Design-Specific Transformations in Visualization

In visualization, the process of transforming raw data into visually comprehensible representations is pivotal. While existing models like the Information Visualization Reference Model describe the data-to-visual mapping process, they often overlook a crucial intermediary step: design-specific transformations. This process, occurring after data transformation but before visual-data mapping, further derives data, such as groupings, layout, and statistics, that are essential to properly render the visualization. In this paper, we advocate for a deeper exploration of design-specific transformations, highlighting their importance in understanding visualization properties, particularly in relation to user tasks. We incorporate design-specific transformations into the Information Visualization Reference Model and propose a new formalism that encompasses the user task as a function over data. The resulting formalism offers three key benefits over existing visualization models: (1) describing task as compositions of functions, (2) enabling analysis of data transformations for visual-data mapping, and (3) empowering reasoning about visualization correctness and effectiveness. We further discuss the potential implications of this model on visualization theory and visualization experiment design.