A Geometric Approach towards Data Analysis and Visualisation
Beginning with the work of Bertin, visualisation scholars have attempted to systematically study and deconstruct visualisations in order to gain insights about their fundamental structure. More recently, the idea of deconstructing visualizations into fine-grained, modular units of composition also lies at the heart of graphics grammars. These theories provide the foundation for visualization frameworks and interfaces developed as part of ongoing research, as well as state-of-the-art commercial software, such as Tableau. In a similar vein, scholars like Tufte have long advocated to forego embellishments and decorations in favor of abstract and minimalist representations. They argue that such representations facilitate data analysis by communicating only essential information and minimizing distraction.
This presentation continues along such lines of thought, proposing that this pursuit naturally leads to a geometric approach towards data analysis and visualisation. Looking at data from a sufficiently high level of abstraction, one inevitably returns to fundamental mathematical concepts. As one of the oldest branches of mathematics, geometry offers a vast amount of knowledge that can be applied to the formal study of visualisations.
``Visualization is a method of computing. It transforms the symbolic into the geometric.'' (McCormick et al., 1987)
In other words, geometry is the mathematical link between abstract information and graphic representation. In order to graphically represent information, we assign to it a geometric form. In this presentation we will explore the nature of these mappings from symbolic to geometric representations. This geometric approach provides an alternative perspective towards analysing data. This perspective is inherently equipped with high-level abstractions and invites generalization. It enables the study of abstract geometric objects independent from a concrete presentation medium. Consequently, it allows to interpret data directly through geometric primitives and transformations.
The presentation illustrates the geometric approach using diverse examples and illustrations. In turn, we discuss the opportunities and challenges that arise from this perspective. For instance, a key benefit of this approach is that it allows to consider seemingly disparate visualization types in a unified framework. By systematically enumerating the design space of geometric representations, it is possible to trivially apply extensions and modifications, resulting in great expressiveness. The approach naturally extends to visualisation techniques for complex, multidimensional, multivariate data sets. However, the effectiveness of the resulting representations and cognitive challenges in the interpretation require careful consideration.
Outline/Structure of the Talk
Related Work (Structural Theories of Graphics, Graphics Grammars)
Data Analysis and Visualisation Challenges
Data Model/Mark Model (Mapping the symbolic into the geometric.)
- Geometric Primitives
- Geometric Operations
- Geometric Transformations
- Unified Framework of Visualisation Techniques
- Interactive Exploration/Trivial Extension and Modification
- Geometric Implications for Data Analysis
- Higher-Dimensional Geometry of Complex Data Sets
- Opportunities/Benefits (Formal/Consistent/Composable/Expressive)
- Challenges/Limitations (Perceptual/Cognitive Challenges, Managing Complexity)
The learning objectives for attendees of this talk are to:
- Understand historical context of visualisation theories and outstanding challenges
- Summarise existing approaches to systematic study of graphical representations
- Relate mathematical/geometric concepts and data analysis/visualisation techniques
- Expand the available design space and repertoire of visualisation techniques
- Show opportunities from geometric approach towards data analysis and visualisation
- Provide critical reflections on geometric approach and its limitations
Data Analysts, Developers of Visualisation Software/Libraries, Visualisation Designers
Prerequisites for Attendees
This presentation is suitable for a general audience with interests in data analysis and visualisation. As the presentation predominantly covers conceptual aspects and theories, experience with specific visualisation software or frameworks is not required. However, an understanding of basic visualisation concepts is beneficial.