An Application of Mosaic Diagrams to the Visualization of Set Relationships

We present an application of mosaic diagrams to the visualisation of set relations. Venn and Euler diagrams are the best known visual representations of sets and their relationships (intersections, containment or subsets, exclusion or disjointness). In recent years, alternative forms of visualisation have been proposed. Among them, linear diagrams have been shown to compare favourably to Venn and Euler diagrams, in supporting noninteractive assessment of set relationships. Recent studies that compared several variants of linear diagrams have demonstrated that users perform best at tasks involving identification of intersections, disjointness and subsets when using a horizontally drawn linear diagram with thin lines representing sets, and employing vertical lines as guide lines. The essential visual task the user needs to perform in order to interpret this kind of diagram is vertical alignment of parallel lines and detection of overlaps. Space-filling mosaic diagrams which support this same visual task have been used in other applications, such as the visualization of schedules of activities, where they have been shown to be superior to linear Gantt charts. In this paper, we present an application of mosaic diagrams for visualization of set relationships, and compare it to linear diagrams in terms of accuracy, time-to-answer, and subjective ratings of perceived task difficulty. The study participants exhibited similar performance on both visualisations, suggesting that mosaic diagrams are a good alternative to Venn and Euler diagrams, and that the choice between linear diagrams and mosaics may be solely guided by visual design considerations. keywords: Set visualization, set relationships, linear diagrams, mosaic diagrams, spacefilling visualizations, visual design.