dependency measures—the Hurst exponent and detrended-fluctuation analysis (DFA)—quantify temporal persistence modulated by motor preparation [69]. KolmEn (permutation/ordinal entropy; Eq 2.3) and the largest Lyapunov exponent capture irregularity and local instability, both implicated in pathological sensorimotor reorganization [70]. Correlation dimension characterizes the fractal geometry of the reconstructed EEG attractor, providing a compact index of dynamical complexity that varies with cortical pathology during motor tasks. Finally, the Short-Time Fourier Transform (STFT) summarizes power in the μ (8–13 Hz), β (13–30 Hz), and task-relevant γ (30–50 Hz) rhythms; under low-latency constraints it offers a robust time–frequency portrait for MI decoding [67,68,71].

Together, these six descriptors yield 8 scalars per channel (3 STFT band-powers Hurst DFA KolmEn Correlation dimension Lyapunov exponent), balancing interpretability and computational tractability for on-device BCI deployment. Exact parameter choices are fixed a priori and reported in Table 1 and Sect 2.3.

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Table 1. Per-channel features and dimensionalities (per 1 s window).

https://doi.org/10.1371/journal.pone.0335364.t001

2.5 Evaluation protocol

Splits and leakage control: All results are reported on a stratified 80/20 train–test split at the window level (stratified by class; subject proportions preserved). This preserves class balance but does not enforce subject exclusivity; we therefore interpret generalization as within-cohort and note that a subject-exclusive split would be more conservative.

Metrics: We report accuracy, macro–F1, precision, and recall. Where two models are compared, we report their scores on the identical test split.

Baseline fairness: All baselines are retrained under the identical preprocessing pipeline (11-channel common montage, 1 s non-overlapping windows, per-recording z-scoring) and evaluated on the same stratified 80/20 split. CNN baselines use raw EEG windows; the CVAE uses the feature vector from Sect 2.3. Hyperparameter grids and best settings are listed in Table 2.

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Table 2. Baseline models and hyperparameters under the harmonised pipeline.

https://doi.org/10.1371/journal.pone.0335364.t002

2.6 Additional experiments

We systematically evaluated the performance of our CVAE model in combination with various feature extraction techniques mentioned previously.

However, upon closer examination, we observe nuanced variations in the loss values across different feature extraction techniques and VAE settings. Particularly intriguing is the performance of the model with the Hurst feature extraction in a β-VAE setting. This configuration exhibited slightly lower losses compared to other feature extraction methods. This is also confirmed by other metrics such as Precision, Recall and F1-Score.

The Hurst feature extraction method captures the long-range dependence structure inherent in EEG signals, providing rich information about their fractal nature. When combined with the β-VAE framework, which encourages disentangled and interpretable latent representations, the Hurst feature appears to enhance the model’s ability to learn discriminative features while minimizing reconstruction and classification losses.

To further validate the robustness of our findings and explore the model’s performance across different feature domains, we conducted a final experiment utilizing features derived from STFT analysis.

For the STFT analysis, we specifically focused on three frequency bands of particular relevance to motor tasks:

1. Alpha Band (8-13 Hz): This band is often associated with relaxed wakefulness and is known to be modulated during movement preparation and execution.
2. Beta Band (13-30 Hz): Beta activity is linked to active movement, motor control, and sensorimotor integration.
3. Gamma Band (30-50 Hz): Gamma oscillations are thought to play a role in higher-order cognitive processes and complex motor coordination.

We retrained our CVAE model on the STFT features computed, using the same pre-processing and enhancement techniques applied to the other feature sets. This experiment provides further evidence of the model’s ability to generalize across diverse feature representations and reinforces the consistency of our findings across different analysis approaches. The results of this STFT-based analysis, including model performance metrics and comparative evaluations with other feature extraction pipelines, are detailed later in the results section.

2.7 Motor task and channel filtering

In addition to the main 11-channel analysis, we performed a compact ablation study that isolates the sensorimotor hotspot C3 and retains only left- and right-hand motor-imagery epochs. After the usual pre-processing steps, the resulting class distribution was balanced with a k-nearest–neighbor synthetic minority over-sampling (KNN-SMOTE via imbalanced-learn). The same CVAE backbone, with a reduced latent size of 8, attained 93.0 % accuracy while maintaining a low reconstruction error (MSE < 0.03). The confusion matrices confirm high true-positive and true-negative rates, indicating that even a single well-placed electrode captures sufficient discriminatory information. However, we stress that all the headline results reported in Sects 4 and 5 rely on the full 11-channel montage and inverse-frequency class weighting; the single-channel study is included only to illustrate the robustness of the model under extreme reduction in dimensionality.

3.1 Conditional variational autoencoder

We model the per-window EEG feature vector (, see Sect 2.3) conditioned on the observed health label . The conditional generative model is

(1)

with an amortized variational posterior

(2)

Decoder conditioning is implemented by concatenating y to z, i.e., .

3.1.1 Conditional ELBO and training objective.

Maximizing admits the conditional ELBO

(3)

Because x are z-scored continuous features, we use a homoscedastic Gaussian likelihood

(4)

i.e., the mean-squared error (MSE) per feature dimension.

The decoder reconstructs the 88-dimensional feature vector rather than raw EEG time series. All reconstruction losses are computed as feature-wise MSE (Eq 4). Feature-domain reconstruction quality is directly relevant to classification because (i) the classifier operates on the latent z inferred from these features, and (ii) lower feature-space reconstruction error typically coincides with more class-separable latent embeddings under the conditional objective (Eq 5).

In addition, we learn an auxiliary discriminative head trained with cross-entropy. The final objective is the negative conditional ELBO with a β-weight on the divergence term and a classification regularizer:

(5)

where is either KL or MMD (see below), , , and unless otherwise stated.

Closed-form KL for diagonal Gaussians: For and ,

(6)

Parameterizing yields convenient gradients:

(7)

Maximum Mean Discrepancy (MMD): When with a Gaussian kernel , we use the unbiased finite-sample estimator on a minibatch and :

(8)

with bandwidth set by the median heuristic. (A multi-kernel sum is also supported but not used in the main results.)

3.1.2 Architecture and parameterization.

We implement conditional distributions with MLPs and dual concatenation of y.

Inputs (feature space): with (11 channels 8 features/channel).

Encoder . We form and apply two linear layers with ReLU:

followed by linear heads to with . Sampling uses the reparameterization trick

(9)

Decoder : We concatenate again in latent space: , then apply

producing in (4).

Auxiliary classifier : A linear head on z outputs logits in :

Shapes:

3.1.3 Concatenation strategy and generation.

We follow a dual concatenation protocol (cf. [77]): for inference and for generation. At test time, label-controlled synthesis uses

(10)

3.2 Back-propagation and optimization

We minimize (5) with Adam (, , ), batch size 128, for 50 epochs. Gradients flow through the stochastic path via (9). With KL, the total gradient decomposes as

(11)

When using MMD, in (11) is replaced by the gradient of (8), which has closed-form derivatives through the kernel.

(i) We do not use KL-annealing; is fixed (see Tables 3 and 4). (ii) The reconstruction term is mean MSE per feature to harmonize scale with the divergence and classification terms. (iii) The prior is class-agnostic in all main results; a class-conditional prior is possible but not used here.

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Table 3. CVAE architecture and training hyperparameters.

https://doi.org/10.1371/journal.pone.0335364.t003

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Table 4. End-to-end pipeline summary (data, preprocessing, features, and model).

https://doi.org/10.1371/journal.pone.0335364.t004

5.1 Overview of results

The results of our study strongly demonstrate the effectiveness of the CVAE in accurately classifying EEG signals for distinguishing between healthy and unhealthy brain activity. The CVAE model, when integrated with various advanced feature extraction techniques (results in Table 7), consistently exhibited high classification accuracy. Notably, the optimal performance was achieved when the Hurst Exponent was employed as the feature extraction method in conjunction with the β-VAE configuration, yielding a classification accuracy of 93.1% on the test set. These findings underscore the potential of the CVAE framework to enhance the accuracy of EEG-based diagnostic systems.

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Table 7. Precision, recall and F1-score obtained on the test set.

https://doi.org/10.1371/journal.pone.0335364.t007

5.2 Impact of feature extraction techniques

The choice of feature extraction method significantly influenced the performance of the CVAE model, as evidenced by the comparative analysis presented in Tables 5 and 6. Among the methods evaluated, the Hurst Exponent emerged as the most informative feature for EEG classification. This exponent, which captures the long-range dependencies and fractal characteristics of EEG signals, provided the most robust input for the CVAE, resulting in the highest observed classification accuracy.

The superior performance of the Hurst Exponent can be attributed to its ability to effectively characterize the temporal structure of EEG signals, which is critical in distinguishing between healthy and pathological states. In contrast, other feature extraction methods such as DFA and CD, while still valuable, did not achieve the same level of accuracy, likely due to their focus on different aspects of EEG signal dynamics. These findings suggest that the Hurst Exponent may capture more relevant features for the specific task of binary health classification in EEG data.

Previous CVAE applications to EEG fall into two categories: (i) unconditioned VAEs that model raw time series for artifact removal [78], and (ii) task-conditioned CVAEs that rely exclusively on deep convolutional encoders without explicit feature engineering [79]. To our knowledge, the present work is the first to (a) inject a binary health label directly into both the encoder input and the latent code, (b) operate on a compact, physiologically motivated feature stack (Hurst, DFA, KS-H entropy, Lyapunov exponent, STFT), and (c) demonstrate that this hybrid, hand-crafted–plus–generative approach yields state-of-the-art accuracy on motor-imagery data while retaining interpretability of individual feature contributions.

5.3 Efficacy of the CVAE architecture

The architecture of CVAE, as illustrated in Figs 1, 2, and 3, played a pivotal role in the success of the model. The inclusion of health condition labels directly into the latent space via concatenation allowed the CVAE to learn more discriminative features, which was reflected in the model’s high performance across various feature extraction techniques. This innovative approach of embedding condition-specific information into both the input and latent representation enabled the CVAE to effectively differentiate between healthy and unhealthy EEG signals.

The training curves depicted in Fig 4 demonstrate the model’s rapid convergence and stable training process, with a clear reduction in loss and consistent improvement in accuracy over approximately 50 epochs. The minimal difference between training and testing losses indicates that the model generalizes well to unseen data, thereby reducing the risk of overfitting.

5.4 Statistical analysis

Because all methods are evaluated on the same test set, we quantify the robustness of the observed performance gap using uncertainty estimates and a conservative significance test. We report 95% Wilson confidence intervals for accuracy (test size windows) and, where available, macro–F1. As paired per-window predictions are not retained in the manuscript, we provide a conservative two-proportion z-test (unpaired, identical n) comparing each baseline to the CVAE; this test understates the power relative to a paired analysis (e.g., McNemar) and thus yields a cautious inference. As summarized in Table 8, the CVAE’s improvements remain highly significant under this conservative analysis.

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Table 8. Uncertainty and significance on the identical test set ( windows).

Accuracy shown with 95% Wilson CIs. Two-proportion z-test compares each baseline to the CVAE (two-sided).

https://doi.org/10.1371/journal.pone.0335364.t008

5.5 Reconstruction capabilities and signal generation

The CVAE’s ability to accurately reconstruct EEG signals, as demonstrated in Figs 5 and 6, is indicative of its potential not only for classification but also for generating realistic synthetic EEG data. The reconstructed signals closely match the true EEG signals, and the generated signals from Gaussian noise exhibit similar characteristics to unhealthy signals. This suggests that the CVAE has effectively learned a meaningful latent representation of the EEG data, which could be leveraged for data augmentation or for simulating EEG signals in the development of advanced BCI systems.

5.6 Analysis of confusion matrices

The confusion matrices shown in Fig 7 for both the training and test sets provide further insights into the robustness of the CVAE model. The high number of true positives and true negatives across both datasets underscores the model’s effectiveness in accurately classifying EEG signals. The low incidence of false positives and false negatives is particularly noteworthy, as it highlights the model’s reliability in real-world applications where mis-classification could have serious implications.

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Fig 7. Illustrative 1 s time-domain visualization over 11 channels based on feature-space reconstructions (blue) for an unhealthy segment (green) and a generated sample from (orange).

The training target is the 88-D feature vector; time-domain plots are for qualitative context.

https://doi.org/10.1371/journal.pone.0335364.g007

However, despite the high overall accuracy, the presence of a small number of misclassifications suggests that there is still room for improvement. These errors could arise from the inherent variability in the EEG signals or from subtle differences that are not fully captured by current feature extraction methods. Future work could explore the integration of more sophisticated or hybrid feature extraction techniques to further enhance the accuracy of the model.

5.7 Comparative analysis

When compared to existing state-of-the-art approaches, the CVAE model demonstrates competitive performance, particularly in the context of EEG signal classification. The model’s integration of condition-specific information into the latent space is a key innovation that enhances its ability to learn and generalize from EEG data. This positions the CVAE as a valuable tool for advancing the field of automated EEG analysis.

However, it is important to recognize that further optimization of the model is possible. For instance, investigating more complex architectures, such as those utilizing attention mechanisms or graph-based neural networks, could potentially offer further improvements in both classification accuracy and model interpretability. Such advancements would not only enhance the CVAE’s performance but also broaden its applicability to more complex and varied EEG datasets.

Because the present study prioritizes generative utility, we nonetheless retrained the canonical discriminative baselines on the harmonized data set using exactly the same pre-processing pipeline (11 common electrodes, 1 s non-overlapping epochs, per-recording z scoring) and the stratified 80-20 train–test split adopted for CVAE. As shown in Table 9, the retraining yielded accuracies of 85.4% for EEGNet [74], 86.1% for DeepConvNet [74], 82.6% for the Riemannian geometry SVM [76], and 87.0% for the TCN transformer [75]. Under the identical protocol, the class-conditioned CVAE attains 93.1%, exceeding the strongest convolutional baseline by roughly 6% and the remaining methods by 7–10%. This controlled comparison confirms that embedding the health label in both the encoder input and the latent representation—coupled with a compact, physiologically grounded feature stack—can outperform deeper, parameter- intensive architectures while simultaneously providing label-conditioned generative capability.

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Table 9. Retrained baselines under the harmonized pipeline (identical preprocessing; stratified 80/20 split).

https://doi.org/10.1371/journal.pone.0335364.t009

The class-conditioned CVAE not only eliminates the performance gap with state-of-the-art, end-to-end CNN architectures but in fact surpasses their best re-trained scores on the identical dataset—despite relying on a markedly lighter network and an explicitly interpretable, hand-crafted feature stack. These results substantiate two central claims: (i) supplying the health label to both the encoder input and the latent code decisively improves class separability, and (ii) a hybrid hand-crafted–feature + generative paradigm can equal or out-perform substantially deeper, parameter-heavy discriminative pipelines.

Accordingly, the proposed CVAE establishes a rigorous baseline for diagnosis-oriented EEG analysis while simultaneously offering the unique advantage of label-conditioned signal synthesis for data augmentation, uncertainty estimation, and latent-space probing.

Our principal evaluation adopts a stratified window-level split that preserves class balance and subject proportions but does not enforce subject exclusivity. While standard and informative for within-cohort generalization, such splits can be optimistic if subject-specific structure is shared across sets. For deployment-oriented scenarios, a subject-independent protocol—e.g., leave-one-subject-out (LOSO)—offers a stricter and more conservative bound on across-subject generalization and is a natural extension of the present work.