EEG-Based Supported Diagnosis of ADHD Using Subject-Specific HMMs and Stationary RKHS Embeddings

Electroencephalography (EEG) provides a non-invasive means of supporting Attention-Deficit/Hyperactivity Disorder (ADHD) assessment. Nonetheless, existing pipelines often rely on handcrafted descriptors, segment-wise decisions, or deep architectures with limited subject-level generalization. This work introduces Hidden Markov Model-Induced Stationary RKHS Distance Learning (HIS), a probabilistic framework that represents each subject by a Hidden Markov Model with Gaussian-mixture emissions trained directly from frontal EEG recordings. Rather than vectorizing model parameters, each HMM is mapped to its induced stationary observation distribution and embedded into a Reproducing Kernel Hilbert Space (RKHS), where pairwise subject similarities are computed through a closed-form Hilbert embedding distance. These similarities are subsequently exploited by precomputed-kernel classifiers for subject-level prediction. The proposed method was evaluated against the Probability Product Kernel baseline using both a controlled synthetic EEG benchmark and a public pediatric ADHD dataset under progressively more rigorous validation protocols, culminating in repeated nested cross-validation with bootstrap confidence intervals and permutation testing. On the synthetic benchmark, HIS achieved 95.0% held-out accuracy and consistently outperformed the baseline across classifiers. On a real EEG dataset with 121 subjects, the primary evaluation protocol yielded a balanced accuracy of 73.5% (95% CI: 69.8-77.0%), an AUC of 79.6%, and an MCC of 0.483 (permutation p < 0.001) using an SVM with compact subject-specific HMMs. Complementary hyperparameter analyses and t-SNE visualizations demonstrated that HIS induces more stable and discriminative subject representations than the baseline. These results establish stationary RKHS embeddings of subject-specific HMMs as a leakage-aware framework for EEG-based ADHD decision support and underscore the critical influence of statistically rigorous evaluation protocols on reported classification performance.