# Visualization of a Multidimensional Point Cloud as a 3D Swarm of Avatars
## 4 Results
### Small-Scale Illustration: Synthetic Politicians Dataset (N = 12)  
This illustrative example utilizes a manually constructed synthetic dataset of 12 fictional politicians, each described by 9 features that reflect both voter perception and performance metrics. Intuitive features (number of promises, fulfillment rate, public sympathy, general popularity) were mapped to avatar visual traits (e.g., smile, nose length, skin color). In contrast, technical features (sympathy, economic views, social views) were assigned to spatial coordinates (X, Y, Z axes). The remaining variables (media activity, voting effectiveness, age) were left anonymous for PCA. The variable group_numeric encodes four archetypes (populists, conservatives, liberals, technocrats), used only for color coding of avatar hair; each sample is labeled by name. To provide a fair comparison with established visualization techniques, Figure 5 presents the same dataset using four classical methods: PCA scatter plot, t-SNE projection, parallel coordinates, and a 4 \(\times\) 3 grid of Chernoff faces. While PCA and t-SNE reveal the grouping structure, and parallel coordinates allow for the comparison of individual profiles, none of these methods offers the same level of simultaneous, intuitive insight into both position and feature profiles as spatial avatars. In particular, Chernoff faces communicate intuitive attributes but lack spatial context; conversely, scatter plots provide structure but obscure the source of differences between cases. Figure 4: A cloud of points intersected by a slab, using a threshold of 1.5. Blue points are accepted for further processing or visualization, while red points that lie outside the slab are discarded. For the twelve synthetic politicians, classical methods highlight some group separation (notably in PCA and t-SNE), but interpreting individual differences remains challenging. The Chernoff faces grid allows for visual comparison of intuitive features, yet it does not convey the geometric relationships between politicians or facilitate the detection of outliers in attribute space. This contrast underscores the unique advantage of spatial avatars in combining the interpretability of individual profiles with structural awareness. Variable assignment:  
Avatar features: number of promises (skin color), promise fulfillment (nose length), general popularity (smile), group affiliation (hair color). Spatial coordinates: sympathy (X),  
Figure 5: Comparison of classical visualization methods for the synthetic politicians dataset. (**Top left**): PCA scatter plot (first two components); (**Top right**): t-SNE projection; (**Bottom left**): parallel coordinates plot; (**Bottom right**): Chernoff faces grid (4 \(\times\) 3) for all twelve politicians, colored and labeled by group. Each approach reveals different aspects of the data: scatter plots show grouping structure, parallel coordinates display multivariate profiles, and Chernoff faces summarize intuitive features—but none allows simultaneous interpretation of both structure and profile as directly as spatial avatars (see Figure 6). Figure 6: Spatial avatar visualization of the synthetic politicians dataset. Avatar features encode intuitive traits (skin color: number of promises; nose length: promise fulfillment; smile: general popularity; hair color: group). Spatial coordinates reflect sympathy (X), economic views (Y), and social views (Z). Names and group colors aid interpretation. This visualization enables direct comparison of political archetypes, identification of outliers, and exploration of individual profiles. economic views (Y), social views (Z). Anonymous/PCA: media activity, voting effectiveness, age. Interpretation and interactive exploration:  
The spatial avatar visualization enables immediate and intuitive comparison of both the position and the profile of each fictional politician. Clusters and polarization become visible in space, while characteristic features (such as promise fulfillment or popularity) are instantly \"readable\" from the avatar's face.