# Getting over High-Dimensionality: How Multidimensional Projection Methods Can Assist Data Science
## 6 Challenges, Open Questions, and Future Research Directions  
Given visual analytics' relevance as a significant part of mining tools in data science applications, multidimensional projection techniques are a powerful resource due to their ability to generate visual representations of complex data instances groupings belonging to high-dimensional spaces. However, significant gaps still need to be addressed in the multidimensional projection context. The trade-off between computational costs and precision is one of the significant challenges regarding the development and application of multidimensional projections. Because of the increasingly large datasets we are facing nowadays, both in terms of the number of instances and the number of attributes per instance (dimensionality), the development of computationally efficient and accurate techniques is a challenging issue that involves research in sophisticated mathematical solutions. This challenge is intensified when applications need to handle real-time or growing datasets, such as time series and streaming data. An open opportunity in the projection domain is to handle time-varying data, i.e., how to project multidimensional time series. Research in multidimensional time series has a long and rich history [110], but properly exploring the time component imposes a major challenge in the projection domain. Though it is possible to project time slices of the data and analyze the evolution of these time slices, it can easily become an overwhelming task  
Figure 8: Correlation matrix across the 78 gene expressions (DNA microarray). Source: elaborated by the authors. Figure 9: Projections of the DNA micro-array, represented by 78 gene expressions characteristics. Source: elaborated by the authors. when a long time series is considered. The literature is not so rich regarding multidimensional projection methods able to capture dynamic data evolving [111]. We can cite some extensions of well-known methods such as t-SNE [112; 113; 114] and even PCA [115; 116]. Real-time data also highlights an issue already identified by the research community in multidimensional projections: stability. A stable method must be able to incorporate new data in the visual space without significant modifications in the position of points already projected. In addition, in a scenario with continuously generated data, it might be too expensive to recalculate the entire projection so that the number of instances is increased/decreased. Methods that rely on matrix decomposition are not stable since the addition/removal of a single instance demands the recalculation of all matrix operations, which can significantly change the mapping [7]. Optimization-based techniques depend on initial conditions, so there is no way to guarantee their stability. Control points-based strategies are more resilient alternatives to perturbations, as long as the control points are kept fixed. However, these kinds of approaches open other questions. As mentioned before, the random sampling of control points has been a commonly applied solution. However, there is no guarantee that a random sample encompasses all the nuances of a dataset (besides may render some confusion when generating different layouts). Another issue we raised in this context is related to the sampling size. How many control points are needed to compose a good sample? Thus, these open questions are waiting for future research that establishes metrics and parameters for the generation of the initial sample subsets. Most of the multidimensional projection techniques were tailored to operate on numerical data. Thus, we identified a gap between projection tools in their ability to handle non-numerical values, such as ordinal, textual, categorical data [117], and so on. For example, one-hot-encoding is a well-known method applied for a long time in digital circuits and machine learning environments that can be used in our context to transform categorical variables into numerical combinations of binary nature.