# Getting over High-Dimensionality: How Multidimensional Projection Methods Can Assist Data Science
## 5 Discussions about the Multidimensional Projection Techniques  
A challenging issue is a balance between projection quality and the required processing amount to generate good mappings. The high computational costs virtually block the application of some projection techniques in medium-sized datasets, even for the accurate techniques. As we saw above, an alternative strategy employed to mitigate the computational bound and enable the use of multidimensional projections, even in interactive and real-time applications, is the sampling of representative instances. From a subset of samples, it is possible to apply a precise (and more expensive) projection technique to generate the control points, which will guide the remaining mapping (now using a less expensive technique) in the visual space. Although the original purpose of control points is to reduce computational time, control points can also be applied to incorporate some degree of user interactivity in projection processes [64]. However, there are still no comprehensive studies that quantify the impact introduced in manipulating control points by users, either in terms of quality or reasonability of generated maps [7]. Furthermore, the proper choice of representative samples is a central question in some circumstances. For example, authors such as [PERSON] et al. [9], [PERSON] and [PERSON] [10], [PERSON] et al. [12], and [PERSON] et al. [6] suggested a random selection of large quantities of instances due to the difficulty in determining an ideal amount that effectively represents all the classes contained in the dataset, but exactly how large this must be this quantity is an open issue. The larger the representative subset, the greater the computational effort required in the initial projection stage. Although it is statistically possible to infer that a random sample contains significant information from the dataset, there is no guarantee that it will always be true. Furthermore, the random selection introduces an undesirable effect: the same dataset is mapped into different layouts, something that can generate some confusion for the users. Thus, there is a need for an alternative to reducing the complexity of multidimensional projection techniques while producing effective and deterministic layouts in a reduced time. Figure 4 presents a performance comparison between some of the state-of-the-art multidimensional projection techniques. According to [PERSON] et al. [6], global techniques usually yield better dissimilarity preservation averages (stress) and computational performance. Note that LAMP, which is essentially a local method, is highlighted as one of the best balances between stress (see Figure 4 left-hand) and computational performance (see Figure 4 right-hand). Table 1 summarizes the main approaches reviewed throughout the text. In addition to these techniques, there are other derivations, modifications, and improvements. [PERSON] et al. [16] also carried out a valuable review of the subject. However, the interest in developing and improving multidimensional projection strategies has been intense over the past ten years. In this scenario, [PERSON] and [PERSON] [7] carried out comprehensive and updated research about multidimensional projection methods, clarifying limitations and strengths from the perspective of visual analytics. As we are demonstrating here, the multidimensional projection has a large field of application possibilities. To finish this Discussion section, we highlight one emerging application in a new effervescent research domain: Explainable Artificial Intelligence (XAI). Artificial Intelligence has a significant growing development interest in the last decade, especially Machine Learning algorithms. On the one hand, Machine Learning models such as those based on Artificial Neural Networks and Gradient Boosting can outperform human capabilities in many tasks and, for this reason, have been often applied in decision-making processes [99; 100].