Parameterized Multimodal Feature Fusion for Explainable Seizure Detection Using PCA and SHAP

Multimodal epileptic seizure detection using physiological biosignals remains challenging due to signal noise, inter-subject variability, weak cross-modal alignment, and the limited interpretability of many machine learning models. To address these challenges, this study proposes a parameterized multimodal feature-fusion framework that unifies normalization, modality weighting, and nonlinear cross-modal interaction within a single mathematical representation. Four fusion parameters, the fusion exponent ρ, interaction weight (δ), normalization factor (λ), and the cross-modal interaction term (η), are introduced at the feature-fusion level, while all classifiers retain their original learning mechanisms. The framework is evaluated using synchronized EEG, ECG, EMG, and accelerometer signals from 120 subjects, segmented into 2 s windows at 512 Hz and analyzed using twelve classical and deep learning classifiers. Principal Component Analysis (PCA) applied to the fused feature space reveals improved class separability compared to unimodal representations, with EEG exhibiting the strongest intrinsic discrimination and peripheral modalities contributing complementary structure when fused. SHapley Additive exPlanations (SHAP) further identify entropy as the most influential feature across all modalities, followed by RMS and energy, yielding physiologically coherent attributions. Quantitative performance evaluation and ablation analysis confirm that the observed improvements arise from the proposed representation design rather than classifier-specific modifications. Unlike existing architecture-dependent fusion strategies, the proposed method introduces a mathematically parameterized feature-space formulation that enhances separability and interpretability without modifying classifier architectures, thereby establishing a representation-driven paradigm for explainable multimodal seizure detection. These results demonstrate that mathematically principled feature-space modeling can simultaneously enhance predictive performance and interpretability, providing a transparent and robust foundation for explainable multimodal seizure detection.