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A Geometric Approach towards Data Analysis and Visualisation

YOW! Data 2017

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.

Daniel Filonik

Postdoctoral Fellow

EPICentre, UNSW Art and Design

Australia

Daniel Filonik is a Postdoctoral Fellow in High Performance Visualisation at the EPICentre, UNSW Art and Design, Sydney, Australia. His research interest are in Information Visualisation, Computer Graphics and Human-Computer Interaction. His current work focuses on developing natural interfaces for data exploration in immersive interaction environments.

Daniel Filonik conducted his PhD research at the Urban Informatics Research Lab, QUT, Brisbane, Australia. His research investigated challenges and opportunities of data visualisation and composition interfaces based on large-scale display walls. In particular, these technologies were applied to explore the notion of Participatory Data Analytics, collaborative, community-led inquiry approach to the interpretation of data.

Previous to his PhD, Daniel Filonik completed a Master in Media Computer Science at the Ludwig-Maximilians-Universität, Munich, Germany. He has also received an honours degree in Technology Management from the Center for Digital Technology and Management (CDTM), Munich, Germany. Furthermore, he was a visiting scholar at the Georgia Institute of Technology, Atlanta, Georgia, USA in 2009.