# Getting over High-Dimensionality: How Multidimensional Projection Methods Can Assist Data Science
## 3 Ground Theory
### Influence of Graphical Perception and Visual Properties in Projection Analysis  
[PERSON] and [PERSON] [41] defined visual perception as the ability of users to interpret visual encodings and understand the information presented graphically. It is challenging to extract the significance of complex data structures since their instances bear multiple attributes that may vary individually and simultaneously. The well-known _Gestalt_ theory states that the global pattern perception of a scene cannot be explained by the sum of parts [42]. In other words, a single element can present a specific context, but when associated with other elements, they can represent different characteristics and contexts. All in all, users need tools that explore the complex data features to reduce the cognitive load involved in analyzing massive amounts of data, such as multidimensional projection. However, how do we present data to users to explore their cognitive abilities to make the information presented significant? In graphical terms, the _Gestalt_ theory formulated some interesting principles to \"setup\" the scenario more understandable, and we summarized it as follows:  
* Proximity principle--visual elements close in the visual space are preattentive (intrinsic and uncontrolled) processed as a group that shares similar features, even if instances are grouped in a not explicit way;
* Similarity principle--elements represented by visual structures that share similar features (size, color, orientation, symmetry, parallelism) are perceptually grouped;* \"Common fate\" principle--visual elements that undergo similar visual transformations tend to be mentally grouped. The dynamism of movement helps the viewer to perceive which objects are related to the same action;
* Closure principle--elements delimited in areas with clear contours tend to be visually grouped, even if they are not entirely continuous. Color, position, size, user interaction, and other graphical properties are essential for a suitable visualization layout. Moreover, a comprehensive MDP tool must present accurate layouts that follow graphical properties that explore the human's cognitive abilities, leading to the visual transformation of raw data into information. The graphic metaphor commonly applied to display data resulting from a projection is the scatter plot [43]. A classical 2D scatter plot maps values of a data object using symbols on the Cartesian plane. For example, let \(S\in\mathbb{R}^{2}\) be a dataset whose \(s\) instances record the mass of an element measured over the interval \(t\). Then, for each \(i\) point, the \(i\)-th symbol position relative to the abscissa axis is horizontally determined through the \(t_{i}\) value in which \(s_{i}\) was measured. At the same time, the position relative to the ordinate axis of that \(i\)-th symbol is vertically determined by the \(s_{i}\) value, measured in \(t_{i}\). The advantage of a scatter plot is the consumption of only a few pixels to represent a single data object, standing out as a space-efficient chart. In addition, they are well-established metaphors commonly used in the scientific and business context [44]. According to [PERSON] et al. [45], to learn quickly about visualization tools, one must explore the user experience and intuition; therefore, graphic representations should be familiar to the user. In this sense, scatter plots are straightforward; however, they have limitations and could suffer from visual scalability. Occlusion occurs as the number of points becomes larger than screen resolution [46]; overlapping occurs when there are very close dots on each other, obscuring the individual legibility of the symbols [44]. An important issue regarding the scatter plots in a multidimensional projection context is: that there are no coordinated axes. The reason is that variables belonging to different scalar types are processed to extract similarity information between each instance, and, in the visual space, the transformed data points must express their relative position as information.