These interactive 3D plots show each participant's facial-expression trajectories embedded into a participant-specific emotional manifold using UMAP. Nearby points represent similar patterns of facial movement within the original 76-dimensional ARKit feature space sampled at 60 frames per second.
Each coloured trajectory corresponds to one of the nine emotion categories. Rather than displaying static facial expressions, the plots show how facial movement unfolds continuously through time as trajectories across each participant's manifold. They reveal both the spatial organisation of emotional categories and the temporal dynamics of expression, including trajectory shape, curvature, traversal speed, directional coherence, and the relative positions of Flow and Neutral within each individual's emotional geometry.
Two versions are provided for every participant: black background (presentation mode) and white background (publication and analysis mode). Individual emotions or emotion pairs can be isolated using the interactive legend.
These manifolds are low-dimensional visualisations of high-dimensional facial movement rather than direct representations of emotion itself. Their purpose is to reveal the geometric organisation of expressive behaviour. One of the central findings of the study is that this geometry is participant-specific: emotion categories remain identifiable within individuals, but no two participants share the same emotional manifold.
Each UMAP was computed independently for a single participant. Absolute coordinates are therefore not directly comparable between participants; the meaningful comparisons are the internal geometry of each manifold and the shared-embedding analyses presented in Section 5 of the paper.
Spatial separation — rotate each manifold and look for how cleanly the nine emotion clusters separate. Participant 3 shows the most dramatic separation: nine completely non-overlapping island clusters visible from any rotation angle, consistent with 99.96% first-dimension LDA loading and 100% personalised BiLSTM classification accuracy. Participant 2 shows comparatively greater overlap between several emotional regions, particularly around Flow, Neutral and Sadness, illustrating a more continuous manifold organisation than P3.
Flow — isolate Flow (orange) and compare its position across participants. In some manifolds Flow is highly isolated (P4, P6, P7), while in others it lies close to neighbouring emotional regions (P1, P2, P5). Its trajectory organisation, traversal speed and curvature also differ substantially between individuals. These differences support the paper’s conclusion that Flow occupies participant-specific geometric and dynamical roles rather than a universal position within emotional space.
Bimodal trajectories — Most emotional trajectories occupy a single coherent region of latent space. An interesting exception occurs in Participant 7, where Flow occupies two distinct regions connected by relatively sparse transitions. This bimodal organisation illustrates that a single emotion need not correspond to one compact region of the manifold, but may comprise multiple dynamically connected modes of expression.
Neutral — isolate Neutral (brown). Within each participant’s manifold, Neutral typically behaves as a stable region characterised by low curvature and repeated self-return. Across participants, however, its location varies substantially. Rather than forming a universal geometric origin, Neutral appears to act as an individual baseline whose position depends on the participant.
Trajectory character — Trajectory length, curvature, density and branching reflect different temporal organisation of emotional expression. These are properties of sequences rather than individual frames and therefore complement the frame-level LDA analysis. Trajectory length, curvature, density and branching reflect different temporal organisation of emotional expression. These are properties of sequences rather than individual frames and therefore complement the frame-level LDA analysis. Rotating the manifold often reveals structure that is not immediately visible from a single viewpoint.
Hull volume — measures the spatial extent of each participant’s emotional manifold in the independent UMAP embedding. Values range from 12.8 (P4) to 516.9 (P6) — an approximately 40-fold difference in geometric scale.
The UMAP and LDA projections are complementary analyses of the same 76-dimensional ARKit data. UMAP is unsupervised and temporal — it preserves the sequential structure of 60fps trajectories and reveals how emotional expression moves through the manifold over time. LDA is supervised and frame-level — it finds the linear combinations of features that maximise separation between emotion categories at the level of individual frames, with no temporal context.
Where UMAP and LDA converge, the geometric finding is supported by independent analytical frameworks. Where they diverge, the differences are equally informative, revealing aspects of emotional organisation that exist only at the temporal level and cannot be recovered from individual frames alone.