Equation-level parameterized fusion reformulation for multimodal epileptic seizure detection using interaction control and data-quality screening

1 Introduction

Epilepsy is a primary neurological disorder affecting over 50 million people globally. It is considered that abnormal electrical discharges in the brain cause recurrent seizures. Primary and accurate seizure detection is vital for active treatment and patient safety. However, traditional EEG-based diagnostic systems rely heavily on expert interpretation, which is subjective and time-consuming (WHO, 2024). This restraint has driven the adoption of automated, data-driven approaches using machine learning (ML) and deep learning (DL) techniques for well-organized, reliable seizure detection. Traditional ML and DL models (see Figure 1 for DQA score visualization) have attained remarkable success in analysing biomedical signals; yet, most of these models rely on a single signal modality, such as EEG. Reliance on a single modality often leads to reduced accuracy and poor generalization across patients, due to noise and motion artifacts. Recent studies show that combining complementary biosignals such as ECG, EMG, and ACC provides a more holistic seizure profile by capturing neural, muscular, and motion dynamics (Zhou et al., 2023; Khan et al., 2022).

This multimodal method improves robustness but presents new challenges, including signal synchronization, data quality evaluation, and actual feature fusion. However, as multimodal studies become increasingly significant, many existing works overlook essential properties of data quality and cross-modal relations. Moreover, most strategies assume equal utility across modalities, regardless of their distinctive characteristics and relatedness.

To bridge the gap, in this paper, we introduce a new multimodal biosignal fusion framework for epilepsy seizure detection that combines four (4) types of modalities: EEG, ECG, EMG and ACC. There are several novelties in the proposed system:

• A DQA equation to measure the completeness, consistency, and validity of each modality quantitatively before fusion.
• A Novel Cosine Similarity (NCS) and Pearson correlation.
• 12 ML or DL models were modified with two additional parameters: ρ (fusion exponent) and δ (interaction weight), to enable adaptive fusion and inter-modality contact.
• The dataset employed in this study is a collection of 120 clinically diagnosed patients with epilepsy; it features 60 recordings from Tamale Teaching Hospital (TTH), and the remaining are publicly available recordings. The data were sampled at 512 Hz with a 2-s window (50% overlap) to generate about 1,024,000 data points (see Table 1 for dataset details).

TABLE 1. Dataset features.

Clarification of “equation-level reformulation.” In this manuscript, “equation-level reformulation” does not claim a new theoretical derivation of the learning algorithms. Instead, it denotes a model-agnostic re-parameterization of the input fusion representation supplied to each classifier, where four interpretable parameters ρ , δ , λ , η. Regulate modality contribution, nonlinear cross-modal interaction strength, numerical stabilization, and synergy amplification within a unified fusion form. The learning rules of the baseline algorithms remain unchanged; the proposed contribution is a consistent mathematical fusion/interface layer that can be injected into both classic and deep learning pipelines.

2 Related work (literature review)

2.1 Unimodal (EEG-only) seizure detection

Although there have been great demonstrations of EEG-only seizure detection in controlled settings, such unimodal systems are often less robust to real-world variability (e.g., motion artifacts, electrode interference, and inter-subject heterogeneity).

Research Gap: Current unimodal EEG-based models are not strong enough and generalize poorly, unable to leverage complementary extracortical activity. Recent multimodal learning strategies emphasize adaptive weighting and cross-modal interaction modeling (Chen et al., 2022).

2.2 Multimodal biosignal combination (EEG + ECG/EMG/ACC)

Weighted multimodal fusion approaches have shown improved robustness in biomedical signal integration (Li and Zhang, 2021). The ECG (autonomic actions), EMG (motor activity) and ACC (motion) are added to the EEG for a more comprehensive picture of seizures (Wang et al., 2024; Bai et al., 2023). Current methods adopt early fusion (feature concatenation), mid-level fusion (shared latent space), or late fusion (score-level voting). However, a large number of them have two remarks: (i) equal channel significance is assumed and a fixed fusion rule is designed in them, respectively, which makes them sensitive to noisy modalities and misaligned sensors.

Identified Gap: Studies on modality-adaptive weighting also do not model inter-modality temporal interactions to handle subject- and seizure-dependent variability (Chen et al., 2025).

2.3 Data quality processing: check and alignment

Signal quality control (QC) is commonly implemented as filtering, artifact rejection and completeness checks (Kang et al., 2023). Apart from simple synchronization, hardly any formal alignment across modalities and sources is established. Several studies were found on the use of correlation-based testing. However, there do not appear to be any works that describe a direct equation for Data Quality Assurance (DQA) that addresses all the aspects of completeness, consistency and validity.

Identified Gap: There is a lack of definition for DQA and a unified similarity index to measure the quality and alignment of multimodal data across diverse acquisition sources (Liu and Zhou, 2024).

2.4 Feature engineering and representation

Deep learning aims at automatically learning good feature representations from the gradient-descent process and representations are learned, thus releasing human experts from manually designing features.

“Is feature engineering dead in the era of deep learning?” as Jitendra Malik put it. Conventional methods are dependent on spectral-statistical parameters, including entropy, variance and PSD (Ali et al., 2023). Deep learning models evade the extraction of manual statistics by learning meaningful hierarchical representations using CNNs, TCNs, RNNs, and Transformer architectures (Rahman and Chen, 2022). However, they can easily overfit to small, heterogeneous datasets when modality noise or failures are present.

Research Gap: Existing work often abandonments modality-aware control in representation learning, leading to lesser performance when domain shifts or missing modalities occur (Singh et al., 2025).

2.5 Model specific extension for multimodal data

Adapted SVM, RF, XGBoost, CNN, LSTM, GRU, TCN and Transformer adaptations have also been suggested for multimodal applications (Zhou et al., 2024; Kumar et al., 2023), but generally concatenate or average inputs. A few of them add explicit recent seizure detection studies emphasize cross-site validation and generalization testing (Zhang et al., 2023) parameters (e.g., m to control the dominance of one modality or quadratic cross-modal terms, such as EEG-EMG coupling strength).

Research Gap: No single formulation has been able to naturally generalize across traditional and deep architectures to balance modality-wise dominance and inter-modality coupling dynamically (Hassan et al., 2024).

2.6 Testing on unseen/external cohorts

The majority of previous studies have validated models only on cross-validated single-site datasets (Wang et al., 2024). Limited patient- or hospital-wide performance validation can lead to data leakage and inflated performance metrics.

Research Gap: The lack of well-defined non-leakage rules, including fixed splits with patient-wise separation and testing on external data, to guarantee true generalization (Yao et al., 2024).

3 Methodology

3.1 Study overview

We develop a unified multimodal framework for epileptic seizure detection that integrates four modalities, EEG, ECG, EMG, and ACC, into a mathematically principled fused representation. A hierarchical evaluation strategy (single → pairwise → tri-modal → complete fusion) is used to quantify incremental information gain at each level.

3.2 Dataset and signal acquisition

The dataset contains 120 patients, combining recordings from Tamale Teaching Hospital with publicly available repositories. For each patient, synchronized EEG, ECG, EMG and ACC signals were acquired at 512 Hz. Signals were segmented into 2-s windows with 50% overlap, producing 1,024,000 windows in total. Each window was labelled as seizure or non-seizure according to clinical annotation.

3.3 Ethics approval and data governance

This study was approved in accordance with the Declaration of Helsinki, and ethics for human studies were followed in accordance with institutional regulations. All patients’ records were retrieved from Tamale Teaching Hospital, fully anonymized, and the authors had no access to any patient-identifiable information at any point in this study. Permission to use hospital data was obtained from the relevant institutional review board, and informed consent procedures were established with the providing institution. Publicly available datasets used in this study were downloaded in accordance with the relevant ethical standards. To protect data privacy and security, we recorded biosignals offline, stored them on secure systems, and used the data only for research. No interventions were performed on patients, and all analyses were retrospective, using previously collected data. The privacy of hospital and public data sets was ensured during preprocessing and patient-level splitting to avoid cross-source contamination or identity leakage.

3.4 Proof of patient-wise data splitting and leakage prevention

To ensure the validity of performance evaluation and eliminate all forms of data leakage, this study enforces a strict patient-wise data partitioning strategy combined with window-level independence constraints.

The mathematical formulation of the dataset partitioning is given in Equations 1–6. Let:

P = p 1 , p 2 , … , p 120 (1)

Denote the set of patients, and let

W p i = w i , 1 , w i , 2 , … , w i , n i (2)

Represent the complete set of segmented windows derived from the patient. p i.

The full dataset is therefore defined as:

D = ⋃ i = 1 120 W p i (3)

Patient-Wise Partitioning Constraint.

The dataset is partitioned into training, validation, and testing sets at the patient level, such that:

P t r a i n ∩ P v a l = P t r a i n ∩ P t e s t = P v a l ∩ P t e s t = ∅ (4)

Correspondingly:

D t r a i n = ⋃ p ∈ P t r a i n W p , D v a l = ⋃ p ∈ P v a l W p , D t e s t = ⋃ p ∈ P t e s t W p (5)

This results to:

D t r a i n ∩ D v a l ∩ D t e s t = ∅ (6)

Proportions: 70%/15%/15%

Validation used to tune ρ , δ , λ , η

Thus, no window from a given patient can appear in more than one subset, entirely preventing subject-identity leakage.

3.5 Window overlap independence guarantee

Although signal segmentation uses a 50% overlap strategy (see Equations 7, 8), overlap is applied only within each patient’s recording. Since patient-wise splitting is enforced before window segmentation, overlapping windows cannot cross dataset boundaries.

Formally, for any two windows w a , w b:

w a ∩ w b ≠ ∅ ⇒ p w a = p w b (7)

Because:

p w a ∈ P t r a i n ⇒ p w b ∉ P v a l , t e s t (8)

No temporal, spectral, or statistical information is shared across training, validation, or testing subsets.

3.6 Window overlap and statistical reporting

Although windows are generated with 50% overlap, overlap occurs only within a patient’s continuous recording, and patient-wise splitting is enforced before segmentation; therefore, no overlapping windows can cross train/validation/test boundaries.

To mitigate correlation effects within a patient, we report performance not only at the window level but also using patient-wise aggregation, where predictions are summarized per patient (mean F1-score and AUC across windows for each subject) and then averaged across patients. This yields a conservative estimate of generalization to unseen subjects.

3.7 Implication for model evaluation

This design ensures that:

• Models cannot memorize patient-specific patterns
• Performance reflects true generalization to unseen patients
• Near-saturation performance metrics arise from substantial multimodal rather than data leakage.

To verify that the near-saturation performance observed after equation-level fusion is not caused by data leakage, metric miscalculation, or unintended information sharing, several explicit sanity checks were conducted. First, a strict patient-wise partition was enforced prior to window segmentation, and we confirmed that there was no overlap in patient identifiers across the training, validation, and test sets. Second, all normalization parameters and data-quality screening operations (DQA and NCS) formal signal quality screening has recently been emphasized in biomedical AI pipelines to enhance reliability (Abebe et al., 2024) were fit exclusively to the training data and applied unchanged to the validation and test data, ensuring that no test-set statistics influenced model learning or selection.

Third, performance metrics were computed using only the held-out test set, and the AUC values were calculated from continuous model decision scores rather than thresholded class labels. Fourth, a label-randomization control experiment was performed, in which seizure labels were randomly permuted; under this condition, model performance collapsed to a near-chance level, confirming that the reported gains arise from learned multimodal structure rather than trivial correlations.

Finally, we conducted cross-source evaluation by training models on Tamale Teaching Hospital data and testing on public datasets (and vice versa). Although absolute performance decreased slightly under this more challenging setting, the proposed fusion framework consistently outperformed baseline models, supporting the claim that the observed high accuracy reflects genuine generalization rather than optimistic bias.

3.8 Data quality assurance (DQA)

The DQA formulation is defined in Equations 9–11. DQA Equation:

D Q I = α C + β S + γ V (9)

C: Completeness.

S: Consistency.

V: Validity (noise-to-signal).

Threshold: 0.85.

The Data Quality Assurance equation is then defined as:

D Q A m , s = α N v a l N exp + β ρ m s max ⁡ ρ m s + γ 1 − N o i s e m , s S i g n a l m , S δ m (10)

D Q A | T o t a l = 1 8 ∑ m = 1 4 ∑ s = 1 2 D Q A m , s (11)

Where:

D m , s Denote the dataset of modality, that is

m ∈ E E G , E C G , E M G , A C C

S ∈ T T H , P u b l i c Represent the source,

N exp = expected number of data points (1,024,000)

N v a l = number of valid points after preprocessing

ρ m s = pairwise correlation (signal alignment across modalities).

δ m = modality reliability factor (derived from noise and artifact removal efficiency).

α , β , λ = Tunable weighting parameters for completeness, consistency, and validity, respectively.

3.9 Justification of DQA form and threshold

We adopt a linear weighted combination for DQA because it provides an interpretable and controllable screening index in which completeness, consistency, and validity contribute additively to overall reliability. The weights (α, β, γ) are treated as tunable hyperparameters selected on the validation set to balance signal retention against noise rejection, while keeping the formulation simple enough to be reproducible and comparable across modalities. A threshold of DQA ≥ 0.85 is used as a conservative operating point that prioritizes high-quality windows for downstream fusion.

In addition, to demonstrate that DQA is not post hoc, we conducted a controlled comparison by training the same models with and without DQA filtering (i.e., retaining all windows versus retaining only windows satisfying DQA ≥ 0.85). The DQA-filtered pipeline consistently reduced misclassification and improved F1-score/AUC, confirming that DQA screening has a measurable influence on model behavior rather than serving as a descriptive statistic.

3.10 Robustness and motivation of DQA thresholds

By enforcing minimum Data Quality Assurance (DQA) requirements to ensure that multimodal fusion is conducted on meaningful, well-aligned data, this work controls the quality of the data involved. The thresholds are ad hoc in this sense, and there is a trade-off between data retention on the one hand and the fusion reliability of the default belief on the other.

3.11 Justification of DQA

Threshold (≥0.85) The DQA index is a combination of completeness, coherence, and signal validity that together measure the reliability of each biosignal window. A threshold of 0.85 was set to keep only windows with sufficiently low noise contamination, fewer missing segments, and stable inter-channel consistency. Values below this cutoff indicate windows that were dominated by motion artifacts, electrode disconnects, or sensor saturation, resulting in inefficient seizure analysis. Similar quality-control cutoffs have been used, implicitly or explicitly, in multimodal biomedical signal processing to balance robustness and dataset volume (Tan et al., 2025; Wang et al., 2024).

3.12 Robustness considerations

To evaluate this, we examined the stability of trends in model performance across thresholds within and around the neighbour range. Small fluctuations in the threshold values (DQA [0.80–0.90], NCS [0.82–0.90]) had little impact on performance, whereas lowering them significantly resulted in slightly worse quality due to the inclusion of noisy or unaligned windows. These observations indicate that the proposed fusion framework is stable under reasonable threshold perturbations and that the selected values represent a conservative operating point that prioritizes fusion reliability without excessive data exclusion.

3.13 Signal preprocessing and normalization

Preprocessing stages are illustrated in Figure 2. All retained windows were normalized using z-score normalization to ensure scale invariance across patients and modalities (Equation 12):

x ∼ t = x t − μ σ (12)

Where:

x t = raw signal amplitude

μ = channel-specific mean

σ = channel-specific standard deviation

Preprocessing specification (Data alignment workflow is shown in Figure 3).

Each modality was filtered using standard biomedical ranges to remove baseline drift and high-frequency noise while preserving seizure-related dynamics: EEG was band-pass filtered to 0.5–45 Hz; ECG to 0.5–40 Hz; EMG to 20–450 Hz; and ACC to 0.1–20 Hz. Artifact rejection was performed by removing saturated or clipped windows and excluding windows with abnormal amplitude excursions exceeding five standard deviations of the patient-specific baseline. Z-score normalization was applied within each patient and modality to standardize the scale without mixing subject identities, ensuring that cross-modal fusion reflects relative temporal structure rather than raw amplitude magnitude.

3.14 Feature extraction

Two categories of features were used: Traditional ML models

Required handcrafted features include (see Figure 4):

• Time-domain statistics (mean, RMS, zero-crossings)
• Frequency-domain features (band power, spectral entropy)
• Statistical descriptors (kurtosis, skewness)
• Alignment-based features derived from NCS

Consumed normalized raw sequences without handcrafted features, enabling automatic temporal pattern learning.

3.15 Model development

Twelve machine learning and deep learning models were used for a unified comparison.

Logistic Regression (LR) models probabilistic binary outcomes through maximum likelihood estimation (Hosmer et al., 2013). Support Vector Machines (SVM) are based on the structural risk minimization principle and maximum-margin hyperplanes (Cortes and Vapnik, 1995). The k-Nearest Neighbors (KNN) classifier follows the foundational nearest-neighbor principle introduced by Cover and Hart (1967). Decision Tree (DT), Random Forest (RF) extends bagging through randomized feature selection to improve ensemble diversity (Breiman, 2001), and XGBoost implements gradient boosting with regularization and system optimization for scalable tree learning (Chen and Guestrin, 2016), Convolutional Neural Network (CNN), Long Short-Term Memory (LSTM) networks mitigate vanishing gradients through gated memory cells (Hochreiter and Schmidhuber, 1997). Gated Recurrent Units (GRU) simplify recurrent gating mechanisms while maintaining temporal modeling capacity (Cho et al., 2014). Temporal Convolutional Networks (TCN) provide causal and dilated convolutions for long-range temporal modeling (Bai et al., 2018). Transformer architectures employ self-attention mechanisms for sequence modeling without recurrence (Vaswani et al., 2017). Transformer, and a hybrid CNN–LSTM.

All models were trained with the same pre-processing, segmentation and normalization to give a fair comparison. A patient-wise split (train–validation–test) was used during training to prevent data leakage across patients. The joint pipeline ensures that all models process an exact copy of the unified fused representations and allows a fair comparison of their relative and combined detection performance. Respectively, the baseline model was mathematically modified by presenting novel parameters. Interaction-aware fusion strategies have been shown to improve multimodal robustness (Amini and Farahani, 2023).

3.16 Sampling-rate formalism and window budget

The comparison in Figure 5 shows that, with a fixed total sample budget of 1,024,000 points, different sampling rates yield markedly different numbers of windows and recording durations when a 50% overlap strategy is applied. A sampling rate of 1,024 Hz yields fewer windows and a shorter recording duration, whereas lower rates, such as 250 Hz, generate more windows but require longer acquisition times. The 512 Hz sampling rate provides an effective balance between temporal resolution, window count, and recording duration, making it a practical and efficient choice for multimodal seizure detection.

3.17 Quadratic–interaction fusion model: reformulating 12 classifiers using new parameters

All twelve models in this study were reformulated (The fusion formulation is defined in Equations 13–20) using the fused multimodal feature representation x ˉ, defined as:

X 1 = X E E G , X 2 = X E C G , X 3 = X E M G , X 4 = X A C C (13)

X = X 1 , X 2 , X 3 , X 4 , K = 4 (14)

GLOBAL MEAN FUSION

Parameter–metric relationship is illustrated in Figure 6.

F P M = 1 K ∑ k = 1 K X k ρ 1 δ (15)

QUADRATIC CROSS-MODAL INTERACTION

ϕ δ X = ∑ i < j X i ⊙ X j δ (16)

RELIABILITY-WEIGHTED FUSION

F x = ∑ m < n x m ⊙ x n W x (17)

FINAL QUASI-QUADRATIC FUSION MODEL

x ¯ ρ , δ , λ , η = λ 1 − ρ F P M + ρ F x + η ϕ δ X (18)

THE SAME FUSED FEATURE IS USED FOR ALL 12 MODELS.

Example:

XGBoost as a Traditional Model is given as:

y ^ i = ∑ m = 1 M f x x ∼ ρ , δ , λ , η , i (19)

CNN as a Deep Learning Model is given as:

h l = σ W l * x ∼ ρ , δ , λ , η + b l (20)

All fusion coefficients and scaling terms in the model reformulations correspond to the parameters defined, ensuring consistency across traditional and deep learning architectures.

Four parameters govern the proposed fusion framework: the fusion exponent (ρ), the interaction weight (δ), the stabilization factor (λ), and the synergy amplifier (η). Together, these parameters control modality dominance, nonlinear cross-modal coupling, numerical stability, and synergistic enhancement, respectively. No additional parameters are introduced, ensuring model parsimony and interpretability.

3.18 Evaluation metrics

Evaluation metrics are defined in Equations 21–23.

Accuracy:

A C C = T P + T N T P + T N + F P + F N (21)

F1-score:

F 1 − s = 2 × P r e c i s i o n × R e c a l l P r e c i s i o + R e c a l l (22)

AUC:

A U C = ∑ i = 1 n − 1 F P R i + 1 − F P R i . T P R i + 1 + T P R i 2 (23)

In this study, the F1-score is adopted as the primary evaluation metric because it provides a single, stable indicator of classification performance in the presence of class imbalance, which is common in epileptic seizure detection. It captures detection reliability without being dominated by the majority class, making it more informative than accuracy alone. In addition, the Area Under the ROC Curve (AUC) is used to evaluate the overall discriminative capability of the models across decision thresholds, offering a threshold-independent assessment of robustness. Together, F1-score and AUC provide a complementary and sufficient evaluation of detection effectiveness and generalization performance.

3.19 Computational tools

All applications were performed in Python 3.10 via TensorFlow and PyTorch on a workplace (Intel i9 CPU, 32 GB RAM, RTX 3080 GPU). Arithmetic operations were implemented in NumPy and SciPy to ensure reproducibility and transparency.

3.20 Ethical considerations

Patient data from TTH were anonymized in compliance with official review board endorsement and the Helsinki Declaration. Public datasets were retrieved under open-data agreements for research use only.

Summary of Novelty (see Table 2 for parameter innovation summary).

TABLE 2. Summary of parameter innovations.

This methodology presents:

• A formal DQA + NCS outline for objective multimodal signal validation and arrangement.
• Unified model modification across twelve (12) algorithms using adaptive fusion (ρ), interaction control (δ), stabilization (λ), and synergy amplification (η) parameters.

These novelties collectively introduce a replicable, mathematically grounded methodology for multimodal seizure detection.

4 Results

Recent benchmarking studies highlight the importance of rigorous validation protocols in seizure detection systems (Ahmad et al., 2023).

4.1 Traditional ML results

4.2 Deep learning results

4.3 Computational efficiency

Traditional machine learning models require significantly lower computational resources but exhibit limited representational capacity. Deep learning models require longer training times and more memory due to their architectural complexity. The proposed MF-QI parameterization incurs only modest computational overhead while achieving substantial performance gains, demonstrating a favourable trade-off between accuracy and computational efficiency.

4.4 Ablation study of ρ , δ , λ , η

Ablation results are shown in Figure 7. The study of ablation provides direct evidence that each adaptive parameter contributes independently to the performance of the proposed fusion framework. Removing a single parameter results in a measurable performance reduction, whereas omitting all parameters leads to a substantial degradation relative to the complete formulation. These results confirm that the observed gains do not arise from a single dominant term, but from the coordinated interaction of modality weighting, quadratic cross-modal coupling, stabilization, and enhancement mechanisms embedded in the fusion model.

Baseline fusion yields 77.56% accuracy, 75.32% F1-score, and 79.77% AUC. Complete quadratic fusion achieves 99.99% accuracy, 99.98% F1-score, and 100% AUC. Removing any single parameter reduces accuracy to approximately 99.45%–99.60% and causes similar small drops in F1-score and AUC.

This shows that:

• The four parameters together produce huge absolute performance gains over baseline fusion.
• Each parameter contributes independently; no single parameter can be removed without measurable performance loss.

The proposed MF-QI framework outperforms existing multimodal seizure detection approaches by explicitly reformulating model equations to control modality dominance, interaction strength, stabilization, and synergy. Unlike prior studies that rely on architecture-level fusion, this work introduces a unified mathematical fusion mechanism applicable across classifiers.

5 Discussion

This section presents the experimental results obtained from evaluating both traditional machine learning and deep learning models under baseline (unmodified) conditions and after applying the proposed equation-level multimodal fusion reformulation. Results are organized to reflect (i) baseline error behavior, (ii) quantitative performance before and after modification, and (iii) cross-model comparison and interpretation.

5.1 Baseline error characteristics of traditional machine learning models

Figure 8 presents the confusion matrices of the six traditional machine learning models prior to equation-level modification, while the corresponding numerical summaries are reported in Table 3. As shown in Figure 8, all traditional models exhibit several false positives (FP) and false negatives (FN), indicating weak discrimination between seizure and non-seizure classes under naive multimodal fusion.

TABLE 3. Summary of confusion matrix results for traditional machine learning models (before introduction of quadratic equation for modification).

In particular, Logistic Regression (LR) records the lowest true positives (TP = 280,000) and true negatives (TN = 270,000), with limited representational capacity when handling heterogeneous biosignals. Tree-based models such as Random Forest (RF) and XGBoost achieve relatively higher TP rates; they still have elevated FP and FN counts, suggesting insufficient modeling of nonlinear cross-modal dependencies. Support Vector Machine (SVM) demonstrates comparatively moderate FN rates, yet still fails to suppress false detections consistently.

Overall, the confusion patterns in Figure 8 reveal that conventional models, when applied directly to multimodal EEG–ECG–EMG–ACC data, are prone to misclassification due to the absence of explicit modality interaction control.

5.2 Performance of traditional machine learning models before and after modification

Figure 9 illustrates the aggregate performance quantitative comparison is summarized in Table 4 of traditional machine learning models before modification, whereas Figure 10 presents the same models after the proposed adaptive fusion parameters are introduced. Quantitatively, these results are consolidated in Table 5.

TABLE 4. Ablation study of adaptive fusion parameters ρ , δ , λ , η .

TABLE 5. Summary of confusion matrix results for deep learning models (before equation modification).

Before modification (Figure 9), the accuracy, F1-score, and AUC values range detailed numerical results are provided in Table 6 from 55% to 67%, confirming limited robustness under baseline fusion. LR performs worst (Acc = 55.0%), while SVM and DT marginally outperform others (Acc ≈ 66–67%), indicating that simple decision boundaries and ensemble averaging alone are insufficient for multimodal seizure characterization.

TABLE 6. Comparison with related multimodal seizure detection studies.

After the equation-level reformulation (Figure 10), improvements are observed across all traditional models. As shown in Table 5, accuracies rise to 82%–92%, SVM achieving the highest post-modification accuracy (92.0%), F1-score (92.6%), and AUC (91.8%). XGBoost and RF also achieved substantial gains, exceeding 90% across evaluation metrics.

These results show that embedding adaptive fusion parameters into the model input representation substantially enhances traditional classifiers, enabling modality-aware weighting and nonlinear interaction modelling.

5.3 Baseline error characteristics of deep learning models

Figure 11 depicts confusion matrices of deep learning models prior to modification, and Table 7 summarizes the numerical outcomes. In traditional models, deep learning architectures improved baseline discrimination, as reflected in higher TP and TN values across models.

TABLE 7. Traditional and deep-learning models before and after adaptive parameters.

The Transformer and CNN–LSTM models achieve the strongest baseline performance, with the Transformer recording TP = 210 and TN = 200, indicating superior temporal feature extraction. Nevertheless, FP and FN values across all deep models, particularly in TCN and GRU, suggest that even advanced architectures struggle to capture complex inter-modal dependencies without explicit fusion control.

Thus, while deep learning models outperform traditional ones at baseline (Figure 11; Table 7), architectural complexity alone does not fully resolve the challenges of multimodal misclassification.

5.4 Performance of deep learning models before and after modification

Figure 12 presents the performance of deep learning models before modification, whereas Figure 13 shows the post-modification results. The quantitative comparison is reported in Table 8.

TABLE 8. Computational efficiency of evaluated models.

Before modification (Figure 12), deep models achieve accuracy values between 70% and 82%, with the Transformer leading (Acc = 82.0%), followed by CNN–LSTM (80.0%). Architectures such as GRU and LSTM exhibit lower performance, likely due to limited cross-modal awareness and gradient instability in heterogeneous data settings.

After the adaptive fusion parameters (Figure 13), all deep learning models exhibit substantial performance. As shown in Table 8, accuracies increase to 89.9%–97.4%, the Transformer having the highest (Acc = 97.4%, F1 = 97.9%, AUC = 97.7%). CNN–LSTM and CNN also show significant improvements, exceeding 95% across all metrics.

These improvements indicate that the proposed equation-level reformulation enhances both temporal modeling and multimodal interaction handling, enabling deep architectures to exploit complementary biosignal information more effectively.

5.5 Cross-model comparison and overall discussion

Table 7 provides a unified comparison of all 12 models before and after adaptive parameter integration. Across both traditional and deep learning paradigms, the introduction of the fusion exponent ρ , interaction weight δ , stabilization factor λ , and synergy amplifier η Leads to consistent, statistically significant improvements in Accuracy, F1-score, and AUC.

Traditional models benefit most in relative terms, with absolute accuracy gains exceeding 25 percentage points in several cases, demonstrating that even simple classifiers can achieve competitive performance when equipped with structured multimodal fusion. Deep learning models, while already strong at baseline, achieve near-saturation performance after modification, confirming that the proposed framework complements rather than replaces architectural learning capacity.

Importantly, these gains are observed under strict patient-wise data splitting and are corroborated by confusion-matrix analysis, indicating that performance improvements arise from enhanced fusion modeling rather than data leakage or overfitting.

5.6 Key implications

The results collectively demonstrate that epileptic seizure detection performance depends not only on model architecture but also on the mathematical formulation governing multimodal data integration. By reformulating the fusion representation at the equation level, the proposed framework provides a general, interpretable, and architecture-agnostic mechanism for controlling modality dominance, nonlinear interaction, numerical stability, and synergistic enhancement.

Consequently, the framework establishes a robust foundation for multimodal biomedical time-series analysis and can be readily extended beyond epilepsy to other clinical and non-clinical multimodal learning problems.

5.7 Contribution

This sharp performance improvement demonstrates the significant contribution of the parameter-enhancement strategy introduced in this research. The results show that traditional models, when mathematically adapted to biosignal characteristics, can achieve competitive performance comparable to that of deep learning architectures. The added parameters provided additional control over signal variability, improved feature weighting, and enabled each model to capture multimodal correlations that were previously overlooked in their raw forms.

In general, results demonstrate that altering the original models can significantly enhance predictive power. This is a significant contribution to biomedical signal analytics, providing a testable system for researchers to extend first-generation algorithms to complex datasets beyond epilepsy prediction.

The significant performance improvement achieved by modifying the model equations also reflects the novelty and contribution of this research. In contrast to most work, which primarily relies on hyperparameter tuning, the proposed model introduces new mathematical parameters into the fundamental equations of current deep methods, enabling information to be weighed and fused across layers. This innovation directly enhanced the models’ ability to recognize cross-modal dependencies between EEG, ECG, EMG, and ACC signals and improved convergence stability during training. Improvements of up to 25% in accuracy and AUC across models demonstrate that the modified architectures are better suited for biosignal-based classification tasks. The modality-specific parameter overview enabled each model to adapt its learning dynamics to variations in signal amplitude, noise distributions, and temporal dependencies. At the end, the deep models became more robust at detecting seizure patterns that were often missed by unmodified equations. Compared with the existing literature, several researchers have attempted to enhance deep architectures for EEG-based seizure detection using techniques such as attention layers and hybrid CNN-RNN combinations (Rahman and Chen, 2022; Hussein et al., 2018). These, however, did not alter the fundamental equations that describe the model’s operation. In this sense, the contribution of the present work is unique, as the reformulation of the model equations was designed to achieve a significant and consistent performance enhancement across all architectures.

5.8 Mathematical novelty

To the best of our knowledge, this is the first approach to systematically generalize equations for both traditional and deep learning algorithms, enabling the use of adaptive, biosignal-specific parameters. This turns the models from static learners to dynamic systems that can adapt themselves to multimodal signal regularities.

5.9 Generalizable framework

Although the main application has been epileptic seizure detection, the proposed methodology is general. It can be reused in other biomedical domains, such as cardiac arrhythmia prediction, muscle disorder analysis, emotion recognition, or sleep-stage classification. The introduced methodology can be utilized to direct future work in finance, climate modelling, industrial fault detection, or any domain that captures complex multimodal time-series data.

6 Recommendations

Considering the remarkable performance gains presented in Modifying Underlying with Traditional and Deep Learning Models, we suggest the following points:

6.1 Model extension and validation

Future work should apply the proposed parameter-boosted and PSO-refined model to analyze medical data on a larger scale and across more diverse datasets, to confirm its generalized applicability across various clinical manifestations.

6.2 Application beyond epilepsy

The proposed framework should be extended to other biomedical applications (such as cardiac arrhythmia detection, Parkinson’s tremor analysis, muscle fatigue monitoring and emotion recognition) because its mathematical flexibility can accommodate any multimodal signal classification problem.

6.3 Policy and research collaboration

Cross-disciplinary collaborations among mathematicians, computer scientists, and clinicians need to be strengthened to transform these research advances into clinical decision support that improves diagnostic accuracy and patient outcomes.

In summary, the proposed framework provides a reproducible and adaptable mathematical foundation for multimodal biosignal analysis, paving the way for future medical AI applications.

6.4 Sanity checks against inflated performance

To reduce the risk of overestimated results, we enforce patient-wise splitting and report additional patient-aggregated metrics. We also compare performance before/after fusion reformulation under identical data partitions and training settings. The ablation results further confirm that performance gains decrease when any single parameter (ρ, δ, λ, or η) is removed, supporting that improvements are attributable to the proposed fusion mechanism rather than accidental data leakage or arbitrary tuning.

Generative AI statement

The author(s) declared that generative AI was not used in the creation of this manuscript.

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Footnotes

Edited by: Ardalan Aarabi, University of Picardie Jules Verne, France

Reviewed by: Ahmed Faeq Hussein, Alnahrain university, Iraq

Tarek Abd El-Hafeez, Minia University, Egypt