Getting over High-Dimensionality: How Multidimensional Projection Methods Can Assist Data Science

Abstract

The exploration and analysis of multidimensional data can be pretty complex tasks, requiring sophisticated tools able to transform large amounts of data bearing multiple parameters into helpful information. Multidimensional projection techniques figure as powerful tools for transforming multidimensional data into visual information according to similarity features. Integrating this class of methods into a framework devoted to data sciences can contribute to generating more expressive means of visual analytics. Although the Principal Component Analysis (PCA) is a well-known method in this context, it is not the only one, and, sometimes, its abilities and limitations are not adequately discussed or taken into consideration by users. Therefore, knowing in-depth multidimensional projection techniques, their strengths, and the possible distortions they can create is of significant importance for researchers developing knowledge-discovery systems. This research presents a comprehensive overview of current state-of-the-art multidimensional projection techniques and shows example codes in Python and R languages, all available on the internet. The survey segment discusses the different types of techniques applied to multidimensional projection tasks from their background, application processes, capabilities, and limitations, opening the internal processes of the methods and demystifying their concepts. We also illustrate two problems, from a genetic experiment (supervised) and text mining (non-supervised), presenting solutions through multidimensional projection application. Finally, we brought elements that reverberate the competitiveness of multidimensional projection techniques towards high-dimension data visualization, commonly needed in data sciences solutions.

ELViM: Exploring Biomolecular Energy Landscapes through Multidimensional Visualization

“…These distortions are caused by data points misplaced in the projection. 9,48 These errors may be due to inherent mathematical limitations of projecting high-dimensional data onto a two-dimensional space. 9 In this context, some quality metrics have been proposed to quantify the extent to which distances or neighborhood relationships are preserved in the projection.…”

“…Finally, the occurrence of projection errors or distortions in dimensionality reduction and multidimensional visualization techniques should be acknowledged. These distortions are caused by data points misplaced in the projection. , These errors may be due to inherent mathematical limitations of projecting high-dimensional data onto a two-dimensional space . In this context, some quality metrics have been proposed to quantify the extent to which distances or neighborhood relationships are preserved in the projection. , However, it is important to note that these metrics primarily assess the effectiveness of the optimization procedure but do not directly measure the method’s capability to represent the unknown topology of the multidimensional phase space …”

ELViM: Exploring Biomolecular Energy Landscapes through Multidimensional Visualization

“…These distortions are caused by data points misplaced in the projection. 9,49 These errors may be due to inherent mathematical limitations of projecting high-dimentional data onto a two-dimensional space. 9 In this context, some quality metrics have been proposed to quantify the extent to which distances or neighborhood relationships are preserved in the projection.…”

Optimization on selecting XGBoost hyperparameters using meta‐learning

“…Additionally, the embedded visualization uses six multidimensional projections (PCA; MDS; Force Scheme; LAMP; t‐SNE; and UMAP) to explicit the existence of groups and the utility of the discrimination through meta‐features. For further information on those methods (Ortigossa et al, 2022).…”