# Visualization of a Multidimensional Point Cloud as a 3D Swarm of Avatars
## 1 Introduction  
Multidimensional datasets are a very rich resource in many applications, constantly gaining importance as both computer hardware and algorithms are increasingly capable of handling them. One element that is struggling to keep up with this development is the human visual system (and human senses in general), which is naturally built for 3D space and cannot perceive or even imagine a space of higher dimensionality. There are two ways to cope with the problem: (i) reduce the dimensionality of the data by taking a 3D projection or cross-section (possibly a thick-layer cross-section) of the data and (ii) increase the dimensionality of the display by bestowing the representations of the points with additional characteristics besides their coordinates. Those additional properties can include color, size, shape parameters, and any quantifiable visual peculiarities. Each data point is then represented by a more elaborate token, which in this text will be referred to as an avatar. One well-known approach to avatar-based representation is the use of Chernoff faces [1], icons resembling a human face, where data values are converted into parameters such as the rounded or oblong shape of the face, hair color, and length, smiling or frowning curvature of lips, etc. Chernoff faces leverage the natural ability of the human observer to identify and interpret facial traits and expressions and have been widely used for intuitive visualization of multivariate data. However, Chernoff faces present several limitations, especially in the context of complex, high-dimensional, or interactive data analysis. The number of distinct visual features that can be reliably mapped onto a face is inherently limited, constraining the dimensionality that can be visualized. Most implementations are static and two-dimensional, limiting opportunities for dynamic exploration or spatial context. Importantly, the human perception of faces is subject to emotional and subjective biases--for example, certain expressions may be perceived as \"friendly\" or \"untrustworthy\" regardless of the underlying data [2]. Furthermore, Chernoff faces typically treat all variables equally without distinguishing between dimensions that are intuitively meaningful to the user and those that are more abstract or technical. It can lead to loss of interpretability or visual clutter, especially as the number of variables increases. To overcome some of these issues, alternative glyphs have been proposed, such as trees [2], which are familiar to humans but evoke less emotion. In this work, we propose a novel approach that semantically separates data dimensions into two groups: those that are intuitively meaningful to the user (e.g., sensory, categorical, interpretable parameters), and those that are abstract or technical. Users may assign meaningful dimensions to either geometric space or avatar visual features. If fewer than the required number of dimensions are assigned, the system automatically supplements them using anonymous dimensions, which are processed via Principal Component Analysis (PCA) to generate missing spatial or visual features. This approach is implemented as an interactive plugin for the dpVision platform [3; 4], allowing users to explore a cloud of 3D avatars positioned in a 4D data space and visualized through dynamic projections into 3D space (see Figure 1). By merging spatial navigation with avatar-based representation, our plugin provides a human-centered and intuitive visualization of complex multidimensional data. To validate the proposed approach, we use two types of multivariate datasets: (a) two synthetic datasets designed to illustrate interpretability and the effects of variable assignment--one modeling fictional politicians and another simulating a diverse set of soft drinks and (b) the publicly available dataset containing 12-dimensional data on Portuguese Vinho Verde wines [5; 6]. The remainder of this paper is organized as follows.