# Getting over High-Dimensionality: How Multidimensional Projection Methods Can Assist Data Science  
[PERSON]  
1 Institute of Mathematics and Computer Science, University of Sao Paulo, Sao Carlos 13566590, Brazil; [EMAIL_ADDRESS] (E.S.O. ); [EMAIL_ADDRESS] (F.F.D.) [PERSON]  
1 Institute of Mathematics and Computer Science, University of Sao Paulo, Sao Carlos 13566590, Brazil; [EMAIL_ADDRESS] (E.S.O. ); [EMAIL_ADDRESS] (F.F.D.) [PERSON]  
2 Departamento de Matematica, Facultad de Ingenieria, Universidad de Atacama, Copiapo 15300 structured data and the inability of these simple techniques to deal with large data volumes on a screen. Information Visualization (InfoVis) aims to develop and apply visual representations to model and understand attribute values, relationships, and extraction of information from data [4; 5]. In this context, a class of InfoVis techniques has been a stand out for some time: the multidimensional projections. These techniques generate injective mappings that transform multidimensional spaces into visual spaces (2D or 3D), preserving structures and similarities of the original spaces as much as possible, such as relationships between data instances or clusters' presence [6; 7; 8]. This transformation is accomplished through mathematical operations to embed the number of attributes to 2 or 3, allowing \(m\)-dimensional data objects to be represented in Cartesian space. Although it is not a recent concept, the research into new multidimensional projection techniques development has been intensified in recent years. This rise of interest is due to the wide range of applications that can benefit from visual representations of large datasets with a large number of attributes [9], and the research into projection methods has promoted the creation of visual tools that reveal relevant patterns and trends hidden in multidimensional data. Examples of successful applications involving projection techniques can be found in the more diversified domains [6; 10; 11; 12]. The current literature on multidimensional projections has followed the recent developments, with many works reviewing fundamental concepts, proposing taxonomies, and performance evaluations [7; 13; 14; 15; 16; 17; 18]. However, due to the profusion of new developments, we have identified some things missing in the literature. Moreover, the different terminologies adopted in previous papers and reviews can be somewhat confusing for the researchers starting into the subject and even for those with some previous knowledge but (maybe) not specialized in InfoVis methodologies. For example, each technique often cannot handle all the data types, as each technique is tailored to efficiently handle one (or some) specific data type(s). In addition, all the projection techniques require careful data pre-processing to explore their embedding abilities properly. Nevertheless, we believe that multidimensional projection techniques are highly informative tools that can add analytical capabilities to data scientists within the context of knowledge discovery and data mining tasks; thus, a comprehensive discussion regarding simplifying the projection technique environment is a need. In this sense, we aim to present to the reader that multidimensional data analyses go far from simple PCA. We will do it with a sufficiently detailed discussion of the leading and more advanced different types of techniques applied to multidimensional projection tasks through a vocabulary that unifies the many and different terms and definitions found in previous works. We will also address taxonomies and essential concepts and considerations that must be taken into account by the reader's interest in applying projection techniques on multidimensional data, from the appropriate data treatment to the possible distortions and limitations of the obtained results.