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.

Electroencephalography (EEG) provides a non-invasive alternative for supporting Attention-Deficit/Hyperactivity Disorder (ADHD) assessment, but existing classification pipelines often depend on handcrafted descriptors, segment-wise decisions, or deep neural architectures whose interpretability and subject-level generalization remain limited. This work introduces Hidden Markov Model-Induced Stationary RKHS Distance Learning (HIS), a probabilistic-kernel framework for interpretable EEG-based support for the diagnosis of ADHD. In the proposed approach, each subject is represented by a Hidden Markov Model with Gaussian-mixture emissions, trained on frontal EEG recordings. Rather than vectorizing the learned parameters, each HMM is mapped to its induced stationary observation distribution, which is then embedded into a Reproducing Kernel Hilbert Space. Pairwise subject dissimilarities are computed through a closed-form Hilbert embedding distance between stationary Gaussian mixture distributions and used by precomputed-kernel classifiers. The method was evaluated on a controlled synthetic EEG benchmark and on a public pediatric ADHD EEG dataset recorded during a visual attention task. The proposed HIS distance was compared against the Probability Product Kernel, a finite-horizon HMM similarity baseline. On synthetic EEG, HIS achieved 95.0% held-out test accuracy and consistently outperformed the baseline across classifiers. On the real EEG dataset, the best configuration used a compact HMM topology and KNN classification, reaching 95.8% held-out test accuracy at the subject level. Qualitative t-SNE analyses further showed that HIS induces more discriminative local subject neighborhoods than the baseline kernel, while avoiding segment-level sample inflation. These results suggest that stationary RKHS embeddings of subject-specific HMMs provide a competitive, leakage-aware, and interpretable framework for modeling variable-length EEG recordings in ADHD classification.