Topological Entropy and Homology Reveal Interpretable and Real-Time Neural Signatures in Pediatric EEG

Decoding neural states from pediatric EEG in naturalistic settings remains challenging due to signal noise, motion artifacts, and intersubject variability. This paper introduces Enriched Topological Features (ETF), a new approach integrating multiscale persistent homology (H0/H1), time-aggregated entropy via sliding windows, and Takens' phase-space embeddings to classify gameplay versus resting states in children. Using 4-channel EEG from 79 subjects recorded during museum-based Minecraft gameplay, ETF achieves 96.90% training accuracy and 94.96% test accuracy (F1 = 97.2%) with XGBoost classifiers, outperforming deep learning baselines by 21.3% and prior topological methods such as nonlinear EEG topological dynamics analysis (NETDA) by 3.0% in test accuracy. SHAP-based attribution reveals topological features reflecting distinct neural dynamics, with gameplay engagement exhibiting elevated gamma-band persistence landscapes at frontal sites (AF8 H1 PL2), indicating executive network recruitment, while resting states show high alpha-band entropy at temporal electrodes (TP9), reflecting metastable disengagement. The framework mitigates class imbalance through SMOTE and random undersampling, and captures developmental dynamics, including a significant negative correlation (r = -0.23, p = 0.0176) between frontal gamma topological stability and age, suggesting frontoparietal network maturation. With computational efficiency of 644 ms per epoch and consistent performance under noise, ETF offers an interpretable, low-latency processing pipeline for pediatric mobile neurogaming and adaptive learning interfaces.