An interactive research companion to Emotional Manifolds
The Shared Emotional Atlas explores how seven participant-specific emotional manifolds occupy a single three-dimensional UMAP embedding constructed from 228,574 facial-expression frames. Unlike the independently fitted participant manifolds, every view in this collection uses the same coordinate system, allowing participant, emotion, trajectory, occupancy, and neighbourhood structure to be compared directly within the shared representation.
The atlas moves from global orientation to increasingly local forms of analysis. It is intended as an exploratory research and learning resource: the paper presents the principal argument, while these interactive views allow readers to rotate, zoom, filter, and interrogate the shared geometry beyond the narrative and space constraints of the manuscript.
The shared embedding places all 228,574 frames within a single common coordinate system. Because this UMAP is fitted jointly across participants, its geometry should not be interpreted as preserving the absolute scale or convex-hull volumes measured in the independently fitted participant manifolds. The shared view is intended for comparing relative position, overlap, trajectory organisation, and local neighbourhood structure within one reference space. Consequently, a participant whose independent manifold is highly compact, such as P4, may appear more spatially comparable with other participants in the shared embedding.
The interactive pages intentionally contain minimal explanatory text so that the geometry remains unobstructed. Descriptions and suggested points of attention are provided here; complete numerical outputs, robustness checks, and computational details are available in the linked analysis notebook.
Emotional categories are shared across participants; their local geometric organisation is predominantly individual.
1. Shared-space orientation
These views establish the global organisation of the shared embedding before the atlas moves into local occupancy and neighbourhood-level analyses.
Shared-space orientation
Shared UMAP coloured by emotion
All participants · nine elicitation states · one coordinate system
All 228,574 frames are embedded together and coloured by elicitation state, providing a global view of where the nine categories occupy the pooled latent volume.
What to notice: emotional categories remain locally coherent in many regions, but no single global arrangement places each category in one universal territory shared by all participants.
Participant distribution across the common embedding
The same shared space is coloured by participant, showing how all seven individuals occupy the pooled latent volume.
What to notice: participants interweave globally, yet distinctive extensions and locally concentrated regions remain visible. P2 contributes much of the outer extent, while P6 contains a particularly distinctive peripheral territory.
Continuous frame sequences are rendered as participant-coloured trajectories, preserving the temporal paths taken through the common embedding.
What to notice: trajectories from different participants cross and thread through the same broad volume, while retaining locally distinctive pathways and peripheral structures. The figure emphasises paths rather than isolated positions.
Mean participant positions within the common coordinate system
Participant centroids are overlaid on the full shared embedding to show their relative mean positions.
What to notice: centroid positions differ, but remain clustered relative to the full extent of the underlying trajectories. This demonstrates why centroid separation alone cannot describe each participant's complete geometric organisation.
Participant hulls summarise the broad volume occupied by each participant in the shared embedding.
What to notice: hulls provide an overview of spatial reach and overlap, but should be read alongside the trajectories and local analyses. Differences in participant scale are preserved rather than normalised.
Selectable participant and elicitation-state combinations
An interactive selector highlights chosen participant–emotion combinations against the complete shared embedding.
What to notice: the same elicitation state occupies different local territories for different participants. Use the controls to compare, for example, all Flow trajectories, P6 Flow, or participant-specific Neutral regions.
The shared embedding is divided into small cubic spatial bins, or voxels. These analyses ask who occupies each local volume, how strongly one participant dominates it, and where genuinely shared territory occurs.
Voxel occupancy
Participant occupancy of local spatial regions
Number of participants represented within each occupied voxel
Each occupied voxel is coloured by the number of different participants contributing frames to that local volume.
What to notice: most occupied regions contain only one or two participants, while regions jointly occupied by many participants are rare. Global visual overlap therefore coexists with strongly participant-specific local organisation.
Each occupied voxel is coloured by the participant contributing the greatest number of frames. Marker size reflects voxel occupancy.
What to notice: the shared embedding forms a mosaic of locally dominant participant territories rather than seven cleanly separated continents. P2 dominates much of the outer region, while P6 contributes a distinctive lower-left territory.
Normalised participant mixing within occupied voxels
Each voxel is coloured by normalised participant entropy. Low entropy indicates dominance by one participant; high entropy indicates more even local mixing.
What to notice: most regions exhibit low participant entropy, with higher-mixing voxels concentrated in comparatively limited portions of the shared space.
A quantitative summary of how frequently occupied voxels contain one, two, three, or more participants.
What to notice: singleton and two-participant voxels account for the great majority of occupied local regions. High-order overlap falls away rapidly, and no retained voxel is jointly occupied by all seven participants.
The histogram shows the proportion of frames contributed by the dominant participant in each retained voxel.
What to notice: the pronounced peak at 1.0 indicates that many local regions are occupied entirely by a single participant. The remaining shared voxels are typically still strongly dominated rather than evenly mixed.
Singleton occupied voxels across the nine elicitation states
For each elicitation state, the plot shows the percentage of occupied voxels containing frames from only one participant.
What to notice: participant-specific territory is pervasive rather than confined to Flow or any one category. Approximately 89–97% of occupied voxels are singleton regions across every elicitation state.
Participant ownership of the outer emotional landscape
Dominant ownership of peripheral occupied voxels
Peripheral voxels are defined from the outer radial portion of retained occupied space and assigned to their dominant participant.
What to notice: P2 contributes more than half of the peripheral territory, while P6 and P7 occupy smaller but substantial portions. The result quantifies the visually apparent differences in how participants extend into the shared embedding's outer regions.
Nearest-neighbour analyses provide a grid-independent complement to voxel occupancy. Rather than dividing space into bins, they ask who surrounds each frame within the continuous shared geometry.
Neighbourhood purity
Local nearest-neighbour purity across spatial scales
Participant and emotion purity for k = 5–50
For each frame, the analysis measures the proportion of its nearest neighbours sharing the same participant label and the same emotion label, compared with shuffled baselines.
What to notice: both forms of purity remain far above chance across all neighbourhood sizes. Participant purity exceeds emotion purity at every scale, indicating that local organisation is influenced more strongly by individual identity than by emotional category.
Participant-specific local neighbourhoods by emotion
Same-participant neighbour purity at k = 25
For each elicitation state, the plot shows the average proportion of the 25 nearest neighbours originating from the same participant.
What to notice: local participant specificity remains high across every state, ranging from roughly 84% to 93%. Flow is the most participant-specific, but the central result is the consistently high purity across the entire emotional vocabulary.
Individual differences in same-participant neighbourhood structure
The analysis compares how strongly each participant's frames are surrounded by frames from that same participant in the shared embedding.
What to notice: all participants retain substantial local identity structure, while differences between participants reveal variation in how compactly or diffusely each individual occupies the shared space.
The Atlas is an interpretive layer. The full notebook preserves the calculations, intermediate tables, parameter checks, and numerical outputs used to construct these views.
Analysis notebook
Shared Emotional Atlas — complete notebook
Computational workflow and full numerical outputs
A browser-readable export of the complete notebook, including voxel construction, occupancy and entropy metrics, dominant ownership, peripheral analyses, nearest-neighbour purity, emotion-specific summaries, sensitivity checks, and figure generation.
Use this resource for: methods, exact values, intermediate tables, robustness checks, and reproducibility.
Interpretive boundary. These interactive visualisations are exploratory and descriptive. UMAP preserves local neighbourhood structure more strongly than exact global distance, while voxel-based summaries depend partly on spatial resolution and minimum-occupancy thresholds. Quantitative conclusions should therefore be read alongside the sensitivity analyses and grid-independent nearest-neighbour checks contained in the analysis notebook.