Cross-subject electroencephalogram (EEG)-based emotion recognition remains challenging due to substantial inter-individual variability and discrete formulation that overlooks affective continuity. Existing methods operate in Euclidean space and focus on marginal distribution alignment, failing to preserve the semantic structure of emotions across subjects. This article proposes MGMCL, reconceptualizing emotion recognition as learning continuous representations on symmetric positive definite (SPD) Riemannian manifolds. The frame?work introduces multi-granularity manifold contrastive learning at instance, emotion, and trajectory levels while preserving semantic ordering. Neural ordinary differential equations on manifolds model continuous emotion dynamics. Cross-subject generalization employs Gromov-Wasserstein manifold alignment. Weakly-supervised learning enables continuous valence-arousal-dominance prediction from discrete labels. Extensive experiments on three public datasets demonstrate state-of-the-art performance: 91.23% accuracy on SEED, 73.82% on SEED-IV, and 76.38% on DEAP, achieving consistent improvements of 1.89%, 1.66%, and 1.28% over previous best methods, respectively.
Learning unsupervised representations of medical imaging cohorts can reveal clinically meaningful prototypes without expert labels, which are often noisy and fail to capture true pathological heterogeneity. However, existing deep latent-variable models estimate Gaussian mixture priors via Euclidean averaging, producing prototypes that drift off the curved data manifold and degenerate as the number of sub-populations grows. We propose a manifold-anchored variational framework built on a geometry-aware Expectation-Maximization (EM) algorithm, whose M-step selects each sub-population prototype as the graph medoid with the highest diffusion centrality on a heat-kernel-weighted latent graph, ensuring that every prototype remains on-manifold. A Dirichlet energy regularizer enforces geometric smoothness of the latent space, and a per-sub-population uncertainty score enables label-free quality assessment. \rev{The manifold-anchored EM is a general-purpose geometric tool that extends standard EM and applies readily to other latent-variable models beyond this setting.} On cardiac scar and brain MRI benchmarks, our framework attains the highest accuracy among all compared methods, produces the sharpest prototypes reported to date, and remains stable at large sub-population counts where all baselines degenerate.