Understanding Visualisation: A Formal Foundation using Category Theory and Semiotics

This article combines the vocabulary of semiotics and category theory to provide a formal analysis of information visualisation. It shows how familiar processes of information visualisation fit the semiotic frameworks of both Saussure and Peirce, and extends these structures using the tools of category theory to provide a general framework for understanding information visualisation in practice, including: relationships between systems, data collected from those systems, renderings of those data in the form of representations, the reading of those representations to create visualisations, and the use of those visualisations to create knowledge and understanding of the system under inspection. The resulting framework is validated by demonstrating how many familiar concepts used in visualisation arise naturally from it; and used to identify some less intuitive distinctions which are useful in comparing visualisation methods. Finally, some suggestions are made regarding further uses to which this framework might be put, particularly as regards the study of multiand cross-modal representations.