Emotion trajectories on a latent affective manifold: a multiview geometric framework

Standard computational models represent emotions as static state points in a feature space. We argue that this representational assumption is structurally insufficient: emotional experiences are better modeled as trajectory objects on a latent affective manifold rather than as isolated points. We introduce a formally defined multiview framework in which a smooth latent affective manifold A generates both high-dimensional observational data (e.g., physiological measurements) and coarse-grained verbal labels via distinct projection maps. Emotions are defined as temporally ordered trajectory objects on A, characterized by intrinsic geometric properties of their paths rather than by their endpoints alone. Under mild smoothness assumptions, intrinsic geometry of A can be approximated from multiview observations using diffusion maps. In a synthetic multiview simulation, we demonstrate that trajectory families with identical endpoint labels achieve strong separation (AUC ≈ 0.90) via intrinsic path features, while endpoint-only representations perform at chance. This illustrates that trajectory-level modeling possesses strictly greater representational capacity than static point-based approaches under multiview observation constraints. The proposed framework provides a computationally tractable foundation for modeling affective dynamics and establishes a basis for future extensions involving metric recovery and manifold-based dynamical analysis.