Motion capture (Mocap) data are widely used as time series to study human movement. Indeed, animation movies, video games, and biomechanical systems for rehabilitation are significant applications related to Mocap data. However, classifying multi-channel time series from Mocap requires coding the intrinsic dependencies (even nonlinear relationships) between human body joints. Furthermore, the same human action may have variations because the individual alters their movement and therefore the inter/intraclass variability. Here, we introduce an enhanced Hilbert embedding-based approach from a cross-covariance operator, termed EHECCO, to map the input Mocap time series to a tensor space built from both 3D skeletal joints and a principal component analysis-based projection. Obtained results demonstrate how EHECCO represents and discriminates joint probability distributions as kernel-based evaluation of input time series within a tensor reproducing kernel Hilbert space (RKHS). Our approach achieves competitive classification results for style/subject and action recognition tasks on well-known publicly available databases. Moreover, EHECCO favors the interpretation of relevant anthropometric variables correlated with players’ expertise and acted movement on a Tennis-Mocap database (also publicly available with this work). Thereby, our EHECCO-based framework provides a unified representation (through the tensor RKHS) of the Mocap time series to compute linear correlations between a coded metric from joint distributions and player properties, i.e., age, body measurements, and sport movement (action class).

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.

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.

Whole-slide images and computed tomography scans are commonly decomposed into patches or slices, whereas diagnostic labels are assigned only at the study level, so that which patches or slices support the diagnosis remains unknown. Multiple-instance learning addresses this weakly supervised setting through aggregation functions, which determine how instance-level evidence produces the bag-level prediction. Several probabilistic MIL methods rely on max-based aggregation, which retains only the strongest instance evidence. On the other hand, the standard noisy-OR combines all instance scores, so that the bag probability depends on the product between the bag cardinality and the average instance activation. As a consequence, a slide covered by thousands of benign patches can receive the same probability as one containing a small tumor region. We introduce Correlated Chained Gaussian Processes with Weighted Noisy-OR Likelihood (CCGP-WNOR), a framework in which each instance is assigned a weight that modulates its contribution to the bag probability, with the weights summing to one so that the aggregation is normalized. Consequently, the bag probability lies between the minimum and maximum instance scores, and a value close to one requires at least one instance carrying strong positive evidence. Instance scores and aggregation weights are obtained by transforming two latent functions coupled through a semiparametric latent factor model with shared Gaussian processes, permitting cross-output dependence in the prior. Posterior uncertainty is propagated through a factorized approximation that preserves marginal means and variances but omits cross-output and cross-instance covariances from likelihood integration and prediction. Scalable inference is performed using inducing variables and stochastic variational inference. Experiments on a semi-synthetic benchmark and three medical imaging datasets show that CCGP-WNOR achieves a competitive performance among the compared state-of-the-art MIL methods.